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ION HOLECULE REACTIONS: CC3RELAII0N TIME-OF-FLIGHT IOS SPECTROSCOPY AND THE CO* - H_ SYSTEM

Contents

ABSTRACT vii

INTRODUCTION 1

CHAPTER I

Ion Beam Experimentation 4

Classical Time-of-Flight Spectroscopy 12

CHAPTER I I

Correlation Tioe-of-Flight Spectroscopy 19

TOF as a Linear System 20

Correlation Functions . . . . . . . 23

Impulse Response Determination . . . . . . . . . . . . . . . 26

Broadband Noise . . . . . . . . . . 28

K-Sequenees 31

Theory of Correlation Detection 44

Applying Correlation TOF 50

Correlation with Neutral Molecular Beams 51

Correlation with Neutron Beams (Reactor Response) 52

The Present Correlation Method for Ion Beams . . . . . . . . 56

The Data Address Method 58

Vector Space Picture 64

Stat is t ical Analysis 7 0

System Optimisation 70

Correlation Measurement Variance 7 1

Detector Paralysis . . .

Shannon's S a i l i n g Theorem

78

84

-iv-

CHAPTEB. III

Computer Organization 90

Operations Codes • • 93

The Omnibus 95

Programmed Operation 95

Data Transfers 95

The Correlation System Computer Interface 98

Overview of Interface Operation 100

I. Bin Time Clock Board i a o

1. Interface Bin Time Clock IQQ

2. Pseudorandom Binary Hoise Sequence Generator . . . . ^QB

3. Classical TOF Capability 105

4. Digital Delay Line XQ5

5. Command Word Control and IOT's ill

6. Detector Input H g

II. Data is ic.sk. Board H9

1. Data Break Hardware 119

2. Generation and Storage of the Break Memory Address . 122

3. Data Overflow 126

IH. Hardware Test Facilities and Checkout Procedures . . . . 127 t

IV. Board Interconnect Cable 129

V. D/A Converter Board 129

VI. Voltage Comparator 131

MI. Ion Beam Chopping 134

The Present Beam Chopping System 143

Computer Program Monitor (see Appendix C) 147

I. Keyboard Monitor 1*7

II. Operational Subroutines I*8

III. Data Overflow Service 155

Experimental Measurements Using the TOF Correlator 157

CHAPTER IV

Reaction of CO- with H, Isotopes 16*

Models for Ion-Molecule Reactions 16*

Experimental Description 169

Ion Source Assembly 169

Scattering Cell 171

Detector Train . . . . . 172

Experimental Procedure and Data Analysis 173

Kinematics and Incensity Distributions 1'6

States and Energetics l f il

Molecular Orbital Correlation Diagrams I 8 6

CO Results and Discussion . I 9 8

DC0 2+ . IS 8

DCO + 211

Honreactive C 0 2+ 2 2 3

C0 + 231 "

0D +t 0 +, H-O^ 2 3 6

Sumaary of Results " 9

Appendix A: The Mathematical Description of Random Processes . 2 * 2

Appendix B: Detector Coincidence Analysis « 2*6

-vi-

Appendlx C: Listing of PDF S/f Cosputer Honitor for TOF

System.- 2SZ

Bibliography for Correlation Time of Flight Spectroscopy . . . . 266

Acknowledgments 269

- v i i -

10N MOLECULE HEACTIOHS: CORRELATION TIHE-OF-FLIGHT ION SPECTEOSCOPY AND THE CO* - H- SVSTEM

Peter J . Schubart

Inorganic Hater ia l s Besearch D iv i s i on , Laurence Berkeley Laboratory, and Department of Chemistry; Univers i ty of Cal i fornia ,

Berkeley* Cal i fornia

ABSTRACT

A tiae-of-flight analysis eye tea for ocas uresis! t of velocity dis­

tributions of the ionic products of gas phase ion-oolecule reactions was

developed. The sysceo enployed pseudorandoa binary noise for ion source

modulation, coupled with detector crosscorrelaticn for extraction of

velocity distribution spectra. Crosseorrelaticn was accaopllshed by

direct cKsory access storage of coded correlation information by a

PDP 8/f ainlcoHputer with subsequent application of a decoding algorithm

for transformation of accunulsted data-

Maximal length shift register sequences were utilized for ion source

Qodulation- The codulation code sequence was transduced for beaa gating

by an electrostatic deflection bees chopper. Storage of the modulation

sequence for later crosscorrelation was accomplished with a variable

length digital delay l ine. The hardware options of the cocputer corre­

lation interface were controlled by a software implemented, keyboard con­

trolled system monitor cocputcr progran.

The tice-of-flight systeo was applied to an existing ion beaa

apparatus for measurement of N * N_, and Kr ion velocity distributions.

Measured N, distributions agreed well with retarding potential energy

analysis neasureEents. The Kr velocity distribution clearly resolved

- v i l i -

taass peaks due to three naturally occurring isotopes.

I.- a separate series of experiments, intensity distribution naps of

the products of the CO- + H- reaction were measured over an in i t i a l CO

laboratory energy range oi" 25-250 eV. At low energies there was strong

evidence of long lived intermediate complex formation. With increasing

relative energy there occurred a transition to a direct spectator s t r i p ­

ping mechanism.

Intensity distributions for six ionic products were measured at

various relative energies. DCO- product distr ibutions reflected a large

amount of direct interaction formation even at low energies, although the

broad distribution at low energy suggested an intensi ty contribution from

complex formation. With increasing energy DCO. distributions continually

reflected a larger proportion of formation by direct stripping interaction

up to 10 eV relat ive energy. Above 10 eV significant intensity loss due

to pro*1-—t 'tissoelation vas noted accompanied by forward movement of the

product intensity peak, indicating product s tabi l iza t ion by forward recoi l .

The DCO product distributions displayed the symmetric behavior of

complex formation at low energy. Increasing energy led to distribution

asymmetry and forward peak movement. High energy distribution peaks and

Intensity levels were explained in terms of two stripping mechanises.

tfonreactive C07 distributions showed broad ine las t ic intensity even at

low relative energies, in contrast with C0_ scattered nonreactively by

He. This was further evidence for low energy complex formation and

showed significant translation to vibration energy transfer.

CO and 0 product distributions showed a coll is ional dissociation

mechanism. OD distributions showed forward scattering and low intensi ty.

- i ^

Ho D~0 product was noted at any energy studied.

The CO- + H. product distributions were analyzed in teres of molecu­

lar orbital correlation diagrams. There was reasonable qualitative

agreement between theoretical expectations and experimental resul ts .

- 1 -

IHTRDDtlCriOH

Although the majority of cheaica l r e a c t i o n s which occur natural ly

r e s u l t from c o l l i s i o n s between neutral molecu les , for a number of years

chemists have s tud ied ion-molecule reac t ions In an e f for t to e l u c i d a t e

the bas i c dynamic mechanisms important i n a l l chemical reac t ions . With

the aid of molecular bean apparatuses, p h y s i c a l chemists have been able

co measure d i f f e r e n t i a l c r o s s - s e c t i o n s for the production of i o n i c pro ­

ducts in ion molecule react ions , a n a l y s i s of these i n t e n s i t y d i s t r i b u t i o n

maps have contributed ouch to the understanding of dynamic i n t e r a c t i o n s

and the e f f e c t s of p o t e n t i a l energy sur faces f o r intenaoleculax c o l l i s i o n s .

Experimental ly, product d i s t r i b u t i o n s f o r ion-molecule react ions are

most often measured wi th energy bandpatb a n a l y s i s sys teas (energy f i l t e r s ) .

However, i t i s o f t en convenient t o aeasure product v e l o c i t y d i s t r i b u t i o n s

using a t i m e - o f - f l i g h t (TOF) p r i n c i p l e . The f i r s t part of t h j t h e s i s i s

devoted t o the development of such a TOF system. This version of the

TOF method employs an ion beam coding algorithm with a companion detec tor

decoding system ( c r o s s c o r r e l a t i o n ) . Th^ system r e l i e s on the tae of a

minicomputer f o r data information s torage ; i t i s an adaptation of a

method which has been applied previously for measurement of neutron 2

reactor response funct ions .

The i n i t i a l d i scuss ion deals with the construct ion of the TOF e x p e r i ­

mental system for study of i cn -co l ecu le r e a c t i o n s . I t includes a pre­

sentat ion of the theory behind t h i s type of experimental measurement as

wel l as l o g i c a l , e l e c t r o n i c , and computer or iented descript ions of the

actual implementation of th i s method.

- 2 -

The experimental results obtained with the computer correlation

system indicate that correlation TOF analysis has a place in che study of

ion-molecule reactions. In fact, i t i s our feeling that this type of

system wil l find bioad application in a variety of experimental discip­

lines including biological science. Although the principles of the

method are well known in engineering c i r c l e s , i t i s only in the last

several years that dissemination of the necessary information to other

disciplines has begun. I t i<s entirely possible that in the future this

method may find a degree of acceptance comparable to that achieved by

Fourier transform analysis in recent years.

In contrast, the second section of the thesis (Chapter IV) presents

a series of experimental measurements made with an existing energy band­

pass system. The CO, + H, chemical system was studied at a variety of

i n i t i a l C0„ energies and the product distr ibutions for six ionic products

were analyzed in terms of kinematic models (intermediate complex forma­

tion vs direct interaction), thermodynamic data and molecular orbital

correlation diagrams. The experimental resul ts were found to be amenable

to such analysis and provide an example or how i t is possible to visualize

a more complicated reaction process in terms of basic electronic and

dynamical pr inciples . The resulCs also provide a further understanding

of the limits placed on the interpretation of reaction systems hy

electronic correlation diagrams.

While the two sections of the thesis are somewhat independent, each

reflects an important aspect of the process of ar.alysis of chemical

reactions. The improvisation of experimental measurement systems i s an

Integral part of the process of product analysis. There is thus an

- 3 -

underlylng u n i t y t o t he d i scuss ions p r e s e n t e d .

REFERENCES FOR THE INTRODUCTION

1 . J . L. F r a n k l i n , e d . Ion-Molecule Reac t ions Vol . I and I I , Plenum

Press 1972.

2a . F. Hoss fe ld , R. Amadori, and R. Scherm, Proceed ings of the Pane l

Conference on In s t rumen ta t ion fo r Neutron I n e l a s t i c S c a t t e r i n g

Research, IAEA, Vienna, 1970.

2b . X. E. S t e r n , A. B laqu ie re and J . V a l a t , J . Nuc lea r Energy, P a r t s

A/B, 16 , 499 ( 1 9 6 2 ) .

_4-

CHAPTER I

ION BEAM EXPERIMENTATION

Molecular and ion bean exper iments as a c l a s s employ a col l imaLed

beam of r e a c t a n t p a r t i c l e s which a r e d i r e c t e d onto a gas phase t a r g e t

s p e c i e s w i t h subsequent d e t e c t i o n of r e a c t i o n products as a func t ion of

p roduc t -mass , - s c a t t e r i n g ang le , and - v e l o c i t y . The v e l o c i t y v e c t o r of

the i n i t i a l beam p a r t i c l e s se rves to d e f i n e a zero degree s c a t t e r i n g ang le

and to s c a l e the f i n a l d i s t r i b u t i o n of p roduc t v e l o c i t i e s . Most o f t e n , a

s e r i e s of exper iments i s conducted d u r i n g which the i n i t i a l l a b o r a t o r y

energy of t he p r o j e c t i l e p a r t i c l e s i s v a r i e d , changing the amount of

r e l a t i v e t r a n s l a t i o n a l energy a v a i l a b l e t o t he r e a c t i o n p a r t n e r s . The

measured a n g u l a r - v e l o c i t y d i s t r i b u t i o n s , when viewed as a func t ion of

i n i t i a l p r o j e c t i l e energy, s e rve t o e l u c i d a t e and support some p o s s i b l e

k inema t i c mechanisms for the r e a c t i o n w h i l e exc luding o t h e r s .

S ince the ob jec t of the p r e s e n t i n v e s t i g a t i o n i s ion beam r e a c t i o n s ,

we w i l l d e a l e x p l i c i t l y wi th t h i s c a s e . As Ions a r e e l e c t r o n i c a l l y

charged, mass and energy a n a l y s i s a r e cons ide rab ly s i m p l i f i e d over the

n e u t r a l c a s e , a l though the expe r imen ta l l y a t t a i n a b l e e n e r g e t i c range i s

l i m i t e d from below by focusing and space charge c o n s i d e r a t i o n s .

For the purposes of d e s c r i b i n g a t y p i c a l ion beam exper iment , we

suppose t h a t an ion A of mass M, and l a b o r a t o r y v e l o c i t y V, i s d i r e c t e d A —A

toward a n e u t r a l t a r g e t molecule BC of mass M and thermal l a b o r a t o r y BC

v e l o c i t y V and which i s contained i n a f ixed t a r g e t s c a t t e r i n g c e l l .

*For a more complete d e s c r i p t i o n , see Chapter IV.

- 5 -

The most convenient method for analyzing such a reaction i s the construc­

tion of an appropriate velocity vector diagram (Fig- 1) . In this diagram

the assumption has been made that since a typical projecti le ion velocity

1G ^ 10 s cm/sec while the target molecule has a low thermal velocity,

V. » V__, and we can approximate V_„ by C. The to ta l momentum of Hiq

system i s then M.V,, which i s of course conserved throughout the reaction.

Though experiments are carried out in a laboratory frame of reference,

theoretical analysis i s considerably simplified i f the reaction i s viewed

in a center of mass (C.H.) coordinate system. The C.H. coordinate system

is a frame of reference which moves with the velocity of the center of

mass for the system of ^a>lllding par t ic les ; an observer in this frame of

reference would say that the tota l net momentum for a l l the particles in

the system was zero. In the present case the velocity of the center of

mass i s

M A

Since the relat ive velocity of A with reBpect to BC i s fixed (equal to

divided between A and BC (Fig. 1) with

*"7" i s used here to denote laboratory velocity while "u" denotes velocities measured with respect to the velocity of the*"center of mass. k prime ( ') denotes a vector after an intermolecular collision.

A + + BC Products

*A

XBL 748-6905

Fig. 1. A velocity vector diagram for A + BC.

V , - uA - u„„ * V.. - r e l -A --BC -A

about the center of mass as a result of deflecting intermolecular inter­

actions. In general, I U A I ^ I U A | due t o Inelast ic or superelastic collision.

processes. (Since only ionic products can be detected, the final vector

of BC, u! , i s of no fundamental interest . ) The vector u* wil l describe

the motion of A after the coll ision, A having been scattered through a

CH. angle X- Viewed from the laboratory frame, the scattered ion wi l l

be found at an angle 3 with a velocity V*.

Experiments in the laboratory measure ion intensi ty as a function of

V' and 9 . Trans formation of the results to a CM. picture gives a

typical scattering map (Fig. 2) which plots intensi ty contours in a

(oli X) representation. In a similar manner, reactive products ( i . e . + +

A + BC -*• AB + C) are also t33pped, the only difference being a change

in the mass which i s selected for detection by a quadrupole mass f i l t e r .

There are two al ternat ive methods of constructing the two dimen­

sional (u ' , X) intensity contour map which represents re la t ive scat ter­

ing probabili t ies. One method, that of energy or velocity bandpass,

consists of measurement of product ion intensi t ies a t a large number of

discrete (V*, 9) points by the use of angular and velocity (energy) f i l ­

t e r s . After coordinate transformation, the in tens i t ies are recorded in

-8-

0 + + D 2 — 0 D + + D(75eV) * Relative Energy = 15.0 eV j s

Q = 0.4 eV

J80"

Fig. 2. A typical product velocity distribution map. The center of the nap corresponds to the velocity of the center of mass of the system. Angles are specified in the center of nass franc of reference. Contours represent points of equal Intensity. Beam profile is full width at 20J maximum.

-9 -

a Cul» X) coordinate system and contours constructed by connecting points

of equal intensity by interpolation.

The angular f i l ter used in the bandpass method consists of a mechani­

cal aperture in front of the detector restricting thv sol id angle viewed

by the detector. The complete detector assembly i s desx£**ed to rotate

through a wide range of laboratory scattering angles, viewing only an

"infinitesimal" cone of scattering at each angle.

A wide variety of energy and velocity f i l ters have been devised*

including spherical and cylindrical electrostatic energy analyzers,

tfien f i l ters , retarding potential filters* -.- (in the case of neutral

products) slotted disc velocity selectors. The advantage of the band­

pass system i s that i t s measurements are made in a nondynamic Banner

Baking the» easily reproducible. Further, the system i s amenable to com­

paratively straightforward data analysis. A disadvantage of the system

i s the large number of discrete measurements which are required to con­

struct a scattering map.

A second method i s that of time-of-flight (TOF) analysis. While

this method also uses angular definition to restrict the solid angle of

scattering viewed by the detector, i t employs a different mode of energy

analysis. This method measures the distribution of arrival times for

pulses of ions which are admitted to the apparatus. As such, the TOF

system does not explicitly cst^loy any energy fi ltering system; rather.

ions of al l energies arc detected as a function of arrival tioc at the

detector and che Arrival d e c used to characterise the energy distribu­

tion of detected ions (at a fixed scattering angle). Thus, a TOF oeasure-

ment provides a one dimensional s l ice through the scattering intensity

-10-

dlstributlon along a constant laboratory angle ray ( i . e . a s l ice taken

perpendicular to the plane of the page in Fig. 2) . In contrast with the

energy bandpass system then, a TOF system produces data as a "continuous"

one dimensional distr ibution of product intensi ty rather than as a series

of discrete points.

The TOF system employs a time domain measurement rather than one in

energy domain. Using a beam chopping device (see below), a short pulse

of projectile beam par t ic les Is emitted Into a reaction chamber. This

i n i t i a l beam pulse contains Ions with a narrow distr ibution of veloci t ies ,

f(V), characterist ic of the i n i t i a l beam composition (weighted by

H(V) "* Vf(V) by flux considerations). Soon after emission, the pulse

Ions interact with the target molecules causing chemical reactions as

well as e l a s t i c and ine las t i c processes, a l l of which a l t e r the I n i t i a l

narrow velocity dis t r ibut ion. The resulting product ions enter an in t e r ­

action-free dr i f t region in which products with different velocities be­

come separated spa t ia l ly . A mass f i l t e r then removes a l l product ions

except those of the desired mass. Subsequently these ions of a l l

velocities are detected as a function of ar r ival time at the detector

which has been stationed at a predetermined laboratory scattering angle.

(The arrival time i s measured with respect Co the time of i n i t i a l beam

pulse emission.) Using the known path length through the apparatus, the

distribution o£ product ar r ival times i s converted to a corresponding

product ion velocity distr ibution. By measuring this distribution for a

single ion product a t several laboratory scattering angles, a complete

( u ' t x) contour map i s developed. The advantage of the TOF system is the

relatively small number of measurements necessary to determine an

in tens i ty d i s t r i b u t i o n . The disadvantage of the syetem i s that the

dynamic nature of the measurement makes the r e s u l t s suscept ib l e to s u b t l e

dynamically induced measurement errors and more complicated data reduc­

t ion schemes.

The object of our current i n v e s t i g a t i o n has been the analys i s and

construction of a modified TOF system. This method, termed "correlat ion

t ime-of - f l ight" t employs an Information coding algorithym by which the

i n i t i a l ion beam i s modulated with pseudorandom binary no ise and the

v e l o c i t y d i s t r i b u t i o n l a t e r extracted by d i g i t a l cross corre la t ion .

After a b r i e f de scr ip t ion of the mechanics of c l a s s i c a l TO? spectroscopy,

we w i l l examine i n d e t a i l the theory and a p p l i c a t i o n of correlat ion TOP,

and H i l l describe a computer based implementation of such a system.

•Although the number of experimental measurements i s smal ler than that required with a bandpass system, the net number of d i s c r e t e data points (data information) required to construct a s c a t t e r i n g map i s the same for both methods.

- 1 2 -

CLASSICAL TIME OP FLIGHT SPECTROSCOPY

In order t o present a discuss ion of c o r r e l a t i o n spectroscopy, i t i s

f i r s t necessary to d i scuss the c l a s s i c a l t i n e of f l i g h t method. C l a s s i ­

c a l TOP spectroscopy has previously been appl ied primarily to neutral

p r o j e c t i l e systems. Beam sources are t y p i c a l l y thermal ovens, supersonic

nozz l e s , or slow neutron sources . The e l e c t r i c a l l y neutral nature of

the p r o j e c t i l e s and t h e i r r e l a t i v e l y low v e l o c i t i e s have encouraged the

use of mechanical beam choupers, such as the s l o t t e d d i s c chopper, for

admitting short pu l se s of beam p a r t i c l e s i n t o the react ion chamber.

In a t y p i c a l n e u t r a l beam experiment, ^ s l o t t e d d i s c beam chopper

cons i s t ing of a r o t a t i n g d i s c with one or s e v e r a l rad ia l s l i t s machined

an i t s periphery i s placed i n front of a been source , as the d i sc

rotates at high angular speed, each time a s l o t passes over the cross

s e c t i o n of the beam, a short pulse of beam p a r t i c l e s passes through the

aperture and i n t o the react ion charier . Often, the s l o t i s a l so used to

tr igger a photodiode which r e s e t s a time of f l i g h t clock such as a t ime-2

Co-pulse he ight converter (F ig . 3 ) .

As the bean p a r t i c l e pulse t rave l s through the apparatus, the pulse

height of the converter ramp voltage increases l i n e a r l y with time u n t i l

the arr iva l of a p a r t i c l e at the detector t r i g g e r s a s top pulse . The

time of arr iva l i s recorded by s tor ing the he ight of the t ime-to-voltage

pulse in a multichannel analyzer. Repet i t ion of t h i s process Leads to

accumulation of a d i s t r i b u t i o n of pulse he ight s in the multichannel

analyzer which represents the overal l TOF spectrum.

There are many var ia t ions of th i s method. Each employs a chopper,

time of f l i g h t c lock , p r o j e c t i l e in teract ion and p r o j e c t i l e d r i f t reg ions ,

-13-

N

« fe\2 g Jo M» IM

JO

ZS S

e

and a time of f l ight storage device.

The steady s ta te beam flux from the beam source is given by

I - / J(s)ds = yn j sf(s)ds

where X = to t a l beam flux a y = most probable velocity

(u = molecular velocity)

s = u/y = dimensionless molecular velocity

n = number density of molecules in the beam

f(s) = beam velocity distribution function

J(s) = flux of beam molecules with veloci t ies between s and s+ds.

As the beam chopper s l i t passes over the beam, an instantaneous cross

sectional area of the beam, A(t ') i s admitted through the s i l t ( t = t* =

o i s taken when the s i l t f i r s t allows beam par t ic les to pass ) . The r e ­

sulting signal measured at the detector Is given by (for a flux sensitive

detector)

K t ) - f J(s) £ =• &( t ' )d t ' J v f c - l : ' ^

2 where L = the f l ight path length and the factor L/Tf(t-t') is a Jacobian factor between ds and a t ' . The quantity of interest here i s the

*t « detector time variable; t ' = chopper time variable

-15-

measured velocity distribution function f(s) which i s contained in the

differential flux, J ( s ) , Since the measured detector signal Is a con­

volution of the gate function and the final velocity distribution, the

measured TOF distribution mist be deconvoluted using numerical approxi-4 5

nation, moaent analysis (Laplace Transform), Fourier Transform inversion,

or integration f i t t ing methods.

The resolution of a TOF experiment i s inversely proportional to the

width of the shucter function. Ideally one wishes to use an extremely

narrow "6-function" gate signal for ^ " ^ resolution and to ^.. iaize

the problems associated with TOF deconvolution. unfortunately, detector

signal intensity i s linearly proportional to the width of the gate func­

tion and the ensuing tradeoff between intensity and resolution sets a

practical maximum on the time resolution possible in any experiment.

Hagerrs and Varna have calculated that for a flight time fit and

shutter function width T, the resolution, R • —-, necessary to achieve a

TOF half width error of less than 2.5Z i s R^5. This i s readily attained

in most experimental systems by choosing a flight path long enough to

increase At sufficiently to achieve Che desired resolution.

Young has recently pointed out that the measured TOF distribution

also contains 3 convolution of a detector response function and the TOF

signal arriving at the detector. The isiportance of the detector response

depends on the relative time constants for the TGF distribution and the

detector response time. In the present system, this factor is of

negligible importance.

rOF systems have been used to study ion-molecule reactions as well q

as neutral molecule reactions. Paulson et al . have used a TOF double

system has been reported by Haier and Murad for the study of the reac­

tions of N ul th N2. A TOF system using a fast cesium ion charge exchange 11 12

source has been described by Leffert. Dittner and Datz have used a TOF system for the analysis of ine las t ic and dissociative processes r e -

+ + 13

suiting from Ha and K ions colliding with H2 and D 2 . Toennies et a l .

have reported similar experiments using Li over an energy range of

6-60 eV.

Though TOF has been applied to ion-neutral systems, the method has

not come into general use. The single most important reason for this i s

the problem of chopping fast ions at a sufficiently high r a t e . Also,

bandpass analysis systems have been highly developed in the ion beam

field.

We .have seen that the classical TGF system provides a useful a l t e r ­

native to energy bandpass systems. In the next chapter we will present

a detailed discussion of the similar correlation time of flight system

which i s a logical refinement of the c lass ical system.

-17-

HEFEREHCES FOR CHAPTER 1

I. Estermann, "Molecular Beam Technique". Reviews of Modern

Physics. 18, 300 (1946)

J. B. Anderson, R. B. Andres, and J . B. Fenn, Advances in

Chatrrlfal P h y s i c s . J . Ross, Ed. (John Wiley & Sons, I n c . , New

York, 1966) Vol . X pp. 275-317.

4th IAEA Symposium on Neutron I n e l a s t i c S c a t t e r i n g . Volume I I

Copenhagen, 1968.

C. B. t e f f e r t , H. H. Jackson, E. W. Rothe S R. W. Fenstermaker.

Rev. S c i . Instrum. « , 917 (1972)

J. A. Alcalay and E. L. Knuth. Rev. Sci. Inscrum. 40, 438 (1969).

See Reference (3).

J. S. Rollett and L. A. Biggs. Proc. Phye. Soc. London A79, 87 (1962).

R. N. Bracewell and J. A. Roberts, Australian J. Phys. 2., 615 (1954).

A. R. Stokes, Proc. Phys.Soc.London A61, 382 (1948)

K. T. Gillen and B. H. Hahan, Journal of Chemical Physics, 56_,

2517 (1972).

J. D. Horrison, J. Cham. Phys. 39, 200 (1963).

0. P. Hagena and A. K. Varma, Rev. Sci. Instrum. 3J3, 47 (1968).

H. S. Young. Rev. Sci. Instrum. 44, 715 (1973).

-18-

9. J. F. Paulson, F. Dale and S. A- Studniarz, Int. J. Mass Spec- and

Ion Physics. 5_, 113 (1970).

10a. H. B. Maier and E. Hurad. J. Chem. Phys. 55_, 2307 (1971)

b. W. B. Haler, J. Chem. Phys. 55.2699 (1971).

11. See Reference (2).

12. P. F. Dlctner and S. Datz, J. Chem. Phys. 4£, 1969 (1968);

J. "hen. Phys. JM 4228 (1971).

13. V. Held, J. Schottler, and J. P. Toennles. Chem. Phys. Lett. 6_,

304 (1970).

- 1 9 -

CBAPTER I I

COEBELaTION TIME-OF-FLKHT SPECTBDSCOPY

Voile the c l a s s i c a l t i c*=-of - f l igh t method i s adequa te fo r experimen­

t a t i o n with r e l a t i v e l y i n t e r n e ion or n e u t r a l b e a m and w i t h favorab le

s i g n a l to no i se r a t i o (S /H) , t h e system becomes l e s s a p p l i c a b l e as s i g n a l

i n t e n s i t i e s dec rease o r as r e l a t i v e background l e v e l s i n c r e a s e . These

f a l l i b i l i t i e s r e s u l t from the sma l l duty cyc le (0.5-1%) neces sa ry t o

achieve reasonable (<5Z) expe r imen ta l r e s o l u t i o n . (The duty cyc le of a

beam apparatus i s de f ined a s t h e t ime f r a c t i o n d u r i n g which t h e beam i s

e f f e c t i v e l y turned " o n . " ) A. s m a l l duty c y c l e , which reduces t h e n e t

p a r t i c l e f l ux by a f a c t o r o f 100, accompanied by an un favo rab l e S/H r a t i o

o r small s c a t t s r e d i on i n t e n s i t y n e c e s s i t a t e s very long d a t a a c q u i s i t i o n

t imes t o accumulate a s i g n a l w i t h accep tab le s t a t i s t i c a l p r o p e r t i e s .

The use of a c o r r e l a t i o n TOF system avoids t h e s e p i t f a l l s . The

c o r r e l a t i o n method p e r m i t s a du ty cyc le of a t l e a s t 5 0 2 ; t h i s , coupled

w i t h the exc lus ion of u a c o r r e l a t e d n o i s e , a l lows e x p e r i m e n t a l measurements

t o be made i n t he face of a d v e r s e S/H r a t i o s (as s m a l l a s 10 o r 10 )

o r i n the case of s m a l l s c a t t e r e d i on i n t e n s i t i e s .

I n t h i s c h a p t e r , we w i l l d i s c u s s t he theory of c o r r e l a t i o n d e t e c t i o n

i n d e t a i l . F i r s t , t he TOF system i s descr ibed i n t h e language of l i n e a r

systems a n a l y s i s . Ther^ fo l lows a d i scuss ion of random i n p u t modulation

wi th subsequent output c r o s s c o r r e l a t i o n fo r c h a r a c t e r i z i n g t h e response

funct ion for t h e TOF l i n e a r sys tem. A d e s c r i p t i o n of c o r r e l a t i o n func­

t i o n s and t h e i r p r o p e r t i ^ i s g i v e n . The gene ra t i on of m-sequencea for

exper imenta l modulat ion, and the p r o p e r t i e s of such sequences a r e d i s ­

cussed . Next, the theory of t h e c o r r e l a t i o n method f o r beams i s de r ived

-20-

and the experimental methods for applying correlation detection axe re­

viewed. A description of our current computer based correlation system

i s presented along with a summary of the s t a t i s t i c a l analysis of the

correlation method.

Time of Flight as a Linear System

In a time of fl ight experiment, a narrow, impulsive input (beam

pulse) i s applied to an experimental system. The molecular interactions

with target molecules and the spat ia l distribution of product ions are,

to f i r s t approximation, l inear processes which act on the impulsive input

to generate the measured system output (TOF function) . As such, the TOF 2 system can be analyzed as a constant parameter linear system. Any such

system i s rather completely characterized by a weighting function, h ( t ) ,

(or impulse response function) which describes the output of the system

a t a time t after application of a unit impulse a t the system's input

(Fig. 4) . In the case of the TOF system, the impulse response, h(t)»

describes the spat ia l (and hence temporal) smearing of an impulsive input

of source particles as the par t ic les undergo collisions and drif t toward

the detector.

Using the principle of superposition, for a constant parameter linear

system the output generated for any arbitrary f in i te system input i s

described by the convolution integral ,

y(t) = J h(t')x(t-t')dt' (1) o

The convolutions! lower l imit i s taken as t 1 = o rather than t b - m since

in order for physical causality to hold, h ( t ' ) = 0 for t T <o.

-21-

x(t) h(t) — - y ( t ) -Output

y'(t) x(t) h(t) — - y ( t ) -Output V

b(t)

y'(t) Input

— - y ( t ) -Output V

b(t)

detected Signal

Noise XBL748-6907

Fig. 4. The response of a einple linear stationary system.

-22-

Some further properties of h(t) have fundamental importance but arc

practically always sa t i s f ied . For a stable system h(t> i s absolutely

integrable, i . e .

/ |b(c)|dc

and for a bounded systen Input the output will also be bounded. A neces­

sary and sufficient condition for system s tab i l i ty is that the transfer

function of the system defined by

H(p) - f h{ t )e~ p C dt p - a+iv

(the Laplace trans form of the response function) have no poles in the 2 RHP or on the imaginary axis . For a physical system this i s equivalent

to a f inite system frequency response (gain) at a l l frequencies.

Sines measurement of any real systea's output (including TOF) will

inelude detection of ran don noise, b ( t ) , the detector output Is

y'CO » y(c) + b ( t ) . (2)

The object of our investigation is chat, given y*(t) as a ceasured de-

tector output, we wish to recsove a l l randon noise and d. ternine the

sys ten response function, h ( t ) , which i s equivalent to the TOF spe certa­

in classical TOF experioencs, the input i s characterized by widely

spaced narrowly shaped pulses which approxicate a delta function. Thus

23-

y(t) nj S U - e O h U ^ d t ' ~ b ( t ) (D o

By measuring signal and noise and noise separately, b{t) la calculated

and Subtracted:

b(tj - y'(e) - bU) (4)

and the TOP spectrum la thus determined.

Correlation Functions

As background for discussion of correlation TOF, we now review the

properties of correlation functions. A correlation Suction la a joint

moment which measure* the similarity between two waveforms (functions)

aa a function of tttalr relative displacement In tlaa with rcspcet to one

another* lhe correlation function la calculated for eeeh temporal dis­

placement by integrating the product of the displaced waveforms over al l

else. For any given cine displacement, two v m f o i u which are similar

wil l have a large positive correlation, while dissimilar waveshapes will

lead to a ssall positive or negative correlation. In general, as the

displacencnt tine i s varied, both the relative similarity of the wave-

fores and their correlation function will change. The correlation

function for repetitive waveform will be repetitive.

There are cue- general types of correlation functions. An auto­

correlation function of a function, x( t ) , denoted by *L_Ct), i s a ceasure

of similarity between the function x(t) and a verscn of i t s e l f displaced

by a t i o c t . Mathematically,

. * / Kir) - Hm 4 / x ( t ) x ( t £ t ) d *

N " 1 1 a J £ x(jAc)x(jic+T) (5)

H * + ° J - l

where the l a t t e r descr ip t ion i s used for a d i s c r e t e parameter function

and the former for the continuous parameter case . Examples of some

autocorrelat ion funct ions are shown in F ig . 5 . 4

Some of the propert ies of the autocorrelat ion are :

(1) R^Cr) - R ^ C - T )

(2) E^CO) ? I R « < T > | V T

(3) ~& - R ^ (T-O)

A croascorre lat ion funct ion measures the s i m i l a r i t y between two

d i f ferent waveforms. For two functions x ( t ) and y ( t ) the crosscorre la­

t ion as a function of time displacement T i s

xy •p++o> » / B (T) - l i o y / x ( t )y ( t+T)dt

= llo i Y>xC}A>:) y(JAM-T) (6)

A crosscorrelation of two seemingly unrelated waveforms can be used to

*See Random Process Appendix.

X(t) R- x (r)

a. Sine wove ' X(t) - R „ ( T )

wk/v b. Square wave

nX(t)

"i n n n , 4R»(r)

A A A A A „

c. Narrow band noise X(t) ."nW

d. Broad band noise > X(t) R X X ( T )

XBL748-6920

Fig. 5. Some RxninplpR of autocorrelation functions (after Bendat'*).

-26-

determine whctlicr Chcy are related by a l i n e a r system; If they are r e ­

lated , the corrc lac lon w i l l allow dctera inac iaa of the t i c e delay between

the input and output of the system.

Soce proper t i e s of the crasscorre lat ion are:

(1) B ^ (-T) - B y x ( T )

(2) I V T ) | 2 s £ R x x C O ) V 0 )

(3) i R ^ W l ^ y l R ^ O ) + R y y (0)J

If for some delay T, R ( T ) = 0 , x ( t ) and y ( t ) are sa id to be un-xy

correlated (assuming the scans , u a u « 0 ) ; i f R ( t ) • 0 for a l l T,

the two funct ions are s t a t i s t i c a l l y independent*

Impulse Response Determination

Using the concept of cross corre lat ion we now derive the method of

ex tract ing the impulse response function for a l i n e a r system using

system input modulation with output c r o s s c o r r e l a t i o n .

Recal l Eq. (1)

y ( t ) - / h(u)x( t -u)du (1)

where x ( t ) i s the input , y ( t ) the output, and h(u) the impulse response

function. To e x t r a c t the function h (u ) , we confute the crasscorre lat ion

of input and output , R ( T ) by mult iplying both s l u e s of (1) by x ( t - x )

and integrat ing:

KIT) £ l im ~ [ x ( t - T ) y ( t ) d t (LHS) (7) \ f *(t o

T » lim i f x ( t -T)dt / h ( u ) x ( t - u ) d (EHS)

-27-

R * y ( T ) ° f h ( u ) d u **• ? / »(t-t)*(t-u)dt x-*«

when change in integration order is justified because of the finite

properties of the inpulse response function. Changing che variable of

integration in the latter integral

R x y ( T ) " / n ( u ) d u U m / *(t ,-Hl-T)x(t ,)dt ,

. / h(u) R<u-T)du (9)

where the limits of integration are left unchanged since the autocorrela­

tion function i s relatively independent of which time interval i s used

for i t s computation. Hote the similarity between Eq. (1) , the determinis­

t ic input-output relation for a Hn«»qr system, and Eq. (9), the analogous

stochastic input-output relation.

Assume for the moment that the system input, x(t) can be chosen such

that i t s autocorrelation function Is of the form, R (x) = C$(T) for some

constant, c (£(x) i s the Dirac delta function.) Then

/ h(u) 6(u-x)d R w (T) = c / h(u) 6(u-x)du - ch(x) (10)

and for this type of input modulation, the measured cross correlation

functions wil l be exactly proportional to the Impulse response function

-28-

of the linear system under examination (TOF). I t remains to determine

which type of input modulation is necessary to achieve a delta function

autocorrelation.

Broadband Hoise

As illustrated in Fig. 5 (c and d) , the width of the autocorrelation

function of a noise signal i s inversely proportional to the bandwidth of

the signal. In the limit of infinite bandwidth, the autocorrelation

function of a noise signal becomes vanishingly narrow, approximating a

delta function. Such infinite bandwidth noise i s called "white noise"

and has a power spectral density function which i s a constant over a l l

frequencies.

Although white noise i s unphysical ( i t would require infinite power

to generate), in practice one can approximate white noise to any desired

degree by using rinite broadband noise ("pink noise"). Pink noise, with

i t s broad bandwidth, has a relatively constant power spectral density

function within this bandwidth (Fig. 6) . The corresponding autocorrela­

tion function i s f initely narrow (width a bandwidth >. To approximate

a delta function autocorrelation to any desired degree, a sufficiently

large bandwidth of random noise is chosen for system input modulation.

*The power spectral density function is the Fourier Transform of the autocorrelation function:

B»<» - 2 / ^™*-MtT * (The two functions are related much the same as position and momentum in quantum mechanics.) ^^(f) describes the frequency composition of a signal x(t) in terms of the spectral density of its mean square value, (Fig- 6).

a. White Noise

tR, xx <T>

(Dirae 8-Function)

* G „ ( f )

oo

b. Broad Band Noise (Pink Noise)

J R x x ( r ) f G . x ( f )

XBL 748-6918

Fig. 6. Autocorrelation and Power Spectral Density functions for broadband and white noise.

-30 -

For the case of TOP, we chose the bandwidth such that the width of

E (T) « width of the TOF function.

In the following section we wil l investigate the application of

random sequences for broadband source modulation.

- 3 1 -

H-SEQUEHCES

For modulat ion of our l i n e a r TOF sys tem i n p u t , we turn t o t he c l a s s

of pseudorandom l i n e a r sequences . We w i l l d i s c u s s t he gene ra t ing methods

for maximal l eng th sequences and i n v e s t i g a t e some of t h e p r o p e r t i e s of

such sequences which favor t h e i r a p p l i c a t i o n t o c o r r e l a t i o n spec t roscopy .

We a re p r i m a r i l y i n t e r e s t e d i n b ina ry n o i s e sequences because e x p e r i ­

mental ly t h e r e a r e only two p o s s i b l e s t a t e s ("on" and "o f f " ) of the i on

beam which i s b e i n g modulated. While t h e r e e x i s t many methods of g e n e r a t ­

ing t r u l y random n o i s e , ' we w i l l dea l e x c l u s i v e l y wi th pseudorandom

no i se sequences ; t h e former methods a r e more d i f f i c u l t t o c o n s t r u c t ,

allow l i t t l e leeway i n t h e a r ea of c o n t r o l and a r e n o t as r e a d i l y r e p r o ­

duc ib le as pseudorandom methods. For t h e s e r e a s o n s t h e use of sequences

generated by l i n e a r feedback of s h i f t r e g i s t e r s h a s found wide a p p l i c a -

.-• 8

t ion.

Of the sequences which can be generated by sh i f t register feedback,

the maximal length sequences (m-sequences) have been used exclusively.

H-sequences have well known properties, a proportionately larger band­

width and more evenly distributed signal s t a t i s t i c s than those sequences

generated by "short-circuited" feedback.

An m-sequence can be generated by the use of an n-stage linear shift

register whose input i s determined ly modulo 2 summation of stage n and

an intermediate s tage(s) , k, with k<n (Fig. 7 ) . The shift register i s

run by an external clock of period 6 and frequency m = 6 . In theory,

the feedback for generation may consist of several loops or of pyramided

registers with separate loops. However, in most applications, as in

the present one, a single register with a single loop and two stage

Y 1 *- Sequence Out

1 2 3 k n-l n

k n\*—

Modulo 2 Adder

Fig. 7. Shift regis ter configuration for m-sequence generation.

X k o 0 0 I

I 0 I

XBL 748-6908

Fig. 8. Exclusive OR Truth Table.

-33 -

feedback is used. Determination, of the necessary feedback circuits will

be discussed la te r .

the two stage feedback i s accomplished by an "exclusive or" gate

which adds modulo 2. the function of an exclusive or gate i s that i t s

output will be logical "one" i f and only if the s ta tes of the two inputs

are different (one 1R a 1, one i s a 0) . Otherwise, the output i s logical

"zero." This i s the characteris t ic of modulo 2 addition ( 0 © 1 = 1 © 0 -

1; QQ^>Q = 1 © 1 = 0) (see Fig. 8) . We note that for pract ical experi­

mental electronic purposes a binary sequence consists of {0, 1} while

for mathematical and computational the sequence i s considered to be com­

posed of {+1, - l } . As long as the use i s consistent, there i s no contra­

diction; because of the manner in which data i s transformed the experi­

mental {0} has the same effect as the computational {-lK

The mechanics of the sequence generation axe simple. I n i t i a l l y , the

s ta te of the shift reg is te r i s some nonzero binary sequence, typically

100.. .0. During each external clock pulse, stages n and k of the register

are sampled, added modulo 2, and the result applied to the input of stage

1. Then a l l stages are shifted one position (to the r ight l a our culture)

and stage 1 Is occupied by the result of the modulo 2 addition. The

final result i s a sequence with one new b i t and a displaced version of

n-1 bi ts of the original sequence.

Each m-sequence has a well defined length. For an n-stage register

there are 2 possible s t a t e s . However, one of the s ta tes 0 forms a

"kernel" of the sequence; that i s , this s ta te generates only i t se l f and

i s generated cnly by i t s e l f . Thus once a non-zero sequence i s placed in

the register, i t wil l remain nonzero throughout the sequence generation.

-34-

The 2 -1 remaining s tates a l l appear once and only once during the period

of the sequence leading to a nonrepetitive sequence 2 -1 b i t s long. Thus

the period of the sequence i s T = (2 -1)6 = N6 seconds long. By choosing

the clock rate and the regis ter length correctly, any "reasonable" band­

width (determined by 6) and sequence period (N) can be achieved. The

sequence i s easily generated, completely reproducible and i s well

characterized. After the complete sequence has been generated, the

i n i t i a l shift register s t a t e wi l l be repeated and the modulation will

consist of repetitions of the unit sequence.

The theory of m-sequence generation has been thoroughly explored.

M-sequences are part of a larger class known as " l inear recurring

sequences." In general, p-nary sequence (modulo p addition) generation

i s described by rings of primitive polynomials in an indeterminate, x,

over a Galois Field of sca la rs . Although this general theory has con­

tributed much to the understanding of simple binary sequences, ve wil l

not discuss i t . The reader i s referred to the sources in Ref. 12.

For the binary case, consider an n stage shif t regis ter which wil l

be described by a state vector, "a = (a , a 1 ( . . . a - t a.) where {a.}, con-' n n-1 e. 1 1 * tained in the set (0, l } , are the bi ts of the reg is te r . The ordering

of state bi ts is inverted because the f i r s t b i t generated is contained

in the last shift register stage. The mode of feedback (Boolean feed­

back function) i s described by a weighting sequence, ( c . , c_, . . . . c )

with {c.} e {0,1} where i f c. = 1, stage k is involved in the feedback

loop.

Given an i n i t i a l regis ter sequence the s tate of the register at

some later tine is determined by the linear recurrence relat ion,

-35-

a = c i a i^c-^a -if*")-*- + c a r 1 r-l^-' 2 r-2 v- / n r-a (11)

where (+) denotes modulo 2 addition.

The operation of generating the sequence is said to be the result

of an operator. T, which is the sua of a feedback operator, C, and a

shift operation S.

f = C + I or in matrix notation: iii . .0 "

. .0

. .0 -

- . 0

+

iii . .0 " . .0 . .0

-+

iii . .0 " . .0 . .0

-+

iii . .0 " . .0 . .0

-+ 0000.

. oooo. . . 1 . . 0 .

-. c x c 2 c 3 . .c

n J

+ 0000.

. oooo. . . 1 . . 0 .

-L c x cz c 3 V .c J

n

(12)

We represent the i n i t i a l vector a by

(13)

Then after k shift pulses the s ta te of the register i s given by:

Since the output of the f i r s t register stage i s used for experi­

mental modulation, and since the sequential titae history of stage 1 is

equivalent to a s tate vector description, i t i s convenient to describe

the sequence generated in teres of the stage 1 output. This output can

-36 -

be associated vlcb a generating polynomial. G(x) by a one to one

napping defined by (assuaiog c • 1)

1 1 1 G(x)

(-!oVr) ( -Sv 1 ) ( » £ • / ) $(x) (15)

where the third equality follows fron the fact that in oodulo 2 arith­

metic, addition and subtraction are equivalent. The polynomial, $(x) is

the adjoint characteristic polynomial of the generating operator. "

*(x) = det (T-x-I) * IT - x«l|

- 1 © c,x + c^x2 + . . . © c x n - 1 + £ e x 1 (16)

where I i s the identity natrix. The characteristic polynomial may also

be represented as a series in D, an algebraic operator whose effect i s to

delay by one bit the variable on which i t operates, each tice i t operates.

(D can be viewed as a sicple pepory element with a one period delay, one 14 input, and one output.)

*(x) = x(l + £ D j) j=l

Thus the generating function (Eq. (15)) is given by

(17)

G(x) = x

- ^ (18)

Equation (18) provides a prescr ipt ion for d e c e m i n i n g the output

sequence given the feedback c o e f f i c i e n t s ( c , } . The c o e f f i c i e n t s (1 or 0)

are used to wri te out e x p l i c i t l y the generating funct ion in teres of the

Delay operator. Hanual d i v i s i o n w i l l resul'. in a polynomial in powers of

D. The elements of the binary sequence vhose sequence numbers appear as

powers of D in the r e s u l t a n t polynomial w i l l be ones; those whose

sequence numbers do not appear as powers w i l l be a e r o .

For c l a r i f i c a t i o n , we w i l l use as an example the case of a four-

14

s tage s h i f t r e g i s t e r . The s h i f t r e g i s t e r conf igurat ion i s shown i n

F i g . 9 . The feedback i s from s t a g e s 3 and 4 . I f we assume an i n i t i a l

sequence of 1000, the outpuc of the f i r s t s tage ( a . ) w i l l be ( s e e F ig . 9

f o r s t a t e vectors)

100110101111000.. . (H - 2 4 - 1 - 15)

For t h i s con f igu ra t ion t h e c h a r a c t e r i s t i c polynomial i s $(X) - Ax 2*! s i n c e c , " c

2

= °» ** " CA m l - A**0 *<*> * * U © D 3 + D 4 ] . Then

G(X) - ^ x * X [ I © D 3 © D 4 © D 6 © D 8 © D 9 © D 1 0 © . . . (I © D J © D ^

So the output sequence I s

1(D°), OCD1), 0CD 2 ) , K B 3 ) , l ( D 4 ) . . . .

= 10011 . . . , the same as computed manually In Fig . 9 .

To ensure that the sequence generated by a s h i f t r e g i s t e r i s maximal,

the feedback connections must be chosen c o r r e c t l y . Fa i lure to apply a

proper feedback loop r e s u l t s i n the l o s s of s i g n i f i c a n t port ions of the

maximal sequence by "short c y c l i n g , " that i s r e s t a r t i n g the sequence

-38-

Figure 9. A 4-stage shif t register configuration

| — > " l a 2 a 3 a 4

a

3 © * 4 T I n i t i a l s ta te <* 0000;

Enter " 1 " into at

with f i r s t shift pulse

Calculated s ta te after k shift pulses

1c = 0 aj az

1 1 0 0 0

2 0 1 0 0

3 0 0 1 0

4 1 0 0 1

a 1 1 0 0

6 0 1 1 0

7 1 0 1 1

8 0 1 0 1

9 1 0 1 0

10 1 1 0 1

11 1 1 1 0

12 1 1 1 1

13 0 1 1 1

14 0 0 1 1

15 0 0 0 1

-39-

before i t has terminated. Tables of appropriate feedback connections

have beea published.

The mathematical cri terion for establishing ^yMfO sequence genera­

tion is that the characteris t ic polynomial of the feedback configuration,

<Kx), must be irreducible and primitive ($(x) i s a minimum polyncmical

of the m-sequence) . A polynomial p(x) of degree n i s called irreducible

if i t i s not divisible by any polynomial of degree less than, a, provid­

ing that p(x) > 0 . The polynomial p(z) of degree n i s said to be

primitive i f i t does not divide x +1 for k<2 n - l . (A primitive polynomial

i s also irreducible.) Since tables of primitive and irreducible poly­

nomials are available, i t i s a simple matter to construct proper feed­

back connections for any reasonable length shi f t r eg i s te r .

Properties_of_M-Sequences

As mentioned above, an m-sequence contains N=2 - 1 b i t s and during the

sequence each possible n-tuple (except 0 } appears once and only once in

the shift regis ter . An m-sequence is an example of a "random telegraph

wave" whose rate of zero crossings i s described by a Poisson distr ibu­

tion (the o-sequence i s often called a Poisson Square Wave). A picture

of the m-sequence in shown in Fig. 10.

If che mean zero crossing rate for the random process i s m sec ,

the Poisson law states that the probability of k crossings occurring

during a time interval t i s given by

P(k;t) = e " m c -rr- (19)

!

"P

This distribution describes the likelihood of the shi f t register output

containing any given nunber of +L*s or - l*s during any interval .

The s ta te of the m-sequence i s +1 one half of the ting, so the duty

cycle of the sequence i s 0*5. The sequence contains subsequences (runs)

of a l l +1 or a l l -1 during which the shif t regis ter output remains un­

changed. During the period of the sequent , one half of a l l runs are of

length 1 (+1, - 1 ) , one quarter are of length 2 (+1 +1, -1 -1) and 1/k

will be of length K ((+1) , (-1) ) . Furthermore, there are exactly as

many runs of +1 of length k as there are runs of —1 of length k (except

( - l ) n =(0) n which i s excluded). 19 An m-sequence i s closed under the operation of shift-and-add:

for a l l s f 0 (cud N), there exists an integer H such that if a i s

any b i t of an m-sequence,

a

r © r+s r+v (20)

The sequence ta^, } is a shifted version of the original sequence. s 20

(The set of sequences {{a }, r:l,H} forms a K-module.)

The most important property of m-sequences i s , for our application,

the autocorrelation function. Recall that we wished to find an experi­

mental modulation function which had an autocorrelation function which

approximated a 5-function. A normalized representation of the autocorre­

lation function for an m-sequence of length N «* 2 -1 (± 1 states) i s

shown in Fig. 11. This function consists of triangular peaks of height 1

and width 26 at T = 0 (modulo H) ?ad an intermittent background of height

+ R x x (r )

-AT =N8-

l l /N

T = 0 XBL 748-6917

Fig. 11. Normalized autocorrelation function - H - 2 n - l , aequonco period • N6.

-43 -

H . By choosing 6 small and H large, this correlation function becomes

very much like a 6-function. For our application, 5^5x10 sec, n c 20,

H=10» so the autocorrelation function wi l l consist of 1 usee wide peaks

spaced 1 sec apart with a relative background level of 10 . The shape

of the autocorrelation function was measured experimentally with an

Hewlett-Packard 3721A Correlator and was found to conform to the expected

shape. The width of the function, M. usee, should be easily adequate

for measuring Time of Flight spectra of 30 usee duration and 10 usee

tota l width.

Now that i t i s apparent that a suitable modulation sequence can be

generated for extracting the TOF impulse response function, ve proceed

to derive explici t ly how the impulse response method i s applied to TOF

spectroscopy.

THEORY OF CORRELATION DETECTION

Though ue have d i scussed the g e n e r a l t heo ry of impulse response

de terminat ion by c r o s s c o r r e l a t i o n , i t remains t o e l u c i d a t e the theory

ce s p e c i f i c a p p l i c a t i o n s . To f a c i l i t a t e an unde r s t and ing of the n a t u r e

and o r i g i n of an expe r imen ta l ly measured c o r r e l a t i o n function and i t s

components, we n e x t p r e s e n t the mathemat ica l theory of c o r r e l a t i o n d e t e c ­

t ion as app l i ed t o beam systems. This theory p rov ides the conceptual

b r idge between random exper imenta l modulat ion and the computation of

c o r r e l a t i o n f u n c t i o n s .

Ue f i r s t suppose t h a t the modulat ing m-sequence can be r e p r e s e n t e d

by a cont inuous func t ion s ign i fy ing a s e r i e s of s t a t i s t i c a l p u l s e s , x . ,

p laced randomly a t u n i t time i n t e r v a l s , t . :

x(t) =Ex. 6(t-t±) (21) i

The actual experimental modulation function is the convolution of this

statistical function with the experimental beam pulse shape (gate

function) , <£( t) :

fT M(t) = f x(tt)4>(t-t,)dt' = E x , *(t-t.) (22)

1

where T is the period of the m-sequence and fT i s the total measurement

interval. 21 Hossfeld has shown that the shape of the modulation pulse must be

of a certain minimum symmetry type to ensure a proper ^-function auto­

correlation and to avoid "input transducer error." This symmetry

condition i s expressed (for al l t ines, T) as

S * . (T-t ) - 1 (23) i J 2

Since the binary sequence always contains one. more (+1) pulse t-ian (-1)

pulses, this condition requires that the t r a i l i ng edge of a modulation

pulse be the mirror image of the leading edge. Connonly used triangular

(trapezoidal) and rectangular pulseshapes sat isfy this condition i n ­

herently .

We also note that the discrete autocorrelation function for the

s t a t i s t i c a l sequence can be written in terms of the duty cycle, c, and 21

the modulation rate, m, of the sequence,

ass<k> - £ Vi-ft = m C 1 " c ) 6 k + • (24)

Now ue reca l l that the measured crosscorrelation with the linear

TOF system i s

H a y'( t )x( t-T)dt - V x , y ' ( T + t )

j= l J J (25)

where only the s t a t i s t i c a l portion of the modulation function i s ueceasary

to confute the correlation, and where

U) = J h(T o

)H(t-T ')dT' + b(t)

= J h(T £N

1=1 x±iKt -h-T') b(t) (26)

is the measured detector output at time t . In Eq. (26), h(T) is the

impulse response function (true TOF distribution), b(t) is the uncorre­

c ted "constant" background signal, and we have changed the upper limit

of integration from +™ to T. since the TOF signal is of finite duration

(h(T) = 0 for al l T>Th) • Equation (22) for the modulation function has

been used to derive (26) .

Putting the expression for detector output (Eq. (26)) into the

correlation function (Eq. (25)) we get:

£N f n fH fH R ay ' ( T ) = .? X j J h ( T ' } S xi(J>(T-ti-T,+tj)dT' + V ^ C ^ ) (27)

J o -'"

T h r N r N

= f £ X

n

X / h(T')*(T-t -T'+CJdT'-H) X! X -(28)

where the averaged noise included in the correlation function will be

independent of T (uncorrelated) and so can be removed from the summation,

by rewriting the double summation as

E V j • ? ? V i 4 k - £ » « * > - S f a ( l - c ) 6 k -mc} x,j J k i k k

= m(l-c) +£mc {lit j

and by no t i ng t h a t

N £ x = m ( t h e number of pu l se s p e r p e r i o d ) j = l - •J

t h e c o r r e l a t i o n expres s ion becomes

R ^ . C T ) = fm { (1-c ) / h ( T ' ) « T - T ' ) jtt-c) / o

f N I J h ( T ' ) ^ ^ ( T - T ' + ^ d T 1 + b [ + C J h ( T ' ) ^ ^ ( T - T ' + ^ d T 1 + b j (30)

o

R e c a l l i n g t he symmetry c o n d i t i o n (23) t t he sum i n t h e second terra is

e q u a l t o u n i t y . We de f ine

H(T) = J h(T,)4>(T-T») (31)

which i s the convolut ion of t h e modulat ing p u l s e shape w i t h t h e t r u e TOF

f u n c t i o n . H ( T ) i s e x a c t l y t h e TOF d i s t r i b u t i o n which would be measured

w i t h a c l a s s i c a l TOF exper iment u s i n g a ga t e func t ion <|>(t) . Thus

/ h

R ,(T) - fm {( l -c)H(T) + c / h (T ' )dT ' + b> (32) xy j

o

The integral in the second term of Eq. (30) may also be expressed In

terms of H(x): let

/ 6 = 1 $ ( t ) d t (33)

be the t o t a l a r ea under a u n i t modulat ion p u l s e . Then

/h r h /-Ti

H(T) dx - / dx / h(x')4i (x-x*)dx f

o o o

T T = f hCT^dx' y

o

T

h(x')dx' / tfx-x^dx

6 / hCxMdT* = 6<h> (34)

(35)

R ,(x) - Era {(l-c)H(x) + § <H> + b} (36) xy u

This i s the desired resul t . The computed crosscorrelation i s proportional

to the classical TOF signal superimposed on two constant background terms.

The background due to the average TOF signal, -r- , has been called the 22 background of ignorance." I t s origin i s the association of each

detector pulse to m modulation pulses during the correlation, whereas

physically the detected ion could have come from only one of these pulses;

the detector signal i s erroneously attributed to the other m—1 modulation

pulses. However, due to the s t a t i s t i c a l properties of the modulating

signal , this error becomes evenly distributed among a l l channels of the

correlation function and assumes the identity of a constant background.

- 4 9 -

The Cera In £q. ( 1 0 ) , a b , i s due Co each true background pulse being

a t t r ibuted to m channels, the r e s u l t being a constant Increased back­

ground.

The method of modulation described in the above d i s c u s s i o n was

assumed Co use a ( 1 , 0) type of corre la t ion , racher Chan a (+1 , -1 )

t y p e . Since our corre la t ion method uses the l a t e r type ( s e e be low) ,

both sources of constant background are removed and the r e s u l t of corre­

l a t i o n i s d i r e c t l y proport ional Co the c l a s s i c a l TOF s i g n a l H ( T ) . . Thus

Che r e s u l t s of Che c o r r e l a t i o n experiment are equiva lent Co Chose of the

c l a s s i c a l TOF method; we now proceed t o discuss how a c o r r e l a t i o n system

may be implemented experimental ly .

- 5 0 -

APPLtlHG CORRELATION TOF

Having shown how random modulat ion of a beam sou rce might be used to

t reasure the TOF spectrum and hav ing d iscussed the g e n e r a t i o n and p r o p e r -

c i t s of the modulation s i g n a l , ve now examine the mechanics of applying

t h e c o r r e l a t i o n or thod to t i m e - o f - f l i g h t systems.

There a r e s e v e r a l d i s t i n c t methods by which c o r r e l a t i o n spect roscopy

has been appl ied to TOF, Each method has i n common t h e concepts of modu­

l a t i o n , c o r r e l a t i o n , and d a t a s t o r a g e . To our knowledge, t h r e e v a r i a t i o n s

of t he c o r r e l a t i o n method have been implemented. The f i r s t , used wi th

n e u t r a l molecular beams, -ropl ies a. r e l a t i v e l y s h o r t modula t ion sequence

which I s coupled synchronously w i t h r e p e t i t i v e c yc l i ng of a mul t i channe l

a n a l y z e r for da t a s t o r a g e . Accumulated da t a i s l a t e r t r ans formed

( c o r r e l a t e d ) by c o r r e l a t i o n of t h e mul t ichannel a n a l y z e r c o n t e n t s wi th

t he r e p e t i t i v e modulation s i g n a l . The sequence of e v e n t s i s then modu­

l a t i o n , da t a s t o r a g e , and c o r r e l a t i o n , a l l r e l y i n g on t h e u s e of the

s h o r t modulation sequence . (The r e q u i r e s e a t t ha t a s h o r t modulation

sequence be used i s the r e s u l t of the l imi t ed number of slots which can

be machined i n a mechanical chopper and the f i n i t e number of mul t i channe l

ana lyze r channels a v a i l a b l e . )

The second method, used i n neut ron spec t roscopy , uses a long pseudo­

random s i g n a l which no t only modulates the source beam, b u t a l s o c o n t r o l s

the s t o r a g e of d a t a by g a t i n g t h e inpu t s of a s e r i e s of d a t a accumulation

s c a l e r s . This method does no t r e q u i r e any l i m i t a t i o n on the pe r iod of

t h e modulation sequence, and f i l t e r e d t rue random b i n a r y n o i s e modula­

t i o n could j u s t as w e l l be employed. The sequence of e v e n t s is modula­

t i o n , c o r r e l a t i o n , and d a t a s t o r a g e .

-51-

The third type of application Is the one developed in our laboratory

for use in ion beam experiments. This method, which i s actually a hybrid

of the other two, can also use long pseudorandom sequences for beam modu­

lation. Data storage i s achieved by storing detector output signal in a

computer core memory by associating individual detector events with the

modulation signal responsible for their genesis. Subsequent transforma­

tion of the stored data using the associated modulation signal leads to

calculation of the correlation function. The sequence of events in this

method i s modulation, data storage, and correlation; the method thus

resembles that used for neutral molecular beams, though no limits are

placed on the length of the modulation sequence and synchronized data

storage i s not required.

Correlation with general Molecular Beams

As previously described, slotted disc rotat ing choppers have been

used to modulate neutral beam systems. Correlation modulation i s achieved

by machining the chopping disc with slots placed in a pseudorandom mannez 23 so that the gate function of the chopper approximates an m-sequence.

The resolution of the chopper i s fixed by the width of the "unit beam

slot" (the circumference of the chopper i s divided in to H unit s lots which

are either open or closed) and by the angular velocity of the disc. In

practice both the number of unit slots and the number of multichannel

analyzer slots are limited to M.000 and this places a l imit on the length,

H, of the binary sequence used for modulation. (This has the effect of

limiting the background height of tne modulation sequence autocorrelation

function to 1/1000 of the peak height. See the description of the m-

sequence autocorrelation function.)

-52 -

Data storage with the s lot ted disc system Is achieved by use of a

multichannel analyzer. The analyzer and the beam chopper are synchronized

so that as the chopper runs through the pseudorandom sequence, the

analyzer i s sequentially stepped through each of i t s memory channels.

Detector events sensed at any point in the chopping sequence are always

stored In a corresponding multichannel analyzer channel associated with

that particular sequence segment. Both the chopper and the analyzer are

cycled repeatedly, always maintaining the synchronicity between the two.

linen sufficient data (empirically determined) have been collected,

the correlation function i s calculated, a single point at a time, by

multiplication of each of the analyzer channel contents by the corres­

ponding value of the modulating function (±1) and summing the result

over a l l analyzer channels. Shifting the phase betweea the multichannel

analyzer channels and the modulating sequence and repeating the multi­

plication and summation provides the value of the correlation function

for different delay times* The resulting plot of net correlated signal

versus phase (time) shif t betweea modulation sequence and analyzer

channels i s the desired correlation function.

Correlation with Meutron Beams

A somewhat different system has been applied in the measurement of 24 neutron beam velocity distr ibutions and the response function of

25 neutron reactors. In the former case an incident beam of polarized 24 neutrons i s chopped using a magnetic flipper chopper, while neutron

reactors are modulated by the use of electrostat ic deflection plates in

the Van de Graaf accelerator used for neutron generation. (Often

mechanical disc choppers have been used to measure the velocity

-53-

distributions for neutron beams in a system analogous to that described

for neutral molecular beams.)

Since these methods of source modulation are e lec t r i ca l rather than

mechanical! and since data i s not stored in a f in i te sized multichannel

analyzer, there i s no physical or memory res t r ic t ion on the length of

the modulation sequence. Depending on the method of data storage, true

filtered binary random noise (such as i s produced by commercial noise

generators) could be used in place of an m-sequence.

The correlation detection system employed for reactor measurements 25

i s shown in Fig. 12, This system achieves a direct correlation between

the neutron source modulation sequence and the detector output. This i s

accomplished by use of a series of scalars which are incremented by

detector events. Each scalar i s gated by one segment of the modulation

sequence; though the segment of the sequence gating each scalar changes

s ta te constantly, tha t segment has a fixed phase with respect to the

sequence segment which i s currently modulating the neutron source.

The experiment i s controlled by a suitable d ig i t a l clock of period

6. The clock runs two shif t registers; one i s hooked up as a binary

pseudorandom noise generator whose output i s an appropriately long

m-sequence; the ether i s a se r ia l in /paral le l out storage register which

stores the sequence which has been used to modulate the source. Consider

the case of an n-bi t storage register . If M(t) i s the current modulating

sequence, the nth stage of the storage, register contains the segment

H(t-n&) since i t requires a time t «• a5 for any segment to be shifted

through the storage reg i s te r . Similarly, any stage k, l£fcsn will con­

tain the segment H(t-^cS). Now the paral lel output of each register

Storage Register

Correlator Scalars Gates

XBL 748-6913

Fig. 12. Crosscorrelatlon with gated scalars.

-55-

stage, k, is applied to a gate, <L , which controls the input of a scalar

(counter), S. . When a neutron is sensed by the detector, each scalar

S, whose input Is gated on by the modulation signal H(t-kfi) will be In­

cremented, indicating a positive correlation between the detector output

and a +1 segment in the modulation signal at a time (t-k6) previously.

All scalars whose modulation segment was 0 rather than +1 will not be

incremented. Since the system does not include the effects of negative

correlation, the scalar 6 is used to record the total detector signal

for later computational correlation adjustment to include negative corre­

lation effects. If after same period of data collection, T (kS) is the

contents of scalar S. , and T_(kS) the total number of counts ignored by

S. , then T , the contents of scalar S , is equal to

T o = T + (k6) + T_ (k5) (37)

for any k. Then the correlation function can be calculated from

H. (i-kfi) a [T+(kfi) - T_(k5)] * [2T+(kfi) - T Q ] (38)

Recalling Eq, (6)

N

K (T) - l i m £ V x ( j A t ) y (jAt+x) (6) W j - 1

we see that the measured correlation function of Eq. (38) i s given by

summing the tota l number of positive correlations (T i s the sum of a l l

cases where x(j"nt)y(.jAt+k5) • +1) and subtracting the t o t a l number of

- 5 6 -

negative correlations (T_ i s the sun of a l l cases for which

x(juT)y(jAc+kS) = - 1 ) . The result i s a net corrected value of the corre­

lation function for T = k.6.

The important concept of the method i s that any point of the corre­

lation function can be calculated direct ly by using the modulating seg­

ment (bit) corresponding to the proper delay to gate a data storage

scalar. Any number of points of the correlation function could be calcu­

lated merely by increasing the number of sea tars and gates and by i n ­

creasing the length of the storage reg i s te r . The modulating sequence

need not be repet i t ive since the correlation i s direct and immediate.

Resolution i s limited only by the number of scalars and the clock rate

for modulation.

The drawbacks of this system are mainly those of electronic com­

plexity and expense. The experimenter oust build a complicated and

dedicated single purpose correlator whose resolution is directly pro­

portional to i t s complexity. For this reason, an alternative method was

sought for use In ion beam experimentation.

The Present Correlation Method for Ion Beams

Prior to constructing a correlation system for ion beam analysis,

we reviewed a l l of the techniques which had previously been applied.

including commercially available correlators , multichannel analyzer, and

gated scaler systems. Each system was found tc have inherent disadvan­

tages which made i t difficult to apply to ion beam analysis.

Commercial correlators employ analog or d ipi ta l delay lines for

signal sampling followed by sequential single point correlation calcu­

lat ion. The comparatively low signal levels (slow repetition rate) of

-57-

an ion bean system make i t infeasible to use sequential single point

correlation since excessively long sampling times would be necessary.

Ion beam TOF experiments typically have a f l ight time of 10-50 \isec

and TOF distribution widths of 2-10 usee. This fac t , coupled with the

problem of synchronicity and the long access time of multi­

channel analyzers (10-100 usee) made the application of a neutral beam

analysis type system impractical.

The gated scalar type of system i s direct ly applicable; however,

i t i s more expensive and difficult to construct. Additionally,

such a system i s to ta l ly dedicated and somewhat inf lexible; i t can

only be used for specif ic correlation analysis without further data

analysis.

A solution to the ion beam problem was found In the use of a mini­

computer based system. Such a system i s comparatively Inexpensive

(<$6,000), requires only construction of an appropriate computer in te r ­

face, and allows the use of available hardware (the computer) which can

be applied to a variety of data analysis problems.

The computer used in the ays tern i s a Digital Equipment Corporation

PDF 8/f which i s a 12 b i t minicomputer with a 1.2 Usee cycle time (see

"Computer Organization" below). I t was decided that simultaneous compu­

tation of 30 points of the correlation function would provide adequate

experimental resolution for viewing the TOF ion spectrum in a maimer

similar to the gated scalar technique. Since the computer has only a

single data input channel (12 data l ines ) , and since i t would require

1.2 usee to add data to each of 30 "scalar" addresses in core memory,

direct Implementation of a "scalar system" would require a 40 Usee

-58 -

downtiae for each detector event accumulated. This i s excessive con­

sidering the s ignal intensi t ies (^10 /sec) typically measured with an

ion beam apparatus; a significant portion of the detector signal would

he lost, negating the duty cycle advantages of the correlation system.

The solution to th is problem l ies in the application of the "Data Address"

concept.

The Data Address Method

While the computer has only one data input channel (even though this

channel contains 12 b i t s ) , i t does have multiple inputs available in the

form of i t s 12 b i t address code. The basic concept of a "data address"

i s that the information necessary to compute a TOF correlation function

is present in the modulation sequence (which has been stored in a

storage shif t regis ter) a t the time of a detector event {as we saw in the

gated scalar system) . I t i s possible to re ta in this information while

simultaneously reducing data storage time for the computer by a factor

of 10 i f the applicable modulation sequence i s used as an address code

for the computer memory. Each code sequence i s uniquely associated with

a core memory address in the computer. Each time a particular modulation

code i s contained in the storage register at the time of a detector

event, the address corresponding to that code in incremented. As an

experiment proceeds, the core memory addresses accumulate as their con­

tents a distr ibution function representing the number of times each modu­

lation sequence code was contained within the storage register at the

time of a detector event. The connection between data addresses and the

calculation of the cross correlation function wi l l be described below.

-59-

Siuce we wish a 30 bi t correlation function, 30 bi ts of the current

modulation sequence must be held in a storage regis ter . For each detector

event, the 30 current bi ts are stored as three 10 b i t segments.

The 10 b i t length is suggested because of an access time-core memory

size tradeoff. This tradeoff can be visualized as follows: i t would

take 30 computer cycles of 1.2 usee or 40 jisec to store 30 independent

data b i t s , but only 30 core memory addresses to accumulate the resul t .

On the other hand, i t would only require one memory cycle to store one

data sequence 30 b i t s long by the data address method; however, to s tore

a sequence k b i t s long by the data address method requires 2 core

addresses since there are that many possible outcomes iu a k b i t sequence.

Thus, for one 30 b i t segment i t would require an astronomically large

C2 3 0

S 10 8 core addresses) core memory, the compromise point is the

use of three 10 b i t segments, requiring 5 usee storage time and 3 x 2

- 3 x 1024 addresses, both parameters tolerable for the present system.

Data transfer of a modulation code sequence i s achieved through the

use of a direct memory access mode of the computer. In this "data break"

mode (see "Computer Organization"), the computer's central processor i s

disabled and program execution is temporarily s ta l led . The actual data

transfer is controlled by the external logic of the computer interface.

To increment the contents of three separate data addresses, 3 sequential

data breaks must be used.

He note that one could store the modulation code just as easily by

using 10 b i t s of the computer data l ines . In this manner, a 30 bi t

sequence would be stored as the contents of three addresses rather than

in the address i t s e l f . For each detector event, three new addresses

-60-

would be required. However, th is method would allow only about 1000

detector events to occur before the memory overflowed. In contrast, the

data address will allow an average of 5 K 10 detector events to occur

before core memory overflow.

A block diagram of the computer system i s shown in Fig. 13. A

feedback shift register generates the beam modulating m-sequence. This

sequence is also stored sequentially in a digital delay l ine and then in

a storage shift register (DBMA) . All registers are controlled by a

variable frequency crystal generated digi tal clock. Detection of an ion

causes the sequence in the storage register to be strobed into the data

break logic, where the sequence i s used to increment three addresses by

direct memory access. By use of a Tektronix display terminal keyboard,

the functions of the Interface may be controlled by programmed commands.

Since the data address method stores correlation information in a

coded manner (the code being that the binary modulation sequence specifies

a 10 b i t portion of a 12 b i t address), a decoding transformation of

the accumulated data i s necessary to compute the desired correlation

function.

The data transformation mimics the function of the gates used in a

gated scalar system (see "Program Description") (Fig. 14). Each address

is examined separately. Since the 10 least significant b i t s of the

address contain the equivalent of the modulation sequence at the time of

detector events, each b i t , k, describes whether (for that part icular

address) the modulation segment, H{t-k6) (where 6 is the clock period),

i s positively or negatively correlated with the number of detector

events contained within the address contents. If bi t k is a " 1 " , the

iX , u , I Z77

a , - - . TOF i y Analysis

--xnr 1% Amplify and Digitize

Chopper < COAX

1 I PRNG j »•

Variable X-TAL

Clock

Variable Delay

Latches D.B.U.A.

Oata Break Logic (IOT, Priority, Control)

POP 8/F (Data Address)

Tekfrcnii Terminal

RECC Line to LBL CDC 6600

Asynchronous Units:

1. Computer 2. X-TAL Clock and Bean Modulation 3. Detector Signal

XBL748-6929

F i g . 1 3 . Correlation TOF Block Diagram.

Figure 14. Data transformation for the data

Transformation of addresses 1325a and 0723B

(10 significant b i t s to be transformed)

1325s:

file position 1 2 3 4 5 6 7 8 9 10

Data address 1 0 1 1 0 1 0 1 0 1

Contents: 34

Result:

add to signal scalar: 34 - 34 34 - 34 - 34 - 34

Add to noise scalar: - 34 - - 34 - 34 - 34 -

Hext address for example:

0723a:

Bit position 1 2 3 4 5 6 7 8 9 10

Data address 0 1 1 1 0 1 0 0 1 1

Contents: 21

Result:

Add to signal scalar: - 21 21 21 - 21 - - 21 21

Add to noise scalar: 21 - - - 21 - 21 21 - -Cumulative result:

Signal scalars 34 21 55 55 - 55 - 34 21 55

Noise scalars 21 34 - - 55 - 55 21 34

Net (^0) 13 - 55 55 - 55 - 13 - 55

-63-

contents of the address are added to signal accumulation scalar k; other­

wise the contents are added to noise scalar k. This process i s carried

out for each c* the 10 b i t s of each address. There are three sets of

Bignal and noise accumulators in the computer memory, corresponding to

the three 10 b i t segments of the modulation sequence uaed as independent

data addresses. When each of the 3K possible addresses have been t rans-

formed in this manner, the resul t ing contents of each of the 30 noise

seal are i s subtracted from the contents of the companion signal scalar .

The result i s the TOF correlation function.

He have seen how the correlation TOF system can be applied In

several ways. In the following section we wi l l discuss a somewhat more

abstract picture of the correlation method applications.

-64-

VECTOR SPACE PICTDRE

Having exp la ined in d e t a i l t h e mechanism by which t h e c r o s s c o r r e l a -

t i o n funct ion i s c a l c u l a t e d , ve now p r e s e n t a more t h e o r e t i c a l c o n s i d e r a ­

t i o n of t h i s process w i t h t h e hope t h a t i t w i l l c l a r i f y how the c o r r e l a ­

t i o n i s accomplished. Th is d e s c r i p t i o n i s couched i n t h e language of

v e c t o r space theory .

He mentioned p r e v i o u s l y t h a t the b i t s conta ined i n random n o i s e

g e n e r a t o r s h i f t r e g i s t e r can be r ep resen ted by a s t a t e v e c t o r , a . I t i s

only n a t u r a l then t o d e f i n e a v e c t o r space , U, which i s spanned by the

c y c l i c l y genera ted s t a t e v e c t o r s . He c a l l V the state or sample s p a c e .

For a s n - s t a g e s h i f t r e g i s t e r , t h i s space i s i d e n t i c a l t o E . The p o i n t s

i n D which a r e a c c e s s i b l e t o t h e s t a t e v e c t o r form t h e v e r t i c e s of an

n—dimensional hyperspace cube . Since t he s t a t e v e c t o r i s r e p r e s e n t e d by

a b ina ry n - t u p l e , a = ( a , a _ . . . a . ) , t h e r e a r e 2 v e r t i c e s of t h i s

cube, a l l of which a r e a c c e s s i b l e except the a l l z e r o n - t u p l e . This i s

cons i s t an t w i th the number, 2 n - l , of s t a t e s which a r e gene ra ted dur ing

the modulation sequence .

We a l s o noted e a r l i e r ( s ee "M-sequences") t h a t t h e genera ted sequence

i s s a i d t o be the r e s u l t of an ope ra to r T o p e r a t i n g on an i n i t i a l s t a t e

v e c t o r . T i s the sum of a feedback o p e r a t o r , C, and a s h i f t ope ra to r ,

S . Given an i n i t i a l s t a t e v e c t o r , a , the v e c t o r space U i s genera ted 27

by T. Because of the s h i f t and add p roper ty of m-sequences , t he

ope ra to r T i s a l i n e a r o p e r a t o r , a l though t h i s i s by no means obvious .

k t h I f T a r e p r e s e n t s the k s t a t e vec to r i n the sequence a f t e r k opera t ions

by T, because of t he s h i f t and add p roper ty i t i s a l s o t r u e t h a t

-65-

aQ + T* aQ £ D, k G l , a Q C 0 (39>

where modulo 2 addition Is assumed. Thus the vector space U Is closed

under operation by T.

Because R Is complete, If we define a scalar product on U, U i s a 28 separable Hilbert space (Euclidean) . This scalar product can be

defined by the modulo 2 addition:

A

<*. y> « 2 x i y i ( 4 0 )

i - i mod 2

Thus we are dealing with a separable Hilbert space and a 1:1 linear

operator for describing the process of sequence generation.

The picture oZ operation i s thus given by specifying an in i t ia l

state vector, a . which is then repeatedly acted upon by the generating

operator, T. This operation moves the state vector about the vertices

of the hyperspace cube in a fixed cyclic manner. The a l l zero vector,

0 , i s excluded because i t i s in the kernel of the operator T. Since

each n-tuple appears only once during the sequence, the state vector

passes through each vertex once and only once during the period of the

sequence.

Because of the nice properties of the state vector space, i t i s 28 possible to define projection operators which act on the state vectors.

One Buch projection operator, G, can be used to represent the generating

polynomial, G(x), which describes the output of the f irst stage of the

shift register. The n-tuple which represents this one dimensional

-66-

projector i s simply 6 = ( 1 , 0 . . . . , 0} and we can make the association,

2 Q -1

We will now describe how the use of projection operators can be viewed

as a method of calculating the TOF correlation function.

The point of this vector space picture i s to gain a better under­

standing of how the crosscorrelation function i s generated by the data

address method. In the vector space representation, the crosscorrelation

i s a measure of the correlation between the position of the s tate vector

and the occurrence of detector events. We can associate with each point

in the s ta te phase space a density in phase; th is density in phase

associates with each s t a t e vector the number of occasions on which a

detector event occurred while that s ta te vector represented the contents

of the modulation generating shift regis ter .

This representation i s especially applicable to the data address

method. In this method the addresses in the computer core memory are

used to represent the phase space points, while the contents of each

address represent the associated density in phase. In contrast with

methods such as the gated scalar scheme (see "Application of Correlation

TOF") the data address method accumulates the density in phase and la ter

computes the correlation function, as we now describe.

In the data address method, the crosscorrelation function is com­

puted from untransformed raw data by the use of a binary mask, (test bit)

and a series of associated signal and background accumulators (see

"Program Description"). The process of using a masking bit for testing

-67-

the bits of each address i s equivalent to defining a series of one

dimensional projection operators vhich act sequentially on each relevant

phase space state vector. A background and signal accumulator are

associated with each projector; i f the result of the projection operation

with any projector acting on a state vector i s a non-zero vector, the

density in phase associated with the state vector i s added to the signal

accumulator ( i . e . there was a positive correlation between the position

of that state vector and the associated detector events). A zero vector

result of the same projection operation results in the associated density

in phase being added to the background accumulator {negative correlation

between the state vector and the associated detector events). The com­

plete calculation of the correlation function then involves the action

of n projection operators on each of the 2 —1 Ftate vectors (assuning n

points of correlation function are being calculated).

If we define the projection operator far a delay time T as R , and

i f a i s the state vector and p(a) the associated density in phase, then

R x y ( T ) " J R x - p ( 2 ) d a ( W )

a l l space

The form of each one dimensional projection operator i s a i-tuple with

a "1" in a position determined by T and the remaining bi ts zero. For a

modulation clock period 6, i f T •= kfi, the n-tuple wi l l contain a "1" in

the k place. For a (1, 0) type of correlation (background not sub­

tracted) the discrete correlation function is then

-68-

2°-l

k-1

For a (+1, -1) correlation, as is used in Che data address nethod to

account for negative correlation effects (background subtracted)

zn-i Exy ( T ) * £ { * A " ( 1" RT )2k } P (5k ) C 4 4 )

k-1

We note that the effect of the projection operation i s really equivalent

to the use of a ser ies of phase density weighted inner products.

Similarly the autocorrelation function for the modulation sequence

can be represented by an inner product sum which i s unweighted. If we

denote the n-tuple representing each projector 8.(10 by a, , then

2 n - l W ^ " < a(t) |a( t+T)> - ^ < a ( t ) | a k Xa k | a ( t+T>> (45)

k=l

where a(t) i s the true s ta te vector at time t .

This view of the calculation of the correlation function calculation

i s a convenient vehicle for displaying the conceptual difference between

the gated scalar system of correlation and the data address system.

While, as we have shown, the la t te r method accumulates the density in

phase before the sequential operation by projection operators, the

scalar system works by immediate and simultaneous projection. Each time

a detector event i s noted by the scalar system, each of the gates in the

scalar system essentially performs the projection operation on the current

-69-

state vector. All n projection operations are accomplished simultaneously

because of the extensive hardware of the system. Thus, rather than using

a single series of weighted projections, this system uses repeated un­

weighted projections.

Summarizing, we see that the vector space picture of correlation

analysis provides a simple view of the operation of the data address

method. Although the formalism i s readily suggested by the framework of

the system, to our knowledge this i s the f irs t time this formalism has

been explicitly developed.

In the next section we wil l discuss the s ta t i s t i ca l analysis of the

system we have described in an effort to see h.-,v the unique method of

data address must be constructed to avoid data transduction error.

-70 -

STATISTICAL ANALYSIS

How t h a t we have erfmrfned the theory of t h e c o r r e l a t i o n method, i t

i s r e l e v a n t t o d i s c u s s the s t a t i s t i c a l e v a l u a t i o n of t he method t o see

how i t may cocpare i n accuracy wi th o t h e r s .

There a r e s e v e r a l p o i n t s of view from which the c o r r e l a t i o n system

may be ana lyzed . F i r s t , i gnor ing expe r imen ta l q u e s t i o n s , we i n q u i r e how

c lose ly t he measured e s t i m a t e of t he c o r r e l a t i o n func t ion corresponds t o

the t r u e TOP s i g n a l . Secondly, we ana lyze t h e s o u r c e s of exper imenta l

d i s t o r t i o n and compare t h e .general r e s u l t s of c o r r e l a t i o n measurement t o

those ob ta ined w i t h c l a s s i c a l TOF sys t ems , ffe t h e n proceed t o examine

the problems a s s o c i a t e d w i t h our own computer based c o r r e l a t i o n system

and d i s cus s t he g e n e r a l problem of d e t e c t o r p a r a l y s i s . F i n a l l y we view

the c o r r e l a t i o n sys tem i n l i g h t of t he Shannon sampl ing theorem i n an

e f f o r t t o e x p l a i n t h e r e l a t i v e e f f i cacy of t h e method.

System Opt imiza t ion

There has been a good dea l of d i s c u s s i o n i n t h e l i t e r a t u r e p e r t a i n -

29

ing t o t he o p t i m i z a t i o n of c o r r e l a t i o n a n a l y s i s s y s t e m s . This d i s ­

cuss ion c e n t e r s about de f in ing the v a r i a b l e s a v a i l a b l e w i t h i n t h e sys tem

and choosing t h e i r v a l u e s so as t o make c o r r e l a t i o n a n a l y s i s broadly

app l i cab l e i n an a c c u r a t e manner. The o p t i m i z a t i o n problem i s beyond

the scope of t h i s t h e s i s s i nce the p r i n c i p a l pa ramete r s (duty c y c l e ,

method of sequence g e n e r a t i o n , modulat ion sequence symmetry) a r e f ixed

by the expe r imen ta l e l e c t r o n i c methods which have been used i n implement­

ing t he p r e s e n t c o r r e l a t i o n system.

-71 -

Correlatlon Measurement Variance

In the process of making a measurement of a correlation function,

one i s actually making an experimental estimate of the function by 25 repeated single correlat ions. Stern e t a l . have derived a detailed

s t a t i s t i ca l analysis of the correlation function "estimator" using the

fundamental lavs of conditional probability, the accumulated single

correlations and a simple assumption about the net steady s ta te part icle

flux as the modulation bandwidth i s increased to a > . They have showed

that in fact the measured estimator of the correlation function i s

equivalent to the " t rue" correlation function. Hence ve may have some

confidence that the accumulation of single correlations wi l l reveal the

true shape of a TOP dis tr ibut ion.

Given that ve are indeed measuring the shape of the TOF distribu­

tion, the next question to be dealt with i s how good i s the measurement.

That i s , given that an accumulation of single correlations wi l l converge

toward the true correlation function, how fast w i l l that convergence be?

A measure of the reproducibility and (in the abeence of systematic

error) accuracy of any experimental measurement i s i t s variance. In

general, any set of measurements of a process can be represented by a mean

value and a variance. He recall that the mean of a set of measurements,

{x.} i s defined as

H T K = H m N X X = 1 ± m k f x(t)dt. (46)

*See "Random Process Appendix".

The variance describes the mean square deviation of the measurements from

the mean value:

N 1

Var(x) = a* = lim 5"2 ] E x k" P x l 2 = U m T / k( t ) -y x ] Z dt <«)

The variance of the correlation estimator has been evaluated by

various means of different authors; the most fundamental method is to work

from single correlations using simple, joint, and conditional probabili­

ties to evaluate explicitly the factors of the correlation estimator

25 variance. This has been accomplished by Stern who has shown that

basically the expected relative error (dimensionless variance) is attribu­

table to three sources: finite counting times, finite counting rates,

and spontaneous source fluctuations:

E r e l - y - * - - 4 + R c + R r <*8 )

** ( T o >

where R (T ) is an average value of the correlation estimator and the X? O

three terms refer to errors (variance) due to measurement time, counting

rate and source fluctuations,respectively. The last term is not applic-3 4 able in the present case; the relatively large numbers of ions (10 -10 )

released with each beam pulse make stat is t ical fluctuations L. the source

output negligible (<12). For the present system, we will evaluate the

magnitudes of the remaining terms.

The remaining terms have been shown to be represented by:

R£ = (2(H)" 1 (491

\2 <-(tf ( rT)" 1 (50)

where o = TOF bandwidth, T = tot- -.aasureosnt time, n = the modulation

index (1 in this case), and r le average counting r a t e . The factor

W i s defined by

„ _ 2m modulation bandwidth o TOF bandwidth

For the praseat system, we can evaluate the magnitude of these variance

terms using:

a = ~~ = 10" 5 s e c ' 1

10 psec

T = 30 seconds

W = 10 n = l

- 2 3 4

for the cases of r = 10 , 10 , 10 counts/sec. He then find that the

error due to counting rate is R ^ (r) = 1 0 , 1 0 , 1 0 for the

above counting ra tes , while R_ <10

Thus we conclude that for the present wideband modulation used and

the relatively intense signal expected, the experimentally generated

variances wi l l be of the order of 12 of the mean correlation estimator

value, an entirely tolerable level.

The fact that these experimental considerations do not lead to

-74 -

s i g n i f i c a n t va r iance does not imply t h a t va r iance i s a n e g l i g i b l e p r o b ­

lem. We have ye t to cons ider the problem of s i g n a l / n o i s e r a t i o (S/H)

and the e f f e c t s of random or c o r r e l a t e d n o i s e ; t h i s w i l l be d i s c u s s e d

n e x t .

I n a c o r r e l a t i o n measurement sys t em, the re i s no p r a c t i c a l method

of removing c o r r e l a t e d n o i s e . For i n s t a n c e , c r o s s t a l k between s o u r c e

modula t ion and s i g n a l d e t e c t i o n w i l l remain i n v i s i b l e to t he c o r r e l a t o r

and y e t could c o n t r i b u t e s i g n i f i c a n t l y t o the measured TOF d i s t r i b u t i o n ,

p o s s i b l y l e ad ing to f a l s e peaks i n t h e c o r r e l a t i o n func t ion . The e x p e r i ­

m e n t e r ' s only recourse i s c a r e f u l d e s i g n t o e l i m i n a t e any p o s s i b i l i t y of

c o r r e l a t e d n o i s e . One hopeful n o t e i s provided by the f a c t t h a t c o r r e ­

l a t e d n o i s e w i l l most probably be measured with a very s h o r t c o r r e l a t i o n

t ime ( T a; 0) s i nce e l e c t r o n i c s i g n a l s from modulation a r e t r a n s m i t t e d a t

h igh s p e e d . This bas the e f f e c t of s e p a r a t i n g any c o r r e l a t e d n o i s e peak

from t h e TOF c o r r e l a t i o n peak s i n c e ion t ime of f l i g h t i s f i n i t e . We

n o t e t h a t as y e t we have seen no ev idence of c o r r e l a t e d n o i s e i n t h e TOF

d i s t r i b u t i o n s which have been measured.

The va r i ance due to unco r r e l a t ed n o i s e has been d e a l t wi th by 22 21

Von Jan and Schena and by Hossfeld and Aoadori. They have d e r i v e d

the fo l lowing express ion fo r c o r r e l a t i o n var iance as a func t ion of delay

time ( s i n g l e poin t c o r r e l a t i o n v a r i a n c e ) :

RT+b where a » and

T R

L T (51)

-75-

R - R ( T ) ( s i n g l e p o i n t of corre lat ion function)

b - average background per channel

L • nucber of channels needed to span the measured TOF function

N •= 2 - 1 • length of the modulation sequence

f • the mnber of t i n e s the modulation sequence repeats during the

measurement

c • duty cycle • 0 .5

- i L

R • — V* R, * the average TOP s i g n a l . T«l

The f i r s t fac tor I s i d e n t i c a l t o the error which would be measured

i n a c l a s s i c a l TOF experiment with a pulse r e p e t i t i o n r a t e S~ . The

f a c t o r £B i s a measure of the t o t a l measurement time and thus f o r f ixed

s i g n a l l e v e l s , the r e l a t i v e error decreases i n an inverse manner as the

measurement time i s increased .

In order to compare the r e s u l t s for c l a s s i c a l end c o r r e l a t i o n

measurements! the " c l a s s i c a l " tern i s often divided out to g i v e a r e l a ­

t i v e gain factor:

2 " ^ " c l a s s i c a l . ( * • « » < * £ ( 5 2 )

t a B W 1 ccrrelacicm ^ * j | -

This gain factor expresses the gain i n accuracy which i s achieved by use

of the correlat ion method. I t i s primarily a function of the r e l a t i v e

s i z e of the correlat ion funct ion at any po int ,

R +b

-76 -

since the duty cycle, c, modulation length H, and TOF width, Lt are

relatively fixed. For a duty cycle of c • 0.5 both Von Jan and Hossfeld

have calculated that the correlation method wil l provide superior results 2

(g >1) i f o", ^ 2; this i spl les that the correlation method wi l l always

give a Bore accurate measurement of the shape of correlation peaks In the

presence of low background levels (large S/N), and wil l give higher

accuracy for the entire correlation spectrum in the presence of large

relative background levels (b>2B). Ac example of this effect is shown 22 in Fig. 15 (after Von Jan and Schero ) . In Fig. 15A a measurement is

made in the presence of a low background level. For portions of the

spectrum below a • 2 the correlation method i s less effective than the

classical method while for viewing the peak the correlation method i s

better. In Fig. 158 a measurement i s made in the presence of a high

relative background level . In this case, a l l of the spectrum l ies above

a • 2, so the correlation method i s better for the entire spectrum.

We note that a l l of the above discussion has assuaed a stationary

experimental system, this i s often not the case; expertmentally a systea

i s rarely stable in a long tern sense since bean energy fluctuates a

finite amount as does beam intensity. Also the vacuus systen nay undergo

pressure fluctuations as may the pressure of target gas contained within

a scattering celL This experimental reality provides further support for

the use of the correlation method since if in some experimental oeasure-

ment classical and correlation methods were to have identical accuracies

(gain factor equal to one), data collection by the classical method would

require a tioe interval at least 10 times as long as that required by a

correlation measurement, making the classical method tsuch core susceptible

-77-

Small Background Case

- 4

" - I

b. Large Background Case XBL748-6922

Fig. 15. Relative efficiency of the correlation taethod for small and large S/K cases.

-78-

to experimental d r i f t . This advantage, which i s e n t i r e l y due to duty

cyc le cons iderat ions , has been widely overlooked.

In summary than, the corre la t ion method i s super ior under adverse

S/N conditions and for examining correlat ion peaks. In both methods, the

examination of l e s s in tense port ions of the TOF spectrum i s accomplished

with lower e f f i c i e n c y , and t h i s face often determines the time necessary

to measure the TOF spectrum with s u f f i c i e n t accuracy; for t h i s case the

bandpass system of measurement has d e f i n i t e advantages.

Detector Paralys i s

He turn now t o the d i s c u s s i o n of measurement accuracy problems which

are part icu lar ly a s soc ia t ed wi th the present computer based system. By

f a r the most important aspect i s the problem of data transduction errors

or detector p a r a l y s i s .

TOF spectroscopy i s a dynamic method of measurement. Consequently,

i t i s suscept ib le to dynamic errors inherent i n the measurement process

which are much l e s s amenable t o analys i s and correc t ion than the errors

of a non-dynamic energy bandpass system.

The most s i g n i f i c a n t type o£ dynamic error to which a TOF system

may be subjected i s the error of data transduction. Any p a r t i c l e de tec ­

t i o n system has a f i n i t e bandwidth capabi l i ty ; hence each detector has

a f i n i t e period of time (deadtime) af ter i t has de tec ted a p a r t i c l e

event during which i t I s unable to r e g i s t e r the appearance of subsequent*

l y arriving p a r t i c l e s . This phenomenon, known as de tec tor p a r a l y s i s , may

have profound e f f e c t s on a dynamic peasureasnt system.

Detectors of events are generally c l a s s i f i e d as being one of two

30 types . A Type I (non-paralyzable) counter which r e g i s t e r s a p a r t i c l e

-79-

arriving at time t , wil l then lock out any further particles arriving

during a (random) period, T (the deadttme). Particles arriving in the

locking interval ( t , t+x) are not registered, nor do they affect the

counter in any way. A scinti l lat ion counter i s an example of a Type 1

Counter.

In contrast, a Type II (paralyzable) Counter does not lock out

particles which arrive during the dsadtlme associated with in i t i a l

particle detection. As each particle arrives, i t locks the counter for

a random locking tine, T , regardless of whether i t was counted or not.

For a sufficiently large particle flux, a Type II Counter can be com­

pletely paralyzed, Che f irst particle being counted and a l l further

particles merely extending the dead tine. A "non-self quenching Geiger-18 duller counter with a high impedance preamplifier" i s an example of a

Type H Counter.

The computer based data acquisition method of the current correla­

tion TOF system i s basically a Type I counter. Since the actual particle

detector i s much faster than the computer data storage part of the

system, the bandwidth (20GkHz) of the interface data storage system

effectively limits the bandwidth of the counting system. This bandwidth

limitation i s due to the necessity of three 1.2 usee memory access cycles

to acknowledge the arrival or a single detected ion. Since the computer

and the detector are asynchronous, a 5-7 usee deadtioe can be considered

as a reasonable worst case estimate of the limit on data storage band­

width.

The question we must deal with i s whether the typical 5 usee counter

deadtime will prejudice the shape of the measured TOF distribution in

-80-

favor of faster particles which may arrive first at the detector, locking

out the slower particles which arrive later.

In general for classical TOF, the effects of Type I Counter deadtime

depend on the relative bandwidths of the detector (B ) and the dynamic

signal being measured (B___) • As we now describe, at each extreme

(B » BxoF* BTQF > : > B D e t ' * t h e raeasured T 0 F s i SPal will be measured

accurately, while the intermediate case (B- ^ B_ -) may lead to data

storage prejudice.

The case of a very fast detector (B_ > > B T Q F ) "^ C n e simplest*

In this case the dead time of the counter is negligibly small and all

relevant signal data will be stored. The opposite case ( B

T 0 F » B } is

that of random phase sampling where the detector is locked most of the

time and randomly samples the TOF signal in a "Monte Carlo" type of

detection. Note that the random phase assumption is of prime importance.

The case of detector downtime being correlated with the TOF signal may

lead to severe distortion.

The median case (B« ** B

T n P ) contains the greatest possibility of

data prejudicing. In this case, given a suitable particle flux, the TOF

signal and the detector are matched in phase in a resonant manner. The

fast particles of any beam pulse are registered and the slow particles

are locked Out. The detector becomes unlocked in time to register a fast

particle from the next TOF pulse, and the scheme is repeated. While a

distribution of arrival times will be measured, i t is conceivable that

the prejudice of the distribution may be so great as to display periodic

structure within the TOF waveform, the period being characteristic of

the detector deadtime.

-81-

Of course this discussion depends strongly on the net particle flux

and the signal repetition rate. In a classical TOF experiment, the

repetition rate i s alvays relatively slow so that given a minimum flux of

particles at the detector (say 5-10 ions/bean pulse) data transduction

would be far from perfect, favoring the high velocity portion of the

distribution.

In the case of correlation analysis, depending on the path length

of the TOF analyzer, ic may often be the case that B- *x* B___. However,

ve maintain that this method avoids prejudice because of i t s inherently

large repetition rate. The beam pulse rate on the average i s great

enough so that several or many pulses are produced within a time charac­

teristic of the TOF function (Fig. 16). As these pulses travel through

the TOF system, they v i l l overlap spatially leading to a net steady state

beam flux. Since the ion flux arriving at the detector i s approximately

constant in time, the detector does not differentiate between fast and

slow ions; the distribution of ions causing detector counts v i l l be dis­

tributed numerically in proportion to their velocity characterized

number density in the ion beam. Similarly, ions which are rejected due

to detect!-r downtime wil l also be rejected in proportion to the velocity

distribution ("counts neglected and not detected can be rejected"). This

i s another example of random phase sampling. "

As an Illustration, consider a measured TOF distribution of 6 usee

width at the detector generated by a mean modulation frequency of 1 mega­

hertz. Since the modulation bandwidth is greater than the TOF bandwidth

(as i t must be for reasonable resolution), on the average, unit beam

pulses will overlap spatially before they approach the detector. Sow

R x y(r)

M(t)

TOF Function

, Modulation Function t —

XBL748-692I

Fig. 16. The high relative repetition rate for the correlation method.

-83 -

slnce there are runs of consecutive " l ' s " and "O's" in the modulation

sequence, there i s the possibil i ty of negligible pulse overlap if a

sufficiently long run of "O's" were present in the sequence- We recall

from the discussion of a-sequences that the probability of having n con­

secutive " l ' s " or " 0 f s " i s 2 . For the 6 usee wide TOF signal, i t would

require a run of a t least 6 zeroes to eliminate beam pulse overlap; thus

runs of length k, k<6, wi l l not be subject to causing distortion. The

total probability of having a run of zeroes greater than 6 i s

5

k=i

where the factor of y i s a result of only one half of the modulation

sequence being comprised of zeroes. Thus, for th i s case, only 1.5Z of

the modulation pul&es wi l l allow the possibil i ty of TOF distort ion.

This necessity for beam pulse overlap puts another c r i t i ca l con­

straint on the length of the TOF flight path. Let ' s assume that one

wishes to allow only a small fraction, £ , of the beam pulses not to

overlap. Further assume that the TOF distribution has a maiHimt velocity,

V_, minimum velocity, V., and velocity bandwidth AV = V„ - V . To

achieve overlap in a fraction of pulses 1-C we determine n from the

following inequality:

n

k=l

The width of the TOF function at a detector placed L cm away from the

source i s

T mh- L. LAV , q a l

TOF V x " V 2 V X V 2 * " '

To achieve t he n e c e s s a r y over lap t h e n ,

T T O F ^ n T H o d ^ B ^ (55)

where Tj. . and B„ . a r e t he modulat ion p e r i o d and bandwidth, r e s p e c t i v e l y .

Equat ing (2) and (3) we f ind

nVV L > M T 5 ^ C56) AV ^ d

P r a c t i c a l l y speak ing , t h i s i n e q u a l i t y w i l l p r a c t i c a l l y always be

s a t i s f i e d s i n c e choosing L s u f f i c i e n t l y l a r g e t o g ive reasonable r e s o l u ­

t i o n w i l l e l i m i n a t e any beam over lap problem. However, t h i s c o n s t r a i n t

warns us t h a t i f t he TOF f l i g h t pa th i s n o t s u f f i c i e n t l y g r e a t , not only

w i l l t h e r e be poor r e s o l u t i o n , bu t t h e r e may a l s o be s i g n a l d i s t o r t i o n .

We have i n c l u d e d as an appendix a more r i g o r o u s d e r i v a t i o n of the

d e t e c t o r p a r a l y s i s problem us ing a mathemat ica l d e r i v a t i o n based on the

a u t o c o r r e l a t i o n func t ion of the modulation sequence . For fu r the r d i s ­

cuss ion , p l e a s e s e e t h i s appendix.

Shannon's SampH"g Theorem

I n viewing t h e c o r r e l a t i o n system, i t seems somewhat l i k e an e x p e r i ­

menter i s " g e t t i n g something for no th ing" by u s i n g su<:h a system t o ga in

inc reased s i g n a l d e t e c t i o n c a p a b i l i t y . The answer t o t h i s a l l e g a t i o n i s 31

contained i n t h e w e l l known Shannon Sampling Theorem.

-85-

Shannon's theorem te l l s us that any in formation channel can be

characterized as having a maximal information transfer capacity, and that

any desired level of accuracy in information transfer through the channel 32 can be achieved by error correcting codes at the expense of lowering

the information transfer ra te .

The TOP system can be viewed as an information transfer channel.

The classical TOF method i s an extremely inefficient mode of data trans­

fer; i t ' s somewhat reminiscent of a trans-Atlantic telephone conversation

in which each word spoken must reach the other end of the line before the

next word i s ut tered. Thus i t i s this tremendous inefficiency which nraifpg

the correlation method look efficient.

The classical method makes no expl ic i t use of any error correcting

code for information transfer. However, the use of single beam pulses

is In real i ty a very simple transmission code. The correlation method

on the other hand expl ici t ly uses an error correcting code (random modu­

lation} which i s much more efficient. Whereas the classical method

simply includes signal errors (noise) with the detected signal and la ter

subtracts i t , the error correcting property of random modulation is used

explicitly to remove uncorrelated noise in the correlation method.

Although the correlation method makes much fuller use of the infor­

mation capacity of the TOF channel, one can only wonder whether s t i l l

more efficient methods might be found, further enhancing experimental

accuracy and speed.

In summary, we have discussed the sources of experimental variance

and found them not overly important. The correlation and classical

methods were compared for accuracy and the former method shown to be

-86 -

superlor In many Instances. The problem of detector par 1 ysls was shown

not to apply to the correlation system providing that the system Is

designed with a sufficiently large fl ight path. Finally, we have reviewed

the information transfer aspects o£ the two systems and saw how coding

led to increased information handling capabil i ty.

-87-

REFg'.EHCES FOR CHAPTER II

1. F. Hossfeld, R. Acadori, and R. Scberm. prnrpg<Hngw nF rtig Panoi

Conference on Instrumentation for Heutron Inelastic Scattering. IAEA,

Vienna, 1970, p.126 f£.

2. P. E. Pfeiffer, Linear Systems Analysis. HcGraa Hill, 1961.

3. See L. I. Schlff. Quantum Mechanics, 3 r d Ed. McGraw Hill & Co.

1968, p.55.

4. J. S. Bendat and A. G. Piersol. Hpasurement and Analysis of Random

Data. John tfiley and Sons, Inc. Hew York, 196e.

5. X. E. Stern, A. Blaqulere, and J. Valat. J. Nuclear Energy A/B, 16_

499 (1962).

6. W. D. T. Davies. Control, June, 1966 p.302.

7. G. A. Eorn. Random Process Simulation and Hpasurement. HcGrsv

Hill, 1966.

8. See References (1) , (21) and (22) .

9. P. H. R. Scholenfield. Electronic Technology 37, 3?9 (1960).

10. T. E. Stern and B. Friedland. IRE Transactions on Information

Theory IT-5, 114 (1959).

11. See References (9) and (10).

12a. References ;i0), (13), and (17).

b. S. W. Golomb. Sequences with Randomness Properties. The Glenn L.

Martin Co. Baltimore, Hd. June, 1955.

13. H. Zlfirler. J. Soc. Indust. Appl. Math. T_, 31(1959).

14. Reference (6), p.304.

15. Heference (7), p.85.

16. Reference (13) and (17).

-88-

17. W. W. Peterson and E. J. Veldon, Jr., Error correcting Codes. H.I.T.

Press, 1972, p. 472 ff.

18. E. Parzen. Stochastic Processes, Holden Day & Co., San Francisco,

1962.

19. S. U. Golomb. Shift Register Sequences. Holden Day & Co., San

Francisco, 1967.

20. Reference (13), p. 32; reference (17), p.59.

21. F. Hossfeld and R. Amadori. On Pseudorandom and Markov Sequences

Optimising Correlation Tlae-of-Flight Spectrometry. DSAEC, JUL 684FF,

(1971) available from HTIS.

22. R. Von Jan and R. Scherm. Hud. Instrum. Heth. 80, 69 (1970).

23. V. L. Hirschy and J. F. Aldridge. Rev. Sci. Instrum. 42, 381 (1971).

24a. I. Pal, H. Kroo, P. Pellionisz, F. Slavifc a I. Vizi in 4th IAEA

Symposium on neutron Inelastic Scattering. Volume II, Copenhagen,

1968, p. 407.

b. P. Pellionisz. Hud. Instrum. Heth. 92, 125 (1971).

25. Reference (5).

26. R. E. Unrig and H. J. Ohanlan In Heutron Hoise Haves and Pulse

Propagation. USAEC, 1967.

27. References (13), (19), and (21).

28. E. PrugoveckL. Quantum Mechanics in Hilhert Space. Academic Pres3,

Res York, 1B71.

29a. K. Veise, Hud. Inscrum. Heth. 98, 119 (1972).

b. C. J. Hacleod. Int. J. Control 14 97 (1971).

c. G. Wilhelmi and F. Gompf. Hud. Instrum. Heth. 81, 36 (1970).

d. Reference (21),'

y

-89-

30. D. R. Cos. Renewal Theory. Matbaene * Co., Ltd., London. 1962, p.31. 31. C. E. Shannon and V. Heaver. Matbeeatlcal Theory of Co—iiiili.nlnn.

University of Illinois Press, Urban* 19*9. 32. Reference (17).

- 9 0 -

CHAPTER I I I ,

COMPDIER ORGANIZATION

This section i s the f irs t of several which discuss the electronic

and informational techniques which have been used to implement a computer

based TOP correlation system. Since the computer interface, the main

object of the discussion which follows, i s intimately connected with the

internal hardware structure of the computer i t se l f , we wil l f irst describe

some of the pertinent organization within the computer. This discussion

i s admittedly brief; since many of the details of the computer's operation

are beyond the scope of this thesis, the reader i s referred to the DEC

PDP8/e Small Computer Handbook.

The POP 8/f i s a 12 bi t minicomputer with a 1.2 usee cycle time.

Overall, the basic computer organization can be described as follows:

"The PDP-8/E system consists of a central processor, core memory, and input/output fac i l i t ies ; a l l of which interrelate by WMK of a **JITIMM"P bus called 'Omnibus.*

"All arithmetic, logic, and system control operations are performed by the central processor. Information storage and retrieval operations are performed by the core memory. The memory i s continuously cycling, automatically performing a read and write operation during each computer cycle. Input and output address and data buffering of the core memory are performed by registers in the central processor, and the operation of the core memory i s under control of timing signals produced by the central processor."

In essence, the central processor, via programmed control, manipu­

lates the contents of the core memory in the process of performing

arithmetic and logical operations in a logically ordered temporal

-91-

Tbe computer's core memory consists of 8 K addresses (IK = 102410)

divided into two 4 K f ie lds . Each field i s labeled by a three bit

Extended Memory Address code (EMA), allowing up to 32 K of core memory to

be employed. Each core address i s capable of storing a 12 bit binary

number. Within each 4 K. f ield, memory addresses are divided into blocks

of 200B, denoted as "pages. thus addresses 0, 200. 400, etc. each de­

note the start of a new cere page. All programming operations are page

relative; that i s . when an address i s named as an operand, i t i s speci­

fied relative to the beginning of the page on which the computer ifi

currently operating. (For example, i f the computer i s operating on the

page starting with address 1200. the address 1302 i s specified as 102.}

This type of addressing i s a result of the 12 bi t configuration of the

computer's central processor. To specify an address In a 4 K. field

uniquely would require a 12 bi t code; page relative addressing requires

only 7 of the possible 12 bits contained as the contents of an address,

leaving 5 bits available for actual operational Instructions. It must

be remembered that there are two 12 bit numbers associated with each

address: the address code i t se l f and i t s contents.

A simplified picture of the computer operation may be described as

follows: the Central Processor (CPU) determines an operator address

whose contents wi l l determine the next operation to be carried out. The

contents of the operator address contain both the operation to be carried

out and an operand address whose contents wi l l be the subject of the

*0ctal notation wi l l be used for describing the operations of the com­puter.

-92-

operation. The operation i s performed on the operand contents and the

result stored either in the operand address or in a storage register

called the accumulator (AC). Next, the CPU looks in a Program Counter

(PC) register to determine the next operator address, and the prices*

then continues. A program consists of a scries of such operations

designed to achieve a mathematical calculation or logical core cecory

manipulation.

The Central Processor (CPU) of the computer consists of a tiding

sequence generator, an Instruction Register for programming operations,

paral lel adders, an Accumulator (AC) for recording the results of a r i th ­

metic and logical operations, and several 12 bi t registers utilized in

programming control. There are also gating networks fur taultiplexing

input to and output from the CPU and the core memory. Mosc important of

the control registers are the Central Processor Memory Address Register

(CPMA) which scores the Memory Address (MA) which i s currently being used

by the CPU as an operand address, and Che Program Counter Register which

stores the memory address from which the next instruction will he taken

ac the completion of the current programming operation. During a pro­

grammed operation, the operand pare of an instruction is stored in the

CPMA, while the operational instruction is stored in the Instruction

Register.

Normally, the Program Counter limits core address manipulation to

one 4 K field of memory unt i l the EMA is explici t ly changed. In the

absence of "jump" commands, programming is sequential; the CPU accesses

the memory location contained in the Program Counter, performs the re­

quired operation(s), increments the Progran Counter by one and continues

- 9 3 -

chc processing. However, manipulation of the contents of the Program

Counter allows non-sequent ia l programing using JHP (Jump) operation codes

and allows the CPU to make t r a n s i t i o n s betvecn the current core page and

any other page.

Opgrations Codes

There are 8 operations codes which ate employed in programming

sequences. Of these , f i v e arc 'memory reference i n s t r u c t i o n s " which

s tore and retr ieve data from core memory, and one i s the s o - c a l l e d "house­

keeping" JHP operation which transfers program contro l t o any neaory

address uncondit ionally (not a subroutine-type t r a n s f e r ) . A l i s t of the

Heaory Reference Ins truct ions* t h e i r operat ions , and o c t a l operation

codes are given In Tabic A. The AND function i s the only l o g i c a l opera­

t i o n . The TAD and DCA I n s t r u c t i o n s are used for a r l t h o e t i c manipulations,

whi le the ISZ ins truc t ion i s used for program looping . JHS transfers

contro l to a subroutine wi th an option for e x i t from the subroutine r e ­

turning program control t o the program locat ion request ing the sub­

routine entry .

The remaining two operat ions codes are c a l l e d "augmented i n s t r u c ­

t i o n s . " Code 6XXn i s used for input/output transfer (IOT) between the

computer and i t s p e r i p h e r a l s , each peripheral being ass igned a s i x b i t

(2 d i g i t ) o c t a l code (XX) which i t alone recognizes . Code 7nnn i s an

operations code which a l lows manipulations of the contents of the AC and

l o g i c a l checking of the contents of the AC.

In the PUP 8, t ee o c t a l numbers 0000-377? are p o s i t i v e whi le the

numbers 4000-7777 are n e g a t i v e . This allows twos complement addit ion

as w e l l as program looping by incrementing negative numbers (or p o s i t i v e

-94-

Table A. Memory reference lnscructions for DPD 87 f

Mnemonic Operation Op. Code (Octal)

(1) AND Logical {+) between AC and memory

Onnn

(2) TAD Two's complement addition between AC and memory

lnnn

(3) ISZ Increment memory, skip next instruc­tion if the result is zero; for program looping

2nnn

(4) BCA Deposit AC in memory, clear AC 3nnn

(5) JHS Jump to subroutine 4nnn

(C) JHP (ho asekeeping) Unconditional jump 5nnn

-95-

numbers) unt i l a zero resul t i s obtained.

The Omnibus

The computer bus (OMNIBUS) i s available to a l l of the computer's

peripherals, as well as the CPU, and transports 96 different signals.

Some of the more pertinent bus lines are as follows: The memory address

lines (MA. 0-11) which carry the Ma being accessed currently by the CPU;

memory data lines (MD 0-11) which transfer the contents of the address

carried on the MA lines back and forth between core memory and the CPU;

data lines (DATA 0-11) which carry the contests of the AC; and the timing

pulses which are used to gate a l l operations both within the CPU and in

the computer-peripheral interfaces.

Progra™»»d Operation

He are now in a position to give a more detailed description of the

sequence of events which occurs in programmed operation. In i t ia l ly the

computer i s halted and the f i r s t address of the program i s entered on

the programmer's console. He assume that a correctly coded program has

previously been stored in the core memory start ing at th is i n i t i a l

address. When the computer Is started, the CPU examines the contents of

the program counter, which now contains the i n i t i a l address. Since the

contents of the i n i t i a l address are the f i rs t operation and operand in

the programming sequence, the CPU gates on the HA lines to access this

address (the operator) . The operations code of the operator address is

loaded into the 3 b i t Instruction Register and the operand address Is

placed In the CPHA regis ter . Using the memory data l ines to access the

contents of the operand address, the CPU carries out the specified

operation on either the operand or the accumulator contents, or both.

-96-

The results of the operation are then either stored in the AC or gated

back to the operand address via the Memory Buffer l i ne s . The Program

Counter i s then incremented and the process continues. We have assumed

here that a Memory Reference Instruction was being implemented. In Che

case of a jump or augmented instruction, the operation i s rather a manipu­

lation of the Program Counter, the accumulator or a peripheral device.

Data Transfers

Besides the augmented 6XXn instruction used for communicating with

a peripheral device labeled XX, there are two additional modes of opera­

tion which are used for data transfer between the computer and i t s per i ­

pherals: interupt transfer and direct memory access (DMA) or "data

break" modes. Both of these modes of operation rely on an interrupting

signal being generated by the peripheral i t se l f ; both modes provide for

data transfer at the request of the peripheral device.

In an interrupt transfer, the peripheral raises a "flag" (pulls down

the "interrupt l ine" on the OMNIBUS) te l l ing the CPU that i t wants access.

The raising of a flag caures the CPU to interrupt i t s normal program

routine and to jump to absolute location 0000 (within the current EMA

field)- Previously a program has been placed s ta r t ing at location zero;

this program acknowledges the interrupt, tes ts to determine which per i ­

pheral has made the request, and jumpB to an appropriate subroutine which

services the peripheral, using IOT'S (6XXn) to complete the data transfer.

Upon completion of the transfer, the subroutine returns program control

to the point of operation In effect prior to the interrupt . Interrupt

programming is used for servicing peripherals which do not have a

cr i t ical ly short access time.

-97-

In comparison with interrupt transfers which modify normal program

operation and require relat ively l i t t l e in the way of peripheral control

logic, the data break (DMA) transfer is a "cycle steal ing" technique

which requires a coicplicated arrangement of control logic to disable the

normal canputer functions and to make the CPU a slave of the peripheral.

With this type of transfer the normal operations of the CPU are tempo­

rari ly suspended; the operational components of the CPU ( i . e . the Program

Counter, CPMA Register, Instruction Register and gating logic) are dis­

abled and substituted for by a paral le l set of logic in the peripheral

device. The peripheral supplies the memory address, controls the opera­

tion to be carried out by the CPU arithmetic and logical elements and

supplies i t s own data (for transfer into memory). Thus the Direct

Memory Access mode can occur at any time and can transfer large blocks of

data into or out of memory without disturbing (except temporally) the

normal programming operation. The DMA mode effects data transfer at high

speed and i s used to service peripheral (such as a high speed disc f i le)

which have a c r i t i ca l access time. I t i s this DHA mode which has been

employed in data acquisition for our correlation TOP system.

Having examined the framework of the computer's operation, we next

discuss the computer interface which allows the computer to acquire data

from an ion beam apparatus, and which forms the heart of the correlation

system.

- 9 8 -

THE CORRELATION SYSTEM COMPUTER INTERFACE

In any computer based d a t a a c q u i s i t i o n sys tem, a c e n t r a l r o l e i s

p layed by the computer i n t e r f a c e l o g i c . By i t s e l f a computer e x i s t s in

an information vacuum. The i n t e r f a c e p rov ides the l i n k between the com­

p u t e r and the o u t s i d e w o r l d . The i n t e r f a c e accep t s i n fo rma t ion from

ex te rna l sources and i s r e s p o n s i b l e for t r a n s d u c t i o n of computer genera ted

commands and c a l c u l a t i o n s f o r a p p l i c a t i o n t o p e r i p h e r a l ou tpu t devices

and the exper imenta l a p p a r a t u s . T^e i n t e r f a c e i s a l s o r e s p o n s i b l e for

synchronis ing the asynchronous units involved i n t h e e x p e r i m e n t a l sys tem.

I n t he p r e s e n t computer system, the i n t e r f a c e h a s t he c e n t r a l r o l e

i n implementing t h e c o r r e l a t i o n method. I t i s t h e i n t e r f a c e which modu­

l a t e s the ion beam a p p a r a t u s , and which p l ays t h e command r o l e i n s t o r i n g

c o r r e l a t i o n in format ion e x t r a c t e d from the e x p e r i m e n t a l sys tem. A gene ra l

p i c t u r e of t he c e n t r a l r o l e o f t he i n t e r f a c e i s p r e s e n t e d i n F i g . 17 .

Ove ra l l , t h e i n t e r f a c e r e s i d e s on t h r e e p r i n t e d c i r c u i t boards which

f i t d i r e c t l y i n t o t h e computer and have access t o a l l of t he computer bus

l i n e s i n c l u d i n g t iming s i g n a l s , memory address l i n e s and d a t a l i n e s . The

Bin Time C l c k Board c o n t a i n s a c r y s t a l o s c i l l a t o r and frequency d i v i d i n g

network, a pseudorandom b i n a r y sequence g e n e r a t o r (PHHG), v a r i a b l e length

s h i f t r e g i s t e r delay l i n e s , d e t e c t o r output s e n s i n g d e v i c e , and a p p r o p r i a t e

con t ro l l o g i c .

The Data Break Boprd con ta in s a l l of t he d a t a b r e a k l o g i c , a device

p r i o r i t y network, an i n p u t / o u t p u t t r a n s f e r (IOT) decoding network and a

s h i f t r e g i s t e r s t o r a g e l i n e fo r r e t a i n i n g the de layed PRHG output for

da t a c o r r e l a t i o n . A d d i t i o n a l l y t h i s board con ta in s a PEHG i-equence sample

and hold network connected i n p a r a l l e l wi th m u l t i p l e x e r s used to ga te

Data Computer System

Control >Data Display and Analysis

Modulation Interface

Correlation Experiment

Detection

XBL 748-6924

Fig. 17. The central role of Che computer correlation Interface.

-100-

the memory address lines for storing data addresses during a data break.

The Digital to Analog Conversion Board (DAC) contains two 12 bi t

d ig i ta l to analog converters used to display accumulated transformed data

graphically on an oscilloscope, as well as a separate IOT decoding net­

work and control logic.

Overview of Interface Operation

A block diagram of the functions contained on the Clock and Data

Break boards is shown in Fig. 18. The time scale of interface operation

i s provided by the digital clock frequency dividing network, one of whose

outputs is chosen to f i t the required time scale of the experiment. The

clock frequency is used to run a l l the registers contained in the in ter ­

face including the random sequence generator (PRHG). The PRNG output is

used t.o modulate the ion beam experiment; this output i s also contained in

a variable length digital delay line and stored dynamically in the shift

regis ter storage l ine. When a detector event i s sensed, the delayed code

contained in the storage l ine i s stored in the computer core memory by

the data address method (see "Application of Correlation TOF") through

three sequential data breaks to three 1 K quadrants of the upper 4 K of

the computer's memory. The sequential storage in each of the three

quadrants is directed by the memory quadrant generator.

tn the following sections we wi l l describe in detail the design and

implementation of the electronic circuitry which comprises the interface.

I . Bin Time Clock Board

1. Interface Bin Time Clock (Figure 19)

The computer interface design using a pseudorandom experimental

modulation requires a stable, reproducible, variable rate clock signal

Experimental Modulation

X-TAL -

PRNG

E^

*N

Select

Load IOT

PDP 8/f Processor

Long Delay

MPLX = = n _ Short =

J Delay

™ • Classical * I TOF In (-

M P I - i< L , , „ . I _f\ iCIoch Out j »

MPLX

Select ' Select J r-

Hold Line

IOT Command

Words

Data Break Control

(Priority)

Data Overflow

Detector Output Detector Input Sense

Data

I i Hold Sample and

Memory Quadrant

Code

Multiplex 10 of 30

Memory Address Lines

Address

-•"To Core Memory

XBl. 748-6927 Fig. 18. Correlation Interface block diagram.

lOmHz X- la l

Pulse Shaping Network

IOmHz = O.I/i5ec SN7490|

+5 1/2 jtsec

1/2 /isec

SN7493|

+ 2 +4 +8

+ 16

•I «sec--2 /isec-

- 4 (1B6C-•8 p s e c -

SN 7490|

+ 10

5 jisec

SN7493| + 2 +4 + 8 + 16

l-IO/isec*-

SN74901

+ 10 IQOgsec |

ISN7490!

+ 2 200 usee

•20 ^sec-•40 (isec-

•80 / i sec -

Multiplex Select

— 8 0 -—too-j -200-

I of 16

Multlplexl

SN74I5I x2

Clock Out

XBL 748-6915 F ig . 19. Clackro te d i v i d i n g network,

clock p u l s e w i d t h . ) Crimen noted a re the

-103-

since i t is this clock signal which determines the absolute time scale

for the time domain measurement of the TOF dis t r ibut ion. The basic clock

rate is produced by an X-tron 10 mHz crystal osc i l la tor which is stable

to within 0.001% (10 ppm). This base rate i s divided by a digi tal

dividing network (Fig. 19) . The outputs from the dividing network are

connected to the input of a digi tal multiplexer (Texas Instruments

SN74151). Using the multiplexer, one of the available clock rates is

selected via four data select l ines, which are enabled by use of a

"command word" decoding network (see "Command Word Control and IOT's"

below) which allows programmed control of the desired clock ra te .

The clock ra te and period were measured using a calibrated Tektronix

Type 555 Dual Time Base/Dual Beam Oscilloscope and a pulse generator for

comparison. The ra te was also measured using a frequency counter; the

measured dock rate was equal to that expected) within experimental

error.

2. Pseudorandom Binary Noise Sequence Generator (PENG)

As was described in the theory of the correlation experiment, a

linear shift register with modulo-2 summing feedback i s used for generat-2

ing an m-sequence to be used in experimental modulation. The PENG used

in this case is constructed from two 10 b i t se r ia l in /para l le l out s t a t i c

shift registers (Signetics 8273) (Fig. 20) . To achieve maximal sequence

generation with a 20 b i t shif t register, feedback from stages 3 and 20 3

are employed. As previously noted, the modulo—2 feedback i s achieved

by use of an "exclusive" or gate whose truth table for the present

application i s shown in Fig. 20. The output of stage 1 of the 20 b i t

register is connected to both the input of the d ig i t a l delay line (see

HhT"^ , l n

3 Out

HhT"^ , l n 1 2 3 4 • • • 18 19 20 20 1} W y 1 2 3 4 • • • 18 19 20 1 2 4 • • • 18 19

Exclusive OR 20 Bit S/ln - P/Out Shift Register

\20 3 \ 1 0

1 0 1

0 1 0

Exclusive OR Truth Table

XBL 748-6909

Fiij. 20. PRNG configuration for maximal sequence generation: N - 20 stages.

-105-

helow) and to a coax ia l cable l i n g driver (5113) which dr ive s a coaxial

cable to the ian beam chopping c i r c u i t ( see below) .

Since the PENG s h i f t r e g i s t e r s are run by the Bin Time Clock, the

c lock frequency e s t a b l i s h e s the base frequency for the PRNG output,

thereby determining the band width of the experimental modulation.

Since the a l l - z e r o s t a t e of the s h i f t r e g i s t e r PENG excludes genera­

t i o n of the desired m-sequence, the input of the PRNG (Stage 1) i s ORed

with the " I n i t i a l i z e " bus s i g n a l which i s generated each t i n e the com­

puter i s turned on. A d d i t i o n a l l y , the clock in , of the PHKG i s a l so

ORed with the " I n i t i a l i z e 1 1 s i g n a l except that the a p p l i c a t i o n o f the pulse

t o the clock input i s delayed by a memos table mul t iv ibrator ("one s h o t " ) .

This c i rcu i t ry insures t h a t each t i n e the power for the i n t e r f a c e i s

turned on, a "1" w i l l be appl ied to the input of the PRHG and strobed

i n t o Stage 1 by the delayed i n i t i a l i z e pu l se ; the i n i t i a l s t a t e of the

PRHG i s always nonzero.

3 . C lass i ca l TOF Capabi l i ty

Although the normal operation of the data a c q u i s i t i o n system w i l l

be in a correlat ion node us ing PRKG output for bcaa s o d u l a t i o n , the

capabi l i ty for operation in a c l a s s i c a l TOF code has been b u i l t into the

i n t e r f a c e . This rode of operat ion allows ca l ibrat ion of the t i c e s c a l e

of the TOF spectrins and provides a Deans of corroborating the r e s u l t s of

corre la t ion TOF oeasur?*ents .

For c l a s s i c a l TOF opera t ion , an external pulse generator (Tektronix

PGS01) i s employed. The pulse width of the generator i s adjusted to g ive

a t o l e r a b l e detector output r a t e whi le maintaining the g r e a t e s t poss ib le

TOF resolut ion (pulse widths of *v2 *.!sec). The pulse r e p e t i t i o n race i s

-106-

adjusted unti l there i s no overlap of individual beam pulses at the

detector {typically 10 kHz). The pulse generator output i s connected

simultaneously to the beam chopping circuit and the input of the digi tal

delay line (via an optical coupler). The output of the PBNG is turned

off using command word I (see below) . Beam pulses then travel through the

ion path of the experimental apparatus as the corresponding digitized

generator pulses travel through the shift registers of the digi ta l delay

line and the sequence storage register (see "Data Break Board" descrip­

tion below) . The mode of data storage is identical to that used in the

correlation mode of operation; using the data address method, detection

of an ion at the end of the ion drif t region causes three data breaks to

record the length of the storage registers traversed by the digitized

generator pulse responsible for admitting the ion to the beam path. The

only operational change in data acquisition comes during the process of

transforming the data stored in the core memory. Since there are only

"positive correlations" between detector events and digitized generator

pulses, i t i s unnecessary to subtract the negatively correlated trans­

formed data (see "Program Description") . This positive correlation

property is the result of the non-overlaping nature of the ion (and

digital) pulse t ra in .

4. Digital Delay Line

Since the interface wi l l be used to examine the TOF spectrum of

a variety of ion reaction products and may be applied to several appara­

tuses with quite different ion flight paths, the mean time of flight

expected may vary from 10 psec to over 100 ysec depending on the ion

product mass and energy and the flight path of the apparatus. I t is

-107-

thus important to have some measure of control over which particular tine

segment of the possible TOF spectrum is to be viewed by the correlator.

For long flight times one could always reduce the Bin Time Clock rate

such that no delay between beam modulation and detector signal would be

required. However, th is would entail a large loss in spectrum resolution

and the measurement of narrow TOF distributions with long fl ight times

would be fruitless (Fig. 21) . By using a delay l ine to store the experi­

mental modulation sequence during a long flight time, short duration TOF

distributions with long f l ight times can be examined without a loss of

resolution.

To be of use, a delay l i ne must retain a faithful representation of

the output of the PEHG; otherwise spurious noise i s introduced into the

correlation calculation. For th is reason a shif t reg is te r delay line has

been applied in th i s case. The delay Use i s constructed in two parts

(Fig. 22). One, the "short delay" is composed of two dual 8 b i t se r ia l

in / se r i a l out s t a t i c sh i f t registers (Signetics 8277) hooked In a head

to t a l l configuration (Fig. 22). The output of each 8 b i t register i s

connected to a one of eight multiplexer ("Short Delay") whose output is

selected via three b i t s of the "Delay Command Word" (Command Word II -

see below).

The "long delay" i s constructed from a single hex-32 b i t s t a t i c

shif t register (Fairchild 3349), also hooked in a head to t a i l configura­

tion (Fig. 22). The outputs are connected to a second one of eight multi­

plexer ("Long Delay") whose output is selected by three separate bi ts of

the delay command word.

-108-

h(t)

0 80 100 usee

Possible "true" TOF spectrum

h(r)

3 . 23 30

T = bin No. Measured correlation function with no delay, clock period = 3 usee

h(r]

_=i~ 30

T = bin No. Measured correlation function with delay - 72 usee, clock rate = lusec

XBL748-6923

Fig. 21. Increased resolution possible using digital delay line.

-109-

TTi

o a! LJ [J =" ^

U\UI uror LJ •II

-110-

All of the delay l ine shif t registers are clocked by the output, of

the Bin Time Clock. Thus the real time delay through any series of

registers i s a direct function of the dock ra t e ; only the number of

clock pulses needed to shif t a pulse sequence through this series of

registers i s constant. To calculate the real time delay, one must

multiply the delay length by the clock period. The tota l delay i s the

sum of the long and short delays. Any delay of from zero bins (clock

pulses) to 224 bins, in steps of 8 bins, i s possible by selection of the

appropriate delay command word co<ie.

The combined use of variable clock period and delay length allows

great f lexibi l i ty in viewing the TOF correlation function. Normally, a

quick law resolution scan using a compar±t±vely large clock period and

no delay serves to determine the mean time of f l ight and i t s approximate

width. Then, by using an appropriate delay and shorter clock period, the

TOF correlation function can be expanded to f i l l the 30 channels of the

correlator in a high resolution scan (assuming a sufficiently long

flight path to establish a 30 usee wide realtime distribution) . In some

cases i t may be desirable to examine only a portion of the TOF distr ibu­

tion using very high resolution. Practically, however, this would only

be applicable to high mass ion products if a reasonable length (100-200

cm) drif t path were being employed.

The delay line precision was examined as a function of delay time

and clock rate by direct cross correlation of the PENG output (delay

input) with the delay output using a Hewlett-Packard 3721A Correlator.

Since the period of the autocorrelation function of the PENG output for

20 stage feedback i s longer than any of the possible delay period, the

- I l l -

peak of the measured cross c o r r e l a t i o n function represented a d i r e c t

measure of the delay time. The measured delay was c o n s i s t e n t l y within

22 of that expected, and t y p i c a l l y was within 0.5%. A p i c t u r e of a

t y p i c a l delay cross corre la t ion measurement i s shown i n F i g . 2 3 .

5 . Command Word Control and 10T*s

The operation of the computer in ter face for data a c q u i s i t i o n

requires that the user maintain e x p l i c i t control over the hardware

generated options of the i n t e r f a c e . This control a b i l i t y i s provided by

a software mediated, hardware implemented decoding network by which the

u s e r chooses from a v a r i e t y o f modes of hardware operat ion .

As has been previously mentioned ( s ee "Computer Organizat ion") ,

computer peripherals , inc lud ing the corre lat ion i n t e r f a c e , are contro l led

from the central process ing u n i t of the computer by use of input/output

t rans fer cmmands (IOT). Each per ipheral device i s ass igned one or more

s i x b i t binary i d e n t i f i c a t i o n codes which i t alone r e c o g n i z e s . In o c t a l

n o t a t i o n , IOT commands are of the format 6XXn, where the 6 denotes that

t h i s i s an IOT command, XX i s the s i x b i t device code, and n represents

the par t i cu lar Cone of 8) command t o the peripheral d e v i c e . S ince the

recogni t ion of each device code requires an independent decoding network,

i t I s advantageous to r e s t r i c t each peripheral device to one or two

device codes. However, s i n c e there are at most 8 independent commands

(3 b i t code; 2 3 • 8) which can be executed with a s i n g l e dev ice code, in

us ing I O T ' S alone a hardware des igner i s faced with a t rade -o f f between

the needed programmable hardware f l e x i b i l i t y and the s i z e of the decoding

network needed to Implement i t .

R X ,W

XBB 748-5796

F ig . 23. C r o s s c o r r e l a t i o n measurement for expe r imen ta l m-sequence (de layed a u t o c o r r e l a t i o n ) .

-113-

This tradeoff can be avoided by the use of a "command word" s t ruc-

ture . In this method the information contained in many (up to 12 with

the present computer) b i t s can be transterred for hardware execution by

the use of a single IOT. The informational b i t s originate in the accumu­

lator of the computer, having been loaded previously into the accumulator

by a program control sequence. On IOT command, the informational bi ts

which are present on the 12 data lines (on the OMSIBUS) leading from the

accumulator are strobed into a series of one bi t larches (D f l ip flop)

which are contained within the peripheral device. The latches record the

information contained in the computer code and execute the coded commands

by enabling gates controlling the hardware options or by selecting the

inputs of multiplexers. Using a command word structure as many as 96

b i t s of information for hardware control can be transferred using a

single IOT decoding network.

In the present interface, one IOT decoding system (code = 33) is

used. A summary of the IOT commands i s shown in Table I ; 3 IQT's are

used for the control of 3 command words (Cammaad Word I . Delay, Clock),

2 IOT's are used for control of the data overflow fac i l i ty , and two

othere are applied to hardware test ing procedures. Coosand Word I is a

general purpose control word which exclusively executes hardware options

by enabling AHD gates on the interface boards (Table I I ) ; these gates

are primarily used for turning on or off several logical units of the

interface hardware such as the Bin Time Clock., the Data Break fac i l i ty ,

the detector input, or the hardware test f ac i l i t i e s .

Conmand Word II (Delay) i s used to control the length of the digi ta l

delay line (Table I I I ) , while Connand Word I I I (Table IV) allows selection

-114-

TABLE I

INTERFACE BOARDS IOT INSTRUCTION SET

DEVICE CODE = 33

Co le Interface Action

6330 Not used

6331 Load command word 1 from AC

6332 Load delay (command word I I )

6333 (Software sequence e n t r y )

6334 Skip on overflow

6335 I m i t a t e d e t e c t o r p u l s e i n p u t

6336 Load b in time clock (command word I I I )

6337 Reset overflow

COHMAHD WORD I ; LOAD WITH 6 3 3 1

D a t a B i t 0 1 2 3 4 5 6 7 8 9 10 U

Gate

Data Break On

Off

1

0

Clock On

Off

1

0

Overflow On

Off

I

0

EHA Field On

Off

1 0

Classical TOF

Correlation

1 0

Detector On

Off

1 0

not used

Normal operation code: Correlation = 7500

Classical = 7700

-116-

Data Bit 0 1 2

Long Delay

0 bits 0 0 0

32 bits 0 0 1

64 bits 0 1 0

96 bits 0 1 1

128 bits 1 0 0

160 bits 1 0 1

192 bits 1 1 0

Short Delay

U bits

8 bite

16 bits

24 bits

32 bits

All zero out

All ones out

COMMAND WBD II DELAY; LOAD WITH 6332

3 4 5 6-11 not used

Code

0000

1000

2000

3000

4000

5000

6000

0 0 0 0000

0 0 I 0100

0 1 0 0200

0 1 1 0300

1 0 0 0400

1 1 0 0600

1 1 1 0700

Long delay + shore delay « long code + short code = total code =3 total delay (i.e. 64 bits + 8 bits « 2000 + 100 = Z1G0 =; 72 bits) -

- 1 1 7 -

TABIE IV

COMMAHD HQBD I I I BIH TIME QDCX; UOAD HITH 6336

(0 Data Bic

-7 not used) 8 9 10 11

Frequenej Code (101)

Bin time (usee)

2000 a Iz 0 0 0 0 0 .5

1000 1

1 0 0 0 1 1

500 2 0 0 1 0 2

250 3 0 0 1 1 4

200 4 0 1 0 0 5

125 5 0 1 0 1 8

100 6 0 1 1 0 10

50 7 0 ^ 1 1 20

25 10 1 0 0 0 40

12.5 11 1 0 0 1 60

10 12 1 0 1 0 100

5 Q 32 13 1 0 1 1 200

- U B -

of the rate for the Bin Tlae Clock. Both of these command words arc

executed by mult ip lexer s e l e c t i o n from mult ip le inputs to give a s i n g l e

desired output.

6 . Detector Input

Since a l l of the in ter face hardware employs TTL, a l l s i gna l s

cooing in to the i n t e r f a c e oust be d i g i t i z e d to the proper voltage l eve l s

before they can be u t i l i z e d . The ion detectors current ly used in our

laboratory for TOP arc of the e l ec tron c u l t i p l i c r type (Channcltron or

Bendix Magnetic Mul t ip l i er ) which, when coupled with an output pre­

ampl i f ier , produce negat ive output pulses approximately one v o l t in

amplitude and SOO nanoseconds in duration. To conform with the TTt l og i c

of the i n t e r f a c e , a comparltor c i r c u i t with a v a r i a b l e discriminator

lower l e v e l and v a r i a b l e width output pulse i s used t o convert the

(0 , - 1 v o l t ) , de t ec tor output s i gna l i n t o a TTL compatible ( 0 , +4 v o l t s )

wave fore ( see below for complete coaparitor d e s c r i p c i o n ) . The coaparitor

output i s connected ay a SOU BHC coble to the input of an o p t i c a l l y

coupled TTL gate (Motorola HOC 1000 or 4825) . The o p t i c a l coupler

e l iminates the p o s s i b i l i t y of external no i se pu l se s overloadin:, the

interface TTL l o g i c causing damage to the hardware.

The output of the o p t i c a l coupler i s used to I n i t i a t e the data break

cycle of the in ter face for s tor ing corre la t ion data in the cocputer's

core memory. (A s i m i l a r o p t i c a l coupling scheme i s employed for inputt ing

pulses from the ex terna l pulse generator when the i n t e r f a c e i s operated

in a c l a s s i c a l TOP mode.)

*Transitor-Transitor Logic Defines l o g i c a l "0" as a vo l tage l e s s than -HJ.8V. and l o g i c a l "l" as a voltage greater than +2.8V.

- lW-

11. Data Break Board

1. 'nic Data Break Hardware

Within the correlation interface, the data break facil ity ful­

f i l l * the Itftportont function of transferring correlation data frco the

Interface to the core aeaory of the computer, where It Is stored for

later analysis, the data break sequence is triggered Into action by the

arrival of pulses fros the 1cm detector; once this triggering has been

effected, a rapid series of hardware events takes place In an orderly

ttaaaer with each event being synchronized by the internal ctwsutcr bus

ciBing signals. As previously noted, during a data break data transfer

the functions of the central processor registers are taken over by the

external logic hardware of the interface while the C?U registers arc dis­

abled. Since the description of the data break event sequence la intl*

aetely involved with the computer*a hardvart structure, we suggest that

at this point the reader should review the "Coeputer Organization" sec­

tion presented earlier.

A acheaatic diagraa of the basic data break hardware i s shown In

Fig. 24. With reference to this figure, we now describe the sequence of

events which cosprlsc a data break transfer.

The data break is initiated when a Break Request latch is triggered

by an Incoalng detector pulse. At on appropriate s asp ling cine, the Hew

Break flip flop is clocked by the Internal Strobe pulse frcn the (kznlbus,

requesting a device priority check, disabling the central processor

Keoory Address register and signaling the CPU that a data break is in

progress,

-120-

r 'm^ ! Urr'i'i i ! !

1 i-CXt

\ , < L

I i-<7

i'^tf '-<•

• O r

;-i

(M Mi

6

Hi

IB

*

iiitirti f7fti<3X ifgt

Kra. T

ni!

' &

T 4L •! a

-m-

The device priority system provides a means for causing the computer

to service peripheral devices requesting a data break according to which

device has been assigned the higher priority. Such a system' is necessi­

tated by the fact that often two or more devices may simultaneously

(within a single computer memory cycle of 1.2 psec) request a data break.

In such a ease, one wishes to allow data transfer from the fastest (heace

highest priority) peripheral f irs t (such as a disc). The priority network

of the correlation interface checks, by use of the data lines of the

Omnibus, whether any higher priority device Is also requesting a data

break* If so, the interface must await completion of the data transfer

from the other device before i t s own data break proceeds. As a practical

matter, there are currently no other data breaking devices presently

incorporated in the computer system and the interface wi l l be permitted

to continue i t s requested data break immediately. However, later addition

of a disc or tape f i l e to the system would require the priority system to

be installed in a l l data break devices, so i t has been included in the

present design as a matter of course. The correlation interface has been

assigned a priority of 3 (out of a possible 12; top priority i s 1).

Once the device priority has been established, the CPU Instruction

Register and the Major State Register (which controls read and write

operations) are disabled and the CPU Memory address (CPHA) loading from

the Program Counter i s inhibited. The direction of data transfer (into

the core memory in this case) i s established and the contents of the

Break Memory Address Register of the interface (denoting the core address

to be accessed during the data break - see below) are gated onto the

Memory Address line of the Omnibus (which are also connected to the CPU) .

- 1 2 2 -

Ac th i s point the contents of the object address (on the Keaory Address

l ines ) arc gated onto chc Heaory Data l i n e s , pass through the CPU p a r a l l e l

adders where the contents are incremented by one (" add-to-iaemory"), and

the resu l t returned v i a the Keaary Data and Hcoory Buffer l i n e s to the

object memory address . The net resu l t i s that the contents of the

address contained l a the Break Hfeaory Address Reg i s t er have been incre ­

mented by one. This completes the task of the o r i g i n a l l y requested data

break. However, in the case of the corre la t ion i n t e r f a c e , we reca l l that

s ince three separate addresses must be incremented to s t o r e the informa­

t ion contained in the 30 b i t s of the Modulation sequence , two further

data breaks w i l l be immediately requested and carr ied out .

In r e a l i t y , there are many addit ional gat ing and d i r e c t i o n a l s i g n a l s

which must be generated for the success fu l completion of the data break.

However, they are not conceptually important i n understanding the method

and w i l l not be d i s c u s s e d . The reader i s again referred to the d i s c u s ­

s ion in the POPS Small Computer Handbook

2 . Generation and Storage of the Break Memory Address

In the descr ip t ion of the corre lat ion method ("Application of

the Correlation Method")* we noted that the c o r r e l a t i o n function i s

accumulated by incrementing three core memory addresses contained in the

delayed PENG output sequence present at the time a detec tor output pulse

arrives at the i n t e r f a c e . The conversion of the PRNG output sequence

in to usable memory addresses i s accomplished in the fo l lowing manner ( see

Fig . 2 5 ) .

The modulation sequence emerges from the d i g i t a l delay l i n e on the

Bin Time Clock Board and i s transferred v i a one l i n e of a 16 l i n e board

Bin Tims Clock Output

' ' " " D J ' T " " a g » "lOS-R. {—» 8Z73 IKIOS.R. ^ | — » | 8273 I» 10 S.R.'' | Holding Lit

Detoctor

J Computer Bus

KBL 7««-69Z8

Fl8 . 25. Generating data break memory addresses .

-124-

interconnect cable Co Che Data Break Board. The sequence i s input to a

shift register storage l ine conprised of three 10 b i t s e r i a l in/parallel

out registers (Signetics 8273) hooked in series and clocked by the Bin

Clock output (also transferred by the board interconnect cable}. The

paral lel output of the storage line is connected to the input of five

he^-latches (Texas Instruments SN74174). Using a monostable multivibrator

(TI SN74123}, each clock pulse i s delayed and then used to strobe the

contents of the storage l ine into the latches after the storage line con­

tents have been shifted (sample and hold). (This strobe pulse is in­

hibited by the arr ival of a detector pulse unt i l the currently stored

sequence in the latches has been used as the Break Memory Address for the

three resulting data breaks.) The storage l ine i s necessary to main tain

the continuity of the PENG output sequence while data breaks are being

completed.

With each detector output pulse, the three data breaks necessary to

record the 30 b i t s of correlation information use a 10 b i t segment of the

modulation sequence which has been stored in the sample and hold latches.

During each break, 10 b i t s of the sequence are concatenated by a data

multiplexing system with a 2 b i t "quadrant code" which supplies the two

most significant b i t s of the Break Memory Address and hence determines

which 1 K portion of the upper 4 K field of memory the least significant

10 bi ts pertain to (Fig. 26) . The quadrant code also provides the data

multiplexer data selection code necessary to choose which ten address

bi ts (of 30) will be gated onto the Memory Address l ines during each data

break. The Memory Quadrant Generator i s a 2 b i t binary counter (TI SN

7490) which is reset to the f i r s t quadrant (01) by the incoming detector

M M I I M M - » 0 0 0 0 0 0 0 0 0 0 - » I O I O I O I O I O I Storage Line

^ ^ ^ 11 i i i i I | I i 11 o6Tb~o~oooo|ooi o i o| i o i o i o| S D m p

L* ,°Jg S

H o l d

Multiple^,

Concatenate Quadrant Code

Ol . l 0,1 I

Resulting 3 BreaK Memory Addresses 01 I I I I I I I I I 1 , 1 0 0 0 0 0 0 0 0 0 0 0, I I I 0 I 0 I 0 I 0 I 0

t t t Quadrant Stored in Stored in Stored in

in Upper 4K= I000 f l - I777 8 2000 8-2777g 3000 8 -3777 8

XBL748-6912

Fig. 26. A sample of break memory address formation.

-126-

pulse and incremented (to 10 and 11} before each of the two subsequent

data breaks. Thus if the 30 b i t modulation code can be represented by

three 10 b i t numbers, Ni, Nz, Ng, the addresses which wi l l have their

contents Incremented by one during the three data breaks wi l l be OlNi,

10NZ, and IIN3.

We have now completed the connection between the delayed modulation

sequence and the storage of correlation information by the data address

method.

3. Data Overflow

As data i s accumulated through repeated data breaks, eventually

the 12 bi t capacity of the core memory addresses wi l l be exceeded causing

data overflew. The effect of an overflow i s to change the contents of a

memory data address from 7777 e to 0000B since 7777 s + 0001s = 10000e =

0000. This i s a total ly undesirable effect since overflow wi l l be corre­

lated with addresses whose address b i t s are representative of sequence

segments which are highly correlated with measured detector pulses.

Preferential overflow and subsequent zeroing of some addresses will cause

distortion of the shape of the transformed TOF correlation distribution

favoring buildup of signal in those channels with smaller net signal

heights.

To avoid this overflow condition, the data break logic i s equipped

with an overflow sense l ine connected to an overflow f l ip flop. During a

data break, when the contents of a data storage address have been incre­

mented, the incremented contents are gated back to the Break Memory

Address en the Memory Data l ines ; i t is at this point that a data over­

flow i s sensed. When the two most significant bi ts of the Memory Data

-127-

l ines are both in a " l " s t a t e (6000a detector counts in the Break Memory

Address) during a data break., the overflow latch is sec raising a flag

which, by interrupt programming routine, causes the computer to cease

data acquisition and i n i t i a t e che data transformation routines. Since

the contents of the core memory data storage addresses never exceed 6000a

(maximum capacity is 7777a), there i s never any real data overflow which

can occur.

This concludes the description of che Daca Break Board Hardware.

I I I . Hardware Test Fac i l i t i es and Checkout Procedures

To faci l i ta te testing of the interface, several software controlled

test ing faci l i t ies were bu i l t into Che interface. We wi l l describe these

and the testing procedures br ie f ly .

Two o_ the available eight device I0T*s have been dedicated to t e s t ­

ing procedures. The f i rs t* IOT3, enables the user Co design a software

program for entering a given binary tes t sequence into the d ig i ta l delay

l ine and subsequently into the Break Memory Address, mimicing the function

of the random sequence generator in a known, predetermined manner. This

IOT loads the least significant b i t of the accumulator (Data 11) into the

delay line by gating Daca 11 onto the delay line input and then clocking

the delay line shift registers to enter the data b i t using the I0T3 pulse

delayed by a memos table multivibrator. One need only load the accumu­

lator b i t 11 and then apply IOT3 to load each b i t of the desired testing

sequence into the delay l ine reg is te rs . By this method a known sequence

can be generated by software for use as a Break Menjory Address. To employ

this procedure, both the Bin Time Clock and the PBHG output must be de­

feated using Command Ward I (Table I I ) .

-128-

Once a test sequence has been entered, the second test IOT, IOT5,

which simulates an incoming detector pulse, is used to cause one or more

data breaks to the known core memory address contained in the software

tes t sequence. Subsequent examination of the contents of th is address

reveals whether the data break system is functioning correctly.

I t should be noted that the connection between Data 11 of the

accumulator and the delay line input was removed after i n i t i a l testing

and the input employed for c lass ical TOF pulse sequence entry. (To re­

establish this faci l i ty , the connections E10-7 •* E26-9 and E31-3 -*• E26-10

must be made on the Clock Board.)

Some further test procedures which have been used are as follows:

1. Clear the memory data storage block, defeat the Bin Time Clock

and use an external f i l se generator for repeated data breaks to the three

frozen Break Memory Addresses by simulating detector input. (The three

addresses can be seen on the programmer's console by single stepping the

computer operation). This process allowed estimation of the maximum

detector input rate which can be tolerated by the data break system

(about 100 kHz) and was used to check the overflow fac i l i ty . I0T5 can

also be used in place of the pulse generator for the l a t t e r t e s t .

2. Rather than using the frozen Break Memory Address in the rests

described above, by selecting the proper short delay code (Table I I I ) ,

a l l ones or a l l zeroes can be loaded into the Break Memory Address for

test ing as above.

3. To check both the function of the data break and the accuracy of

the data transformation, the PRNG is allowed to supply random Break

Memory Addresses while the unrelated asynchronous output of an external

-129-

pulse generator i s used to simulate detector output. (I0T5 can also be

used.) Since the "detector output" i s uncorrelated with the "modulation

signal" of the PRNG output, the net transformed correlation function

should be zero everywhere (except for small s t a t i s t i c a l fluctuations), as

was found to be the case.

4. The Classical TOF distribution provides an additional check, on

the operation of the data break system.

All of the above procedures were found helpful for electronic de­

bugging of the correlation interface. While constant interface testing

should be unnecessary, periodic checks of the interface functions are

certainly in order.

IV. Board Interconnect Cable

Since signals are generated on each of the two main interface boards

which are required for use on the companion board, a 16 l ine interconnect

cable i s used to transfer signals between the two boards. A l i s t of

these signals is shown in Table V.

The potential user i s cautioned that both of the two main boards

must be emplaced in the computer bus and the interconnect cable must be

connected between the two i f either is to be put into the bus. Failure

to follow this rule w i l l cause destruction of core memory software and

generally will make the computer nonfunctional. I t i s also quite impor­

tant to ensure the proper connection of the interconnect cable on both

ends, or damage to the interface may result .

V. D/A Converter Board

The Digital to Analog Converter Board i s used to display accumulated

transformed data. Two 12 b i t DAC'B (11 signal b i t s + sign b i t ; Hybrid

INTERCONNECT CABLE (CLOCK BOARD *» DATA BREAK BOARD)

ElO <-* C7

Pin Line

1 Clock output 9 NC

2 Delayed PENG sequence 10 NC

3 NC 11 IOT 6 [10-7]

4 NC 12 Hy device [14-3]

5 IOT 1 [10-2] 13 EHA f i e l d [E19-10]

6 IOT 2 [10-3] 14 Break on/off [E14-2] [E19-7]

7 IOT 3 [10 -4 ] 15 Overflow on/off

8 NC 16 Detector on/off [E26-3]

-131-

Syscems DAC372-11 with 0.0252 l ineari ty, 2 volt/usec slew rate, and 5 usee

maximum settling time) were chosen which were sufficiently fast and

reasonably inexpensive. One DAC i s used for converting the X-axis of the

display (TOF distribution Bin number) and the other for converting the

Y-axis (relative correlation function height). The conversion of each

axis i s accomplished by clearing the accumulator of the CPU and giving

an appropriate IOT causing the proper DAC to be loaded from the data

l i nes . The board has i t s own device codes (05, 06; see Table VI) and

IOT decoding networks. The display of data i s controlled by a software

subroutine of the main program monitor (see "Computer Program1* below)

which automatically scales the X-axis to allow 30 TOF channels to span

the entire voltage range of the X-axis DAC. The result ing analog X-T

plot of the data i s displayed on a Tektronix 545B oscilloscope.

VI. Voltage Comparator

As noted above, a voltage comparator circuit i s employed to convert

the preamplified electron multiplier detector signal into a TTL-Campatible

Have form. This c i rcui t (see Fig. 27) employs a voltage comparitor

(National Semiconductor LH306) to determine when the output voltage of

the ion detector circuit becomes more negative than a variable reference

threshold voltage which i s controlled by a potentiometer. The comparator

c i rcui t has the abil i ty to use either positive or negative going pulses

as i t s input.

When the comparator i s turned on by the magnitude of the detector

output voltage surpassing that of the reference threshold, a variable

*0riginally designed by the D.C. Berkeley Dept. of Chemistry Electronics Shop.

D/A CQHVEBIER BOARD IOT INSTRUCTION SET

DEVICE CODES = 05, 06

Code Action

6051 Clear X

6053 Clear X and load X

6054 Intensify X

6057 Clear X, load X and intensify

6061 Clear Y

6063 Clear Y and load Y

6064 Intensify Y

6067 Clear Y, load Y and intensify

HD 11 -+ load registers

HD 10 -*- enable data lines

HD 9 -*- intensify sequence

| Comporotor

*&: - A W 1 • • S

• Q - P OUTPUT

All Bmtlori l/4'W All Poll IT , 2W

1H —6\p-o-'o— LGJ—i 1/2 A On

XBL74B-69BI Fig . 27. Voltage comparator c i r c u i t for reversing detector output p o l a r i t y .

-134-

width output pulae i s generated by a monostable multivibrator (Tl SN74121) .

The width of the output pulse i s controlled by a potentiometer which

varies the RC time constant of the multivibrator. Finally, the output

pulse is driven from the comparator circuit to the computer interface on

a BUG cable by a Dual Differential Line Driver (Rational Semiconductor

DM 8830).

VII. Ian Beam Chopping

In ion beam TOF experiments, a central problem i s the construction

of an adequate beam chopping mechanism. In this section we wi l l define

the chopping problem and describe the simple electronic circuitry which

ve have applied to the correlation TOF system for beam modulation.

There are two types of problems associated with ion beam chopping:

the effects of modulation bandwidth on signal resolution and the e lec­

tronic problem of implementing wide bandwidth modulation of an ion beam

using large amplitude voltages. The f i r s t problem i s more subtle and

arises from the intimate connection between modulation and detection.

The second problem i s an obvious one whose basis is technological. To­

gether they require careful design of a beam chopping system to ensure

successful measurement.

In part, the difficulty in chopping an ion beam ar ises from the

large ion velocities which are typically found in ion beam experiments.

While neutral molecular beam projectiles typically have thermal velocities

of " lO1* cm/sec, slow enough to permit mechanical chopping, the pro­

jec t i l es in an ion beam have velocities of the order of 10 cm/sec. This

higher velocity makes mechanical chopping of ion beams impossible. How­

ever, since ions are charged par t ic les , e lectrostat ic deflection methods

-135-

are readily applicable to an ion beam system.

in an electrostat ic chopping system, one or more metal deflecting

plates (grids) are positioned paral le l to the path of the ion beam in

close proximity to i t . An electronically generated chopping signal is

used to apply voltages to the gr ids . Depending on the voltage applied

to the grids, the beam i s e i ther allowed to pass into the TOF apparatus

undeflected (beam "on") or deflected away from the apparatus so that no

ions reach the detector. Thus the problems associated with, actual beam

chopping are basically e lectronic .

Even with the fast electronic components available currently, the

problems associated with chopping an ion beam are nontr iv ia l . As has been

previously noted, a TOF experiment has i t s resolution limited by the

width and precision with which pulses of ions are admitted to the appa­

ra tus . With electrostat ic chopping, the maximum chopping ra te i s deter­

mined by several experimental variables: the ion mass, the deflection

required to remove ions from the beam path, the ion velocity, the r ise

time of the deflecting pulses and the width of the chopping region. All

of these variables bear on the problem of adequate deflection while ion

velocity and the width of the chopping region are responsible for signal

resolution.

The signal resolution question can be summarized in the following

way: for any TOF experiment there are two natural time periods whose

diaenslonless rat io serves to scale the experiment. These are the over­

a l l time of flight and the width of the TOF distr ibution, denoted by xTOF a n d T,respectively. Of course, each of these i s a function of the

length of the flight path; however, for any given experiment the ra t io ,

-136-

a = T

w / T Topt " i l l be invariant . Typically this ra t io i s less than Q.1D,

i . e . Che width of the distr ibution i s less than 102 of the tota l flight

time. This fact by i t s e l f presents no problem. However* as we wil l

discuss below, there exis ts a fundamental limitation on the modulation

bandwidth which can be applied with a beam chopper. Since the modulation

bandwidth fixes the time resolution with which the TOP signal i s viewed,

to achieve a given resolution a severe limitation i s placed on the mini­

mum flight path that must be used for experiments.

More explicitly, consider that one wishes to view a TOF distribution

with a resolution E. R I s determined by the number of discrete time

channels which span the TOF distribution as i t i s measured at the detector.

If the bandwidth of the source modulation i s such that each channel i s of

width T J , then

Recalling that x y = a r T 0 F .

n = " * » , ^ R X o l ° r T ro F = —

where again, a is the dimension less time scale which fixes the relative

width of the TOF distribution in terms of the total time of flight.

A typical limit an the modulation band width is 1 megahertz so that

the minimum T , = 1 usee. To see how this poses a restriction on the mo J

time of flight (path length), l e t ' s suppose that we desire a resolution

of 20 ( i . e . 20 points of the calculated correlation function will define

the shape of the TOF distr ibution) and that a has the value 0.05, not an

unrealist ic value. Then

-137-

. (20) (1 Usee? M A 0 ( J v n c t

i U i r 0 .05

For a typ ica l ion of mass 30 a t an energy of 5eV, the v e l o c i t y i s approxi­

mately 5 x 10 5 cm/sec.

Therefore, to achieve a re so lu t ion of 20 for such an i on i n a T0F

experiment a 200 cm f l i g h t path would be required. This i s a somewhat

l arge f igure; i t becomes apparent how important the l i m i t a t i o n on modu-

l a t i n bandwidth i s .

This l imi ta t ion on bandwidth a r i s e s i n the fa l l owing manner: the

time width of an ion beam p u l s e cannot be made shor ter than the time i t

takes for an ion of nrfTHimtm v e l o c i t y ( for whatever experiment ±& at band)

t o traverse the chopping reg ion . As ions pass through the chopping

reg ion, only those d e f l e c t e d l e s s than a m n-fumm amount (d i scussed below)

w i l l pass unhindered i n t o t h e TOF analys i s system. I f the pu l se r e p e t i ­

t i o n rate for modulation were l arge enough so tha t s e v e r a l d e f l e c t i n g

pul ses were applied to the d e f l e c t i n g grids during the time each ion

traversed the grid reg ion, every ion would be p a r t i a l l y d e f l e c t e d as i t

passed through. (Here ve are assuming the use of c o r r e l a t i o n modulation

which cons i s t s of a rapid t r a i n of modulating p u l s e s . For c l a s s i c a l

modulation the analogous statement concerning ion transmiss ion i s that

the de f l e c t i on vol tage i s never turned off long enough t o a l low ions to

pass through the chopper.)

For correlat ion modulation, only nh t>^ ions which e n t e r the d e f l e c ­

t i o n region at a time when a s e r i e s of consecutive "bean on" pulses were

applied to the chopper (a run of " l ' s " in the chopping sequence) would be

- 1 3 8 -

al lowed t o pass Chrough unhindered. Depending on Che ac tua l modulation

bandwidth, a l l s ing l e "beam on" pu l se s which were contained i n runs of

one or two (or more) would be i n e f f e c t i v e for causing i o n s to enter the

TOF ana lys i s system; the ne t r e s u l t i s that no matter how large a modu­

l a t i o n bandwidth was applied to the beam chopper, the e f f e c t i v e modula­

t i o n bandwidth would be H a l t e d by the ion passage time Chrough the

chopper. (The problem of Ions pass ing Chrough Che beam chopper i s some­

what reminiscent to the fo l lowing phys ics problem: An e lectromagnet ic

wave of a s i n g l e frequency (photon; i s propagating chrough s p a c e . Being

af a s i n g l e frequency, of course i t s pos i t ion i s completely indeterminate.

I f Che wave passes chrough an open door and you proceed t o c l o s e the door,

which s ide i s the photon on?)

A separate problem which must be overcome i n ion beam chopping i s

tha t of achieving f a s t r i se t ime chopping pulses s u f f i c i e n t to provide a

good approximation to a square wave modulation s i gna l us ing short (0 .5 cm)

chopping g r i d s . A schematic diagram def ining the system i s shown In

F i g . 28 . A pair of d e f l e c t i n g gr ids separated by a width d and of length

£ are placed in a region of t o t a l length L. A d e f l e c t i n g vo l tage of

magnitude ±V/2 i s applied to the grids to turn Che beam o f f . He assume

here that the ion beam i s of n e g l i g i b l e width, that a l l beam ions are

moving p a r a l l e l to the beam a x i s , and Chat a p o t e n t i a l of V = 0 i s

appl ied co the grids when the beam i s turned "on." The e x i t of the

chopping region i s defined by an aperture of diameter b; a co l l imated ion

beam enters Che chopping region from Che l e f t and i n the absence of de ­

f l e c t i n g vo l tages , passes chrough the e x i t aperture and i n t o the TOF

a n a l y s i s region. When che d e f l e c t i n g vo l tage i s appl ied , a uniform

V) E

fe lys 0>

1 - o k to

(O I

09 T

i ^ (HJ o

01 o

-140-

transverse electr ic f ield of strength V/d is present between the deflect­

ing pla tes . For simplicity, we wi l l assume that the most efficient space

u t i l iza t ion (A = L) i s being employed.

The object of our investigation i s now to determine the voltage

necessary to be applied to the grids to cause sufficient ion deflection.

An ion of mass m, longitudinal velocity u and charge e entering the

chopping region will traverse that region in a time r = £/u. Using

Newtonfs laws, the to ta l deflection caused by the ion when the grids are

charged wi l l be

Ax = 1/2 aj^t2 = 1/2 e V/d (Z/u)Z

For successful deflection Ax > b/2 so the required voltage i s

V ^ ^ <u/JL)2

e 2

Mote the 2- term in the denominator. Since we wish to make the chopping

region as short as possible* i t i s easy to see how the voltage required

for deflection can increase rapidly as 2. i s diminished.

The above discussion has assumed that the deflecting voltage has

been applied before the ion enters the chopping region. For a more

general analysis we assume the modulating pulse has the r is ing shape

shown in Fig. 29. The to ta l grid voltage, V, is a l inear function of

time until i t reaches i t s "steady state" value, V :

V = ktV 0<t:£,t ; kt = 1 (linear approx.) o o o

o o ^ 1

where t . is the time the ion e i ther exits from the region or i s deflected

XBL 748-6911

Fig. 29. Voltage character of the deflection pulse.

-142-

onto the plate of the collimator. If the deflecting pulse is initiated

at t = o when the ion has already traversed a distance e into the de­

flecting region there are two possible cases to consider:

{ 1 , i t s ! < t 0 : ta . !/« . Jk*,)3

u o V u /

(2) i»=a . > M : A. - 1/4 a t 2 + 1/2 a ( & ! > - t ) * u o o o \ u o /

eV where a = —j- and the results come from simply integrating F = ma. A

similar se t of equations wi l l hold for the case of an ion being present

in the chopping region when the deflecting pulse is turned off. These

expressions allow the calculation of the maximum distance, E., which the

ion can traverse before the deflecting pulse is applied and s t i l l be

deflected out of the beam path suff icient ly. In practice there wi l l

always be some ions in the chopping region which wil l not be deflected

suff icient ly. These ions wil l be negligible in number (compared to the

tota l flux in a beam pulse) provided that the deflecting voltage i s suf­

ficiently large and if the risetime of the chopping pulse is small

enough.

I t has been recently pointed out that such sampling of a continuous

ion source may lead to distortions in the TOF spectrum. We have noted

some broadening of the TOF spectrum when a single deflection grid i s used.

In this case the potential along the ion path becomes nonzero when the

deflecting voltage is applied, allowing both fringing field effects and

risetime and falltime accelerating effects to affect the TOF spectrum.

The use of a symmetrical grid system removes the possibility of such

-143-

effects.

For our current TOF system, we have determined that for a 1 mega­

hertz chapping ra te , a deflection voltage of ±30V wil l be sufficient to

deflect ions with a 0.5 cm grid length. The application of a 30 volt

signal at 1 megahertz leads to restr ict ions on the RC time constant for

the system. Vfe have achieved a 100 nanosecond risetime using the chopping

circuit described below by mounting the chopper as close to the chopping

grids (M. foot) as possible in order to cut down stray capacitance.

We note that there are two methods by which chopping might be im­

proved. One i s to reduce the space between the chopping grids as ve i l

as the diameter of the ex i t aperture. This, however, w i l l be limited by

the increasing capacitance of the paral lel grids as they are moved

closer, and by the loss of ion flux due to the smaller aperture size.

The other means by which chopping might be improved would involve de­

celeration of the ions after they have passed through the target in ter­

action region of the TOF analysis system. This has the effect of in­

creasing the effective f l ight time and hence the re la t ive resolution

which can be achieved with a given beam chopping modulation bandwidth.

The Present Beam Chopping System

The beam chopping system which we are currently using i s shown in

Fig. 30. The circuit i s essentially composed of two transistors which

control the grid voltages. When the transistors are turned off (beam

off) the grids float a t ±30 vol ts . When the t ransis tors are turned on,

current passes through the emitters, causing a voltage drop across the

voltage adjustment potentiometers. Thus by adjusting the potentiometers,

the grid voltages are selected to pass a "layftti"™ amount of the ion beam

. + 30V

+5V J * .

PRNG Sequence

OM 6830 Line Driver/

Receiver

Ik i i 2W

SN7545IP -+V/2 --V/2

SN7440

I H V) wv

30V

F i g . 30. Beam chopping c i r c u i t : .

XBL748-69I9

-145-

through the deflection region when the beam i s turned on.

The input of the chopping system can be chosen from two modes. In

the "adjust" mode, the input to the DM8830 l ine receiver i s held high so

that the transistors are turned on and the potentiometers can be adjusted

for maximum detector s ignal . In the "run" mode, the l ine receiver input

i s switched so that the output of the random noise generator i s applied

to the chopping c i r cu i t , turning the beam on and off randomly. The

chopper i s mounted as close to the beam apparatus as i s possible to r e ­

duce the capacitance of the input to the grids (<100 pf) to reduce the RC

tine constant of the grid c i rcu i t .

Because of l imitations on the interface e lect ronics , a maximum modu­

lation band width of 1 mHz has been used with th i s system. For the Sen

length of the deflecting grids this i s close to the maximum chopping

rate which can be tolerated for most ions. We have determined empirically

that pulse widths of less than 1/2 Usee lead to severe attenuation of the

transmitted ion signal , so that the 1 rfig limitation i s pretty much

applicable tc each of the components within the system.

the chopping system has worked more than adequately at the lHHz

bandwidth for both classical and correlation TOP measurements. Ve note

that the chopping c i rcui t in i t s final form was designed by Hr. Paul Salz

of Lawrence Berkeley Laboratory. I t i s remarkably effective considering

i t s simplicity.

This concludes our discussion of the conceptual and electronic

methods which together comprise lite correlation TOF interfacing system.

He have shown how the use of an electronically generated modulation

system coupled with a direct memory address data storage system can be

-146-

used to extract the correlation information which describes a TOP dis­

tribution.

In the following section we will describe the computer program which

controls this experimental system and which is used for data reduction.

Storage Register

Correlator Scalars Gates

XBL 748-6913

Fig. 12. Crosscorrelatlon with gated scalars.

-148-

from a peripheral device causes program control to be transferred to a

service routine appropriate to the particular device. A sample skip

chain program is shown in Fig. 31.

The keyboard monitor i s the primary control fac i l i ty for the com­

puter system. This monitor i s a keyboard service routine which responds

to the ASR33 Teletype or the keyboard of a Tektronix 4010 Display Ter­

minal. When an alphabetic key on either keyboard i s struck, the service

routine determines which l e t t e r was sent from the peripheral and searches

through an. alphabetically coded table of subroutine addresses. Once the

alphabetically coded address i s found, the computer jumps to the s ta r t

of the corresponding subroutine. With this method, as many as 26 inde­

pendent entry points into system monitor subroutines can be accessed at

any time when the interrupt system of the computer i s enabled. To add a

new entry point for a subroutine, the user has only to place the sub­

routine's starting address in the coded table position corresponding to

the (previously unused) desired code l e t t e r . The keyboard monitor re­

jec t s a l l numerical and punctuation characters by typing a "?" and re­

turning to a wait loop where program control normally res ides . The same

rejection procedure i s also applied to unused alphabetic codes.

1 1 . The Operational Subroutines

We will now describe the subroutines which actually control the com­

puter interface and data acquisition. Each i s accessed by a separate

alphabetic code.

An important "subroutine" which i s used i s the Octal Debugging

Technique (ODT) program which i s a standard DEC program (access code = A) .

This program allows communication with and alteration of any other source

-149-

Figure 31. A skip chain

Location Command

0000

0001

0002

0003

0004

0005

0006

0007

0010

0011

Turn off interrupt

Skip if TTY flag Bet

Skip (unconditionally)

Jump to TYZ service routine

Skip i£ overflow flag set

Skip

jump to overflow service routine

Skip if printer flag set Skip

Jump to printer service routine

-ISO-

program in the lower 4 K field of memory. I t i s used in the system

monitor because i t f ac i l i t a t e s program statement modification (changing

the contents of addresses which contain other programs) . This statement

modification is used for inserting different command word options (see

"Interface Description")* for entering new subroutines and modifying them.

ODT also contains a braakpoiat faci l i ty which i s useful for debugging new

subroutines -

The "Start" subroutine (access code = S) i s used for interface

ini t ia l izat ion and to clear the date acquisition portion of the core

memory (2000a-7777e of the upper 4 K f ie ld) . This routine resets a l l

interface command words to zero and clears a l l interrupt flags. I t zeroes

the data addresses in the upper 4 K field of core memory and then sequen­

t ia l ly loads each of the three command word codes in to the accumulator

and strobes them into the interface latches using the proper IOT's. The

interrupt facil i ty i s enabled, the data break system i s turned on to

in i t i a te data acquisition and program command i s then transferred to the

keyboard monitor wait loop.

The "Classical TOF" subroutine (access code = B) i s used when a

classical TOF mode of t»pe>-Stion i s desired. This routine al ters the

command word I code to enable classical TOF operation and makes a minor

change in the data transformation routine (see below) by program address

modification. I t then jumps to the "s tar t" subroutine which carries on

as before, except that a different command word I code i s loaded.

*The breakpoint faci l i ty allows the user to run a program up to any pre­determined internal point (breakpoint) at which t ine program control i s returned to ODT for program analysis and modification.

-151-

The "Correlation TOF" subroutine (access code * C) i s used for corre­

lation 70^ measurements. As with the classical mode* th i s routine modi­

fies the Command Word I code and the data transformation subroutine and

then enters the "s tar t" procedure.

The "Data Transformation" routine (access code = U) i s exceedingly

important, as i t hal ts further data acquisition and extracts the corre­

la t ion function information from the data stored in the "data addresses"

of the upper 4 K of core. Since this routine i s fundamental to the com­

puter correlation method, we w i l l describe i t i s some d e t a i l .

We f i r s t recal l that the correlation information is stored within

the configuration of each address and that the contents of each address

merely denotes the number of times that address code was stored in the

Break Memory Address Hegister a t the time a detector event occurred.

What we wish to compute i s the t o t a l number of times a par t icu lar b i t

was equal to " 1 " during a detector event; this corresponds to a positive

correlation between a one being in that b i t position and a detector event

occurring. Similarly, the number of times a b i t was "0" a t the time of

a detector event provides the number of negative correlation between the

b i t position and detector events. The net value of the correlation

function associated with any b i t position i s the number of positive cor­

relat ions minus the number of negative correlations.

Since the data i s stored as three 10 b i t sequence representing 30

b i t s of the correlation function, we wi l l require 30 double precision

signal {+ correlation) accumulators and 30 d?ub..e precision background

(- correlation) accumulators. Since the information was stored in 10 b i t

segments! one 1 K portion of the uppermost 3 K of the core memory i s

-152-

transformed at a time, leading to accumulation of signal and background

in 20 different signal and noise accululators at once (10 signal , 10

background).

The accumulation of signal and background i s accomplished by using a

single masking bi t ("1") in a 10 bi t binary mask in conjunction with the

logical AND function (code 0nnn) of the computer. To s t a r t the transfor­

mation, the f i r s t address of the lowest 1 K section of data addresses

(2000a) i s generated. The masking b i t i s placed in the most significant

b i t position of the 10 b i t mask (corresponding to the third most s igni f i ­

cant b i t of the address—the f i r s t two b i t s being the quadrant code).

The address code and the mask are then AHDed together. If the third b i t

of" the address was 1, the result ing number lef t In the accumulator wil l

be nonzero; otherwise the resu l t wil l be zero. Depending an this resul t ,

the contents are added to e i ther the f i r s t signal or f i r s t background

accumulator (see Fig. 31A).

Hext, the masking b i t I s shifted right one place and the next b i t

of the address (fourth most significant) i s tested In the same manner,

the result being stored (added) to either signal or background accumu­

lator number 2. The process then continues unt i l a l l 10 b i t s of interest

in the address have been tested and the contents of that address have

been added to exactly 10 signal or noise accumulators depending on the

s ta te of the bi ts of the address. Then the address i s incremented and

the process i s repeated s ta r t ing with the masking b i t in the third s ig ­

nificant bi t of the address. The same 20 signal and bsjcground accumu­

lators are used.

-153-

Figure 31A. Masking addresses for data transformation

Example: A 4 Bit address, 0010 has contents = 0042

Address: 0010 •» 0010 •* 0010 * 0010

Mask: 0 1 0 0 0 © 0 1 0 0 00010 © 0 0 0 1

Resu l t : 0000 0000 0010 0000

I i 1 i Add 42 Co background accum, #1

Add 42 Co background accum, #2

Add 42 Co s i g n a l accum #3

Add 42 to background accum #4

Test address 0010 next.

-154-

When the f i r s t 2000a (2000-3777) addresses have been transformed, a

second group of 10 signal and 10 background accumulators are then used to

transform the second 2000s (4000-5777) addresses, and a third set i s then

used for addresses 6000-7777. The overall net resul t i s that the contents

of each of the 3 K addresses have been added to 10 signal or background

accumulators depending on the particular configuration of the bi ts of

each address.

Once the transform i s complete, the contents of each background

accumulator are subtracted from the contents of the companion signal

accumulator, and the resul t i s stored in the signal accumulator. Next a

display setup routine compresses the most significant portion of the 24

b i t signal accumulators into a 12 b i t format and stores the

result in a 36 a address display buffer. (This action scales the T «?Hp

for the display.) When th i s has been completed, the program clears the

data acquisition section of the core memory, reloads the proper command

word codes, and resumes taking data via the data break system.

The above discussion re la tes to the transformation of correlation

data. In the case of c lass ical TOF operation, only posit ive correlations

between address bi ts and detector events is possible. This is the result

of a slow repetition rate which unambiguously associates each detector

event with the modulation pulse responsible for i t s genesis. Since there

are no negative correlations, background accumulators are not used in

transforming classical TOF data; the formated signal accumulator contents

are rather displayed di rec t ly .

The "Display" subroutine (access code = D) is used to display trans­

formed data on a Tektronix Type 545B oscilloscope using the D/A Board

-155-

(see "Interface Description"). The routine automatically scales the X

axis of the display so that the 36 a addresses of the display buffer will

span the entire range of the X axis D/A converter. The routine then

sequentially loads the X and Y D/A converters using the computer's accu­

mulator and intensifies each display point. This process i s repetitively

cycled so that the display i s maintained even on a non-storage osci l lo­

scope until the routine is interrupted by a keyboard command or a data

overflow flag. The display i s of the form of a histogram whose height i s

the value of the correlation function.

Data storage was i n i t i a l l y achieved by taking a Polaroid picture of

the displayed data. However, a l l future data storage wi l l be in the form

of punched paper tape which can be used to transmit data to a CDC 6600

computer over a telephone l ine for further data analysis.

I I I . Data Overflow Service

As we noted in the "Interface Description," the correlation in te r ­

face i s equipped with a data overflow facili ty which pulls down the com­

puter interrupt bus line when the data addresses have been f i l led suffi­

cient ly. A data overflow interrupt will be serviced by checking the

interrupt skip chain of the computer program and jumping to a data over­

flow service routine.

This routine immediately turns off the data break system, turns off

the computer's interrupt fac i l i ty and jumps to the data transormation

subroutine. The use of the overflow system thus allows repeated f i l l ing

of the memory with raw data followed by automatic transformation of the

data. The only restr ict ion on the amount of data accumulated i s the

capacity of the double precision sigual accumulators which store the

-156-

accuimilated transformed data.

In summary, the system monitor pro"ides a versati le means of con­

t ro l l ing tho functions of the correlation interface and of accumulating

and transforming data. In the in teres t of saving core memory for storage,

the monitor has been kept comparatively simple. However, i t wi l l be easy

to add new subroutine blocks in the future if additional programming

functions are deemed necessary.

-157 -

EXPERIMEHTAL WEASUHEMEHTS OSIHG THE TOF COEBELATOR

In order to demonstrate the appl icat ion of the TOF corre la t ion

system, we have measured the v e l o c i t y d i s t r i b u t i o n s of s e v e r a l ion beam

s p e c i e s . Although there i s no e x i s t i n g beam apparatus i n our laboratory

with a s u f f i c i e n t l y long i o n d r i f t path for TOF experiments , these low

reso lut ion measurements were made to demonstrate the operat ion of the

correlator for viewing ion velocity distributions.

The apparatus employed (which was constructed by James Fair) i s

similar to the one described in Chapter IV. An electron bombardment ion

source i s used to generate an ion beam which i s then momentum selected

with a sector electromagnet. Two beam deflection plates normally used

for beam alignment were connected to the ion beam chopper in a syanetric

(±) voltage configuration. Ion scattering takes place in a fixed

scattering cel l mounted Immediately forward of the beam chopping region.

(Bo scattering gas was employed since measurements of primary beam

velocity distributions were made.) Product ions are mass selected using

a radio frequency quadrupole mass f i l ter . In normal operation of the

apparatus in a bandpass mode, a Wien f i l ter (crossed e lectric and mag­

netic fields) i s employed for velocity analysis of the mass selected

products. During TOF experiments, the Uien f i l ter was disabled so that

ions of al l velocities were transmitted to the detector, a Bendix mag­

netic electron multiplier.

The apparatus, including the detector train, i s in a linear configu­

ration appropriate for use in TOF measurements. The total ion flight

distance between chopping region and detector was estimated to be 40 cm.

-158-

To measure the effective path length of the apparatus (taking into

account the voltage distr ibution along the f l ight path due to focusing

elements), a 10 eV beam of N was observed by both classical and correla­

tion TOF methods. The measurement confirmed the approximate figure of

AO cm for effective f l ight path and both TOP methods measured similar

flight times (30 ysec) and TOF distribution widths (2 usee). Since the

mass of N is comparatively small, no analysis of the beam velocity d i s ­

tribution was possible (short flight path + fast ion -+ low resolution) .

To study the velocity distribution of a primary ion beam, an H2 beam

approximately 12 eV in energy was employed. Correlation TOF spectra

were measured and compared with the velocity distr ibution measured by an

accurate retarding potent ial analysis. Measurement of an entire N,

spectrum required only 20 seconds. When the correlation spectra were

scaled to account for beam intensity fluctuations, the points of each

neasured spectrum were consistently reproducible within a 10% range,

although most spectrum points fe l l within a 5% range of the mean intensity

measured for each TOF channel.

The shape of the TOF spectrum was quite similar to that measured by

retarding potential analysis (Fig. 32) . For purposes of comparison, the

velocity distribution measured with the retarding potential were con­

verted to a TOF spectrum by consideration of the potential distribution

along the ion f l ight path and integration of the to ta l time of flight

(Fig. 32a). The TOF measurement had a FWHM width of 2.5 psec while the

retarding potential measurement corresponded to a FWHM of 1.6 usee. The

low resolution of the TOF spectrum (T_-_/T , , _, <= A) and the flat-v TOF modulation ness of the correlation peak suggest that the additicnal width of the

Ol£_L 44 45 46 47 48 49 SO

Flight Time (usee) XBL 749-7310

Fig. 32. H„ velocity distributions measured by retarding potential analysis (A) and TOF correlation (lu sec channel width) (B).

-160-

TOF measurement can be at tr ibuted to counting of ions a t the peak of the

velocity distribution by more than one TOP channel (the peak velocity

l i e s between two channels so that each accounts for half of the peak

in tensi ty) . This results in an apparent flattening (and increased FHHM

dimension) of the velocity dis t r ibut ion.

To overcome the resolution problem associated with short ion drif t

path, a measurement of the TOF spectrum of Kr was made. Krypton gas

contains several naturally occurring isotopes: Kr 8 2 (112), Kr B l t (572),

and Kr B S (17Z). Hhile formation and momentum analysis of a Rr besm wil l

cause distortion of these re la t ive isatopic abundances from those of

natural krypton, i t was expected that due to the large mass of Rr

(t*84 amu) compared to the isotopic mass differences (2 ami) some of each

isotope would be transmitted by both the momentum analyzer and quadrupole

mass f i l t e r . Measurement of the Rr velocity distr ibution should thus

reveal three mass peaks in the form of one major peak bracketed by two

s a t e l l i t e s .

As with H-, several spectra of a 10 eV Rr beam were measured and

the results averaged (again the spectrum shape was consistent) . A com­

plete spectrum required 20-30 seconds to acctmn ""ate. The resul ts are

shown in Fig. 33. There i s clear resolution of the three mass peaks

(beam intensity was maximized at a QPHS sett ing of 84) . The intensi t ies

of the peaks are approximately equal to the expected isotopic abundance,

although the mass 86 peak was both somewhat smaller than expected and

positioned closer to the mass 84 peak than expected.

Hhile i t i s not passible to make any definitive statement about the

efficacy of the computer correlation system on the basis of these resul ts ,

6S*

o o

ro

3

Kr + Relative Intensity

T r T 1 1 1-

-162-

they do demonstrate that the correlation method can be applied to an ion

beam system. In large par t , the need for an adequate f l ight path

(>100 cm) to increase resolution places a severe constraint on measure­

ments uhich can be made with the apparatus in i t s present form. In the

near future, the flight path of the apparatus wi l l be enlarged with a

d r i f t tube and AC quadrupole lens system. After this modification, i t

wi l l be feasible to study the TOF spectra of ionic products of ion-

molecule reactions in greater de ta i l and provide a clearer indication

of the capabilities of the correlation system.

-163-

REPEBEHCES FOB CHAPTER III

1. Small Computer Handbook. Digital Equipment Corporation. Haynard,

Mass. 1972.

2. H. Davles. Control. June 1986, p. 302.

3. G. A. Korn. Bandog Process Simulation and Measurement, HeGraw Hill,

1966.

4. E. Soucek. Minicomputers In Data Processing and Simulation. Wiley

Intersdence, Hew York, 1972

5. H. A. DiValentin and J. E. Dove. Int. J. Haas Spec. Ion Physics 11,

359 (1973).

6. Programming Languages, Vol. II. Digital Equipment Corporation.

Haynard, Mass., 1972.

-56*-

REACTTON OF CO* WITH H- ISOTOPES

The second s e c t i o n of t h i s t h e s i s dea l s w i t h expe r imen ta l e l u c i d a ­

t i o n of the r e a c t i o n s of CO- i o n s wi th t he i so toye ; ; of H_, p r i m a r i l y D„.

This system wi th f ive atoms and 17 va lence e l e c t r o n s i s somewhat more

complicated than t h o s e p r e v i o u s l y s t u d i e d ; hence i t p r o v i d e s i n s i g h t

i n t o how mult iatom complexes might be v i s u a l i z e d and how molecular

o r b i t a l c o r r e l a t i o n diagrams can be app l i ed t o p r e d i c t i n g t h e shape of

m u l t i c e n t e r p o t e n t i a l s u r f a c e s and t h e i r e f f e c t on t h e format ion of

r e a c t i o n p r o d u c t s . A f t e r p r e s e n t i n g i n more d e t a i l t h e mo t iva t i on fo r

t h i s work, we w i l l d i s c u s s t h e system i n d e t a i l and o u t l i n e t he e x p e r i ­

mental appara tus which was used t o a c q u i r e d a t a . We then p r e s e n t t he

exper imenta l r e s u l t s and a d i s c u s s i o n of t h e p e r t i n e n t c o r r e l a t i o n d i a ­

grams along wi th an i n t e r p r e t a t i o n of the r e s u l t s from b o t h k inemat ic

and p o t e n t i a l su r f ace p a i n t s of v iew.

Hodels for Ion-Molecule Reac t ions

For purposes of d i s c u s s i o n , we w i l l assume t h a t t he hydrogen i s o t o p e ,

D„, has been used for s t u d y of t he r e a c t i o n s of CO.. ( In f a c t , D_ was

employed i n most e x p e r i m e n t s . ) Our s tudy of C0„ +D„ h a s been aimed a t

unders tanding t h e e lementary dynamics of the r e a c t i o n through t h e eva lua ­

t i o n of exper imenta l ly determined product v e l o c i t y v e c t o r d i s t r i b u t i o n s .

Chemical r e a c t i o n s have ge ne ra l l y been c l a s s i f i e d as be longing t o

one of the two broad c a t e g o r i e s : those p roceed ing through the formation

of a l ong- l ived i n t e r m e d i a t e c o l l i s i o n complex and t h o s e proceeding v i a

a s h o r t l i v e d d i r e c t i n t e r a c t i o n mechanism. The t ime s c a l e of the r e a c ­

t i o n i s provided by the p e r i o d , x , r e q u i r e d fo r a complete r o t a t i o n of

-165-

the collision intermediate formed as the reactant molecules approach each

other closely (with a distance comparable to that of a chemical bond).

If the time of this close interaction i s less than T, the reaction i s

said to occur by a direct mechanism, while i f this interaction time i s

greater than T the collision i s said to proceed through intermediate

complex formation. Whether a reaction i s direct or proceeds through a

complex i s determined by the potential energy surface representing the

total electronic energy of the react ants as they -interact and form

products, and by the in i t ia l relative translational energy of the system.

Host ion-molecule reactions previously studied have been found to

evolve by a direct mechanism. The simplest and ac31 often applied model

of direct interactions i s that of spectator stripping. For the reaction

A + BC •*• AB + C, the spectator stripping model assumes that A interacts

with B, while C remains unaffected (a spectator). The model assumes that

that as A approaches BC, the BC bond i s dissolved so that when A hits B,

C has no momentum imparted to i t . By the conservation of momentum, the

velocity of AB formed by spectator stripping i s

where M. and H„ are the masses of A and B and V. i s the i n i t i a l velocity

of A. Products formed by spectator stripping are most often forward

scattered (relative to the center of mass) anJ appear at a 0° scattering

angle relative to the direction of V.. This follows again from the con­

servation of momentum; since no transverse momentum is imparted to C, the

same must hold for AB.

In the spectator s tr ipping model the internal energy of the AB

product 1B the relative energy of A with respect to B (E ) less the exo-

thermicity of the reaction:

AEW

and

" . - T - i - M r t - L

V " W'OM ~ I n i t i a l reduced mass of A an :

E_ = i n i t i a l laboratory energy of A.

As E_ i s increased, U,_ increases unt i l eventually the internal energy of

AB exceeds i t s dissociation energy. At this point AB formed by spectator

stripping i s no longer s tab le , and any product intensity peak due to a

s t r i c t spectator interaction i s expected to disappear. In fact, the d i s ­

appearance of product fo ; aed by spectator stripping i s often reflected

by apparent movement of peak intensity forward to a velocity greater than

Xss-The intermediate complex model assumes the existence of a strong

chemical attraction between the reactant molecules which binds them

together into a transitory unit of unspecified geometry which lives for

several rotational periods. During this time the complex rota tes ,

finally dissociating into products which are symmetrically distributed

in angle (the angular distribution of products i s uncorrelated with the

i n i t i a l relat ive velocity vector) . This random dissociation leads to

the measurement of product intensi ty distributions which are symmetric

about the ±90° axis in the center of mass coordinate system.

As a rule, complex formation occurs uhen the Internal energy of the

may allow the possibility of complex formation, at high re la t ive energies

temporary disposition of large amounts of (ABC) internal energy may

preclude complex formation. I t should also be noted that though a

potent ial energy well for complex formation may exis t , there are cases

where th i s surface i s inaccessible to the reactants leading to reaction 2 by a direct interaction mechanism or no reaction at a l l .

The formation of a long lived complex suggests that I t should be

possible to predict the relat ive frequency of formation for competing

product channels using unlmolecular decomposition (REKH) theory or a 4

s t a t i s t i c a l phase space model*

For the CO? - D_ system there exists the possibility of forming a

bound intermediate, D_C0_. t h i s species i s the molecular ion of formic

acid and i s known from photoionization measurements to be bound by

approximately 1.75 eV. Especially at low relative energies, one might

expect that there i s a sizeable probability of forming D~C0_ during

CO. - D„ collisions, and that such intermediate formation wi l l be r e ­

flected in the distribution of product intensi t ies as a function of

barycentric velocity and scattering angle.

The conceivable products of the C02 + D_ reaction are numerous and

include CO* BCO*, DC0+, 0D+, D 2 0 + , D£, 0 + , C0+ and d j . As such we have

-168-

been interested not only in the distributions of products as a function

of i n i t i a l translational energy, but also in the re la t ive cross sections

for formation of each product. In measuring product intensi ty distribu­

tions there are several questions which we have sought to answer:

(1) At low relat ive energies does intermediate complex formation

occur? If so, at what re la t ive energies does the complex persist?

(2) How important i s the large number of internal degrees of free­

dom in the CO. - D„ system? Does this fact influence the amount of trans­

la t ional •*• vibrational energy transfer or complex formation?

(3) If complex formation, occurs are re la t ive product intensi t ies

explainable in terms of RfiKU or phase space theories?

(4) If reaction proceeds by direct interaction, i s a spectator

stripping model applicable?

(5) Are the a t t rac t ive forces associated with a potent ia l energy

well displayed in product intensi ty distributions; i f not, i s i t passible

to explain the result-, by use of molecular orbital and s ta te correlation

diagrams? (See below.)

We have found that the C0? - D_ system appears to interact by way

of complex formation at low re la t ive energies (<1.5 eV) and that the

reaction mechanism gradually becomes more direct at higher energies.

After describing the apparatus used for experimental measurement, ire will

discuss the thermodynamics of the CO- + H- eystem, the pertinent correla­

tion diagrams, before detai l ing the experimental results which support

the above mechanistic description.

-169-

Egperimantal

The experimental apparatus used to study the C0„ + D2 system has

been applied to the study of a large number of ion molecule reactions

and has been described in de ta i l previously. I t basically consists of

three independent regions: an ion sour: f.cr preparing a narrow beam of

incident icns of known mass and enerf -. c-cs-ctexi ce l l where the

incident ions undergo intenr leculai i l l s cms, and a product analysis

region where ionic products are counted as a function of the i r mass,

f inal energy and laboratory scat ter ing angle.

The apparatus i t se l f i s composed of two connecting vacuum chambers:

a small source chamber pumped by a single 6" o i l diffusion pump* and a

much larger (^4 ft ) reaction chamber containing the scat ter ing region

and the i n i t i a l stages of the detector t ra in , pumped by two 6" o i l diffu­

sion pumps. Each diffusion pump i s mounted on a liquid nitrogen cooled

baffle to reduce o i l backs creaming and increase effective pumping speed.

The main chamber typically has a pressure of 3 x 10 Torr (in the

absence of scattering gas) .

Ion Source Assembly

For the current experiments, a Broida type microwave discharge

source was used. This source consists of a 1 cm diameter quartz tube

mounted on one side of the source chamber surrounded by a microwave

cavity. Microwave radiation supplied by a 3GHz conmserical diathermy

source maintains c steady discharge through a desired source gas once

the discharge has been in i t ia ted by a spark from a tes la co l l . - The dis­

charge i s confined to a 2 cm length by a piece of platinum mesh placed

within the discharge tube.

For producing CO, ions a mixture of CO. and helium i s used. While

the actual pressure within the discharge tube is uncertain, i t i s approxi­

mately 50u. The rat io of CO„/He in the discharge, as measured by an

ionization gauge i s 30/1; however, the relative efficiency for ionization

of these gases suggests that the actual rat io i s closer to 2 / 1 . From

this discharge mixture not only CO. ions, but also CO , 0 , and C ions

may be extracted. In most cases, larger fluxes of ions can be achieved

i f the CO. gas pressure in the tube i s kept just above the minimum

pressure necessary to maintain the discharge.

As has been noted previously, a primary advantage of the microwave

discharge source over electron bombardment sources i s the relat ively low

electron temperature of the discharge. While electrons in a bombardment

Bource typically have energies of 50-100 eV, the electron temperature in

the microwave discharge i s of the order of 5 eV. The r^Jult of the low

electron temperature i s that CO. ions wil l be formed almost exclusively

in the ground ionic s tate (AE = 13.78 eV) rather than in excited 2-n , Z Z + or 2 Z + states (AE ^ 17.3 eV) . u g

Once a steady discharge i s achieved, ions are extracted from the

discharge region by a 700 volt extraction potential . They then pass

through a series of e lect ros ta t ic focusing lenses and into the entrance

of a magnetic mass spectrometer. As the ions enter the spectrometer,

the beam passes through an e lec t ros ta t i c quadrupole lens which converts

the beam from one of circular cross section to one of rectangular cross

section and focuses the beam on the entrance to the analyzer; after

momentum analysis, a second quadrupole forms the ions again into a beam

of circular cross section. This maneuver increases the effectiveness of

-171-

the momentum analyzer by causing a l l ions in the beam to traverse the

analyzer in a single horizontal plane. The quadrupole lenses also aid

in focusing and shaping the ion beam before i t enters the scattering

region. The momentum analyzer i t se l f i s a 66* sector electromagnet. By

varying the energy at which ions traverse the analyzer and the strength

of the naguetic field (by adjustment of the current through the magnet)

any of the ions produced by the source discharge nay be selected for

use.

The momentum analyzer has a resolution of 2X of the energy at which

the ions are analyzed. This fact coupled with the natural isotopic

abundances relevant to CO* (C 1 3 - 1.112; 0 " - 0.0371; 0 i a - 0.20Z)

supports the experimental observation that l , 5 C0 2 and V*C0. from the ion

source do not play a significant role In interfering with Intensity dis­

tribution measurements. Any such interference would be removed by

measurement of relative background levels.

Scattering Cell

As the beam of the momentum selected ions exits from the momentum

analyzer, i t i s again re focused by electrostatic lenses onto the fixed

entrance to the target gas scattering cel l . This target ce l l basically

consists of two tightly fitted concentric cylinders, capped at both ends.

The interior cylinder i s fixed in position relative to the ion source

train and contains a 2 mm x 2 cm square entrance aperture for tue cel l .

The outer cylinder i s fixed to a rota table lid mounted on top of the Daln

vacuum chamber. The complete detection train, as well as the scattering

cel l exit rotate with the movable l id , allowing analysis of ionic pro­

ducts at a wide range of laboratory scattering angles. The exit s l i t of

-172-

the collision cel l i s a Z ma diameter round hole.

The path length through the scattering ce l l i s 3.8 ma. Target gas -3 pressures of approximately 10 Torr are maintained within the scattering

cel l and lead to bean attenuations of 15-202 during passage of the beam

through the cel l . This ensures that only single scattering events are

responsible for the final distribution of reaction products. The scatter­

ing cell pressure is measured with a capacitance bridge manometer (HKS

Baratron) whose advantage over an ion gauge i s that i t i s insensitive to

the ionization efficiency of the gas which i s being monitored.

For the reactions of CO-, He, H-, HO, and D» gases were used in the

scattering cel l . The small size of the ce l l apertures allowed the use of

iotracell pressures 1000 times greater than the background chancer

pressure; a 10" Torr ce l l pressure typically caused a two-fold increase

In chamber pressure, an entirely tolerable figure. Since only relative

cross sections for reactions were measured, no effort to calibrate the

absolute pressure within the collision cel l was required.

Detector Train

As mentioned above, the entire detector train i s mounted on the

20 irch diameter rota table l id (which i s counted on a differentially

pumped double tec-ring seal) . Product loos emerging from the collision

cel l enter a 90° spherical electrostatic energy analyzer which passes

ions of the desired final energy into the vertical plane of the detector

train. The energy analyzer has an angular resolution of 2.3° full width

and energy resolution of 32 5WHH. The transmitted ions are focused by

a series of electrostatic lenses onto the entrance of a quadrupole nass

f i l ter and then into the ion detector.

-173-

The detector itaelf consists of a polished aluminum plate which i s

maintained at a potential of -25 kilovolts. As the highly accelerated

product ions strike the plate, they cause ejection of secondary electrons

which are then accelerated by a +28 kilovolt potential and impinge on a

lltbium-drif ted silicon semiconductor wafer which transduces the pulses

of secondary electrons into electrical pulses which are amplified by an

FET preamp and linear amplifier and counted with a Hamner HS-11 10 He

scalar. Using a Teletype Scanner, the resulting scalar counts are typed

out on ASR33 teletype along with the counting time and col l is ion ce l l

pressure for later analysis.

Experimental Procedure and Data Analysis

In undertaking an experiment an this apparatus, the f i r s t order i s

to achieve a steady gaseous discharge. The appropriate momentum analysis

energy i s chosen so as to guide extracted ions to a beam flag positioned

at Che scattering cel l . The ion current at the beam flag (10 - 10~

A) i s monitored using a Keitheiy electrometer. The gas pressure, quad-

rupole lens voltages and microwave power are used in a concerted manner

to achipve a steady discharge which yields ma***"" ion beam intensity.

At this point the bean flag i s rotated out of the beam path and the beam

current monitored using a Oary 31 electrometer connected to one of the

lens elements of the detector train. This allows monitoring and

optimization of the angular and energy widths of the beam. When this

final beam i s determined to be stable, i t i s characterized as to energy

and angular distribution. Liquid nitrogen i s then added to a reservoir

which cools the eeuiconductor detector, and after a 20 alnute cooling

period, the detector i s turned on.

- 1 7 4 -

Measurements of product i n t e n s i t y are comoLonly Bade according to

one of two schemes: the d e t e c t o r i s pos i t ioned a t a constant laboratory

angle and the energy of the product energy analyzer i s scanned, or the

product energy i s l e f t f i z s d and the laboratory angular d i s t r i b u t i o n i s

scanned. The former method i s termed as a "scan" w h i l e the l a t t e r i s

referred to as a "cut". Typica l ly one scan i s taken a t the i n t i a l labora­

tory angle corresponding t o the inc ident ion beam ( c e n t e r l i n e ) to give an

idea as to the extent of the energy d i s t r ibut ion and subsequently betveen

10 and 20 cuts i n angle are taken t o span that energy d i s t r i b u t i o n .

Using the t e l e type , the i n t e n s i t y at each energy-angle po int i s recorded

u n t i l a complete map of the product i n t e n s i t y d i s t r i b u t i o n i s accumulated

c o n s i s t i n g of between 200-300 i n t e n s i t y measurements. This process takes

from 3-6 hours and requires frequent monitoring of the primary beam i n ­

t e n s i t y and energy-angular p o s i t i o n . Changes i n these parameters are

automatical ly taken i n t o account by l i n e a r i n t e r p o l a t i o n during data

a n a l y s i s . We note that though the time required for each i n t e n s i t y

measurement i s a funct ion of r e l a t i v e product i n t e n s i t y , each measurement

i s t yp ica l ly made over a 15-20 second in terva l to average out any i n ­

stantaneous beam f l u c t u a t i o n s .

The information pr inted on the te le type i s transferred to computer

data cards which arc then analyzed on the LBL CDC S600 computer.

At e*»ch energy-angle p o i n t for which product i n t e n s i t y i s measured,

the s i gna l and background counts are normalized us ing the i n t e n s i t y

conversion | = 10 7 (S-B)

T i o P g ( 6 ) E ^ / 2

-175-

where

S * signal counts

B • background

X - counting time in seconds —12 i tt peak incident beam intensity (in units of 10 A)

P = scattering gas pressure (In units of 10 Torr)

g(6) = detector angular viewing factor through the scattering cel l

(a function of scattering angle)

E- = electrostatic energy analyzer Betting 3/2

The E factor normalizes the measured intensity to the detector volume

in velocity space.

Calculated intensities are plotted by a Calcomp plotter as a function

of barycentric velocity and scattering angle. Using the plotted intensity

points, contours of equal intensity are drawn onto the array ana the

result i s an intensity contour map of the final product distribution.

One sucl. map i s required for each individual product of the reaction at

each i n i t i a l relative energy for the react an to. Comparison of the maps

for any product as a function of i n i t i a l relative energy yields informa­

tion as to the mechenism(s) important for the reaction.

The resolution of each experii^ent i s a function of the angular and

energy distribution of the incident beam, as well as the thermal motion

of the gaseous target molecules. This coupled with incident beam inten­

sity fluctuations makes the resultant intensity maps something less than

a high resolution picture, yet there i s a surprising amount of infatua­

tion which can be inferred solely from the general shape of the distribu­

tions. Put another way, the detail of the information provided i s at

-176 -

l e a s t as g r e a t as our knowledge of t he a p p r o p r i a t e p o t e n t i a l energy

s u r f a c e s (of ten much g r e a t e r ) s o t h a t t h e t e s t s which might be a p p l i e d

t o t ' -• exper imenta l da t a a r e p r e t t y much p o s s i b l e w i t h c u r r e n t v e l o c i t y

and angu la r r e s o l u t i o n .

Kinemat ics and I n t e n s i t y D i s t r i b u t i o n s

Though we b r i e f l y a l l u d e d t o t h e i n t e r p r e t a t i o n of t . o t t e r i n g d i a ­

grams i n Chapter I ( see P i g . 1 ) , t h e r e a r e a broad range of s c a t t e r i n g

p r o c e s s e s ubich may be i n t e r p r e t e d wi th the a id of v e l o c i t y v e c t o r d i a ­

grams. Figure 1 d e a l t w i t h t h e g e n e r a l case of an i on A which i s i n ­

c i d e n t on a n e u t r a l molecule , BC, whose thermal v e l o c i t y was cons idered

n e g l i g i b l e . The r e s u l t s of such a c o l l i s i o n can be c l a s s i f i e d i n t o

s e v e r a l broad c a t e g o r i e s :

(1) E l a s t i c s c a t t e r i n g : A + + BC •* A + + BC

(2) I n e l a s t i c s c a t t e r i n g : A + + BC + A + * +• BC

•* A + + BC*

+ A + + B+C

(3) React ive s c a t t e r i n g : A + BC * AB + C

+ AC* + B

•* AB + C +

•* A + BC + e t c .

The v e l o c i t y v e c t o r diagrams p e r t i n e n t t o each of t h e s e c l a s s e s a r e

shown i n F i g . 34.

I n an e l a s t i c s c a t t e r i n g e v e n t , no chemical r e a c t i o n o c c u r s , and

t r a n s l a t i o n a l energy r e p r e s e n t i n g r e l a t i v e motion of t he p a r t i c l e s i s

s t r i c t l y conserved ( i . e . remains w i t h i n t h e t r a n s l a t i o n a l mode) . Only

t he ang le of motion r e l a t i v e t o t h e i n i t i a l v e l o c i t y v e c t o r i s changed,

-177 -

a. Elastic collision1 A + + BC —»- A + + BC

b. Inelastic collision1 A + + B C — - A + + B C *

c. Reactive collision: A + + BC —»- A B + + C (exothermic)

XBL 749-7312

Fig. 3«. Velocity rector diagrams for elastic, Inelastic and reactive collision processes.

-178-

the amount of change depending on the strength of the e l a s t i c interaction

and the impact parameter (aiming error) of the col l i s ion. This type of

collision i s often represented as the type occurring between colliding

b i l l i a rd ba l l s .

For a l l three classes of collisions, i t i s possible to define a

quantity, Q, which denotes the amount of re la t ive t ranslat ional energy

which i s converted from trans lational to internal modes during the

collision process. If E . denotes the i n i t i a l re la t ive trans la ticraal

energy (E = •=• ug 2 ; u = i n i t i a l reduced mass, g = i n i t i a l relat ive

t 12

"rel " 1 » 1

products (E . = •=- \i g ) we define

If Q i s negative, t h i s implies that some I n i t i a l re la t ive trans l a ­

tional energy has been converted to electronic, vibrat ional , or rotational

internal modes of the products. If QX>, i n i t i a l in ternal energy has been

converted Into the trans la t ional energy code (superelastic col l is ion) . i

Since the e las t ic coll is ion process by detinit ion assumes E « *

E . , elast lcally scattered projectiles wil l be found at the Q = 0 locus

of points (Fig. 34a) which forms a circle about the center of mass in

the appropriate velocity vector diagram. This c i rc le represents a l l

points at which a projec t i le , A , say be found after simple rotation of

the relative velocity vectors about the center of mass following an

e las t ic collision.

-179-

By conservation of to ta l energy, a l l relat ive trans la t ional energy

lost during a collision must be found in internal nodes (electronic, i

vibrat ional , rotational or heat of formation). If U. and U, represent,

respectivelyi the energy contained in internal modes before and after a

col l is ion, then

-« - " in t " " in t

and the e las t ic case (Q » 0) i s consistent with a zero net change in

internal product energy.

For the Inelastic class of coll isions, Q<0 and

since trans la tional energy i s converted into internal modes. This case i s

represented in Fig. 34b, For th i s type of collision there i s again no

chemical transfer, only a rearrangement of the available trans la t ional

energy among translational and internal modes.

The reactive case (Fig. 34c) i s a further extension of these con­

cepts. The only additional complications arise because the reaction may

f a i l to be thermoneutral, and because the product masses differ from

those of the react ants (u f1 u ) . In this case the change in energy of

formation (exo- or endo-thsrmicity) must be taken into account in

balancing the distribution of energy before and after the reaction.

Conservation of energy i s then represented by

-180-

if AE i s defined as negative for exothermic reactions following the

normal convention.

For a reactive process, i t i s apparent that if D = U. that

Q = - AE . Thus, even if the in te rna l modes of the products remain in

the i r i n i t i a l energy s tates (though of course different modes are avail­

able before and after the col l is ion since chemical transfer has occurred)

there must be a net conversion of energy into (from) bond energy from

(into) translation in the case of an endoergic (esoergic) reaction. This

i s represented by the Q = - AE° c i rc le in Fig. 32c.

Thus we can begin to see how a particular coll ision may be visualized.

The vector scattering diagram for reactants ( i n i t i a l vectors) and products

( f inal vectors) i s constructed. At any point an the diagram, Q may be

calculated knowing E . = •=- pg z , E t = y u g z . Using a known value of

AE , i t i s then possible to compute the amount of internal energy con­

verted into internal modes. This quantity provides information as to the

chemical state of undetected products (whether they are dirsociated) and

provides some clues as to the nature of the reaction mechanism (see

below). In real i ty , for a multiatcm system such as CO- + D_ there are

many fewer Inferences which can be made concerning energy disposal in 9

internal modes as compared with systems of two or three atoms. never­theless, such analysis dees yield some UTTy*1"" on which products can be

-181-

formad at any init ial relative energy and maintains same usefulness in a

more complicated system.

States and Energetics

Before discussing the distributions of reaction products, i t is

°2-H2 appropriate to present the energetics of the CCL-H- system. We begin

Heutral C0„ has been thoroughly studied previously. I ts ground

electronic state is lZ and has the molecular orbital population shown

in Table 7. CO- is linear and has an equilibrium interouclear distance

r = 1.16A. Formation, of ground state CO, (2K„) occurs when one of the

nonfaending IT electrons is removed. The ITT orbitals essentially repre­

sent the lone pair oxygen electrons; the nonbonding character of the

Iff orbitals is supported by the fact that the rotational constants for

CO, (^A) and CO- (*£ ) are almost equal, both species being linear.

Formation of C0o (2II ) requires 13.78 eV. 2 g

The excited states of Col" are also listed in Table 7. The 2 H u

results from removal of an electron from the bonding Iff orbital of CO,

and requires 17.32 eV. While the ZH state is also linear* both excited

£ states are known to be bent.

The vibrational frequencies for CO,, (*E ) and C0„ (2H ) have been

12 —1* determined from photcelectron spectroscopy (PES) to be (In cm )

co* co 2

V 1250 1388 (symmetric s t r e t c h )

\> 2 530 66? (bend)

\>_ 1469 2349 (asymmetric stretch)

TABLE 7. Electronic States of CO, and CO,

Species State Orbital Configuration r (A) Geometry

"8

2 U h ( l og lou2og 30g 2<iu Aog 30u) lira lirg

U 3 ltfu lug

11TU lTTg

1.16

1.17 linear 13.78

17.32

2- + IB.OB

2r + Eg 19.4

•Relative to C02 ( 1Eg +)

and the Franck-Condon factors for transitions CO- (000) •*• CO. (2II ) have

(0,0,0) (.82)

(1,0,0) (-15)

(2,0,0) (-02)

(0,0,0)

Thus, one expects that In the case of ver t ical ionization, predominantly

present in the microwave discharge source may indeed lead to adiabatic

rather than vert ical t rans i t ions , and neutral CO» may be vibrationally

excited within the discharge. However, since the equilibrium geometries

of CO- and CO, are quite similar , one expects that similar F.C. factors

wixl pertain to ionization of vibrationally excited C02 and that C0„

produced in the discharge wi l l approximately reflect the vibrational

energy distribution of neutral C0_. Moran and Friedman have discussed

the problem of vibrational excitation and determined that an upper limit

of 1 eV for the internal durat ional energy of CO- is l ike ly .

As has been reported previously, the electron temperature of the

CO- discharge i s approximately 5 eV. This makes i t unlikely that the

excited states of C0„ are produced in any quantity. Moran and Friedman + ? +

have reported that CO, ( I I ) (the excited state of CO- most likely to be

produced) decays to CO_ (X ZH ) in 10 seconds. The resul t i s that we

may assume with some certainty that the CO- ions undergoing reaction are

almost exc7usively in the ground 2II s ta te .

The thermodynamics of the CO- - H? system are presented in Table 8.

The heats of reaction have been derived using predominantly the heats of

formation tabulated in Ref. 5. Formation of H_CO_ is 2.5 eV exothermic.

The value for formation of H + HCO„ is derived using the measured proton

affinity of C0„. ' A value for the proton affinity of 5.1 eV (used in

subsequent calculations) reported in Ref. 15 represents the average value

of those reported. The resulting value for the well depth with respect

to dissociation of H2C02 to HCO- or UGO Is approximately 1.7 eV.

Although not a l l of the processes l isted in Table 8 are expected to

occur in H- + CO, coll is ions t the exhaustive l i s t ing is helpful for

evaluating the energecic l imitations placed on the formatioa of the actual + + + + + +

reaction products (CO-, HCO_, HCO , OH , CO , 0 ) . As the experimental resul ts are evaluated below, frequent reference to Table 8 wi l l be made.

3

TABLE 8

Primary Reactioas tlit^a (eV)

C 0 2 + B 2 + B 2 C 0 2

H + UCO, + i

BCO + OH

- 2 . 5 6

+

B 2 C 0 2

H + UCO, + i

BCO + OH - .75

- .77

+ HCO + OB + +3.7 + BCO+ + 0 + H + 4 . 4

-* CO+ + H 2 0

CO + U 2 0 +

CO+ + H 2 + 0

CO+ + OB + B

+0.7

+1.58

+5.79

+5 .9

- > •

0 + + H 2C0 0 + H 2 CO +

0 + + H + CO

+5 .33 +2 .58 +5 .4

- 2B + C0 2 +4 .5 - * •

H 2 + C 0 2 +1.66

Secondary Reac t ions 4H? 9 a (eV)

HCO* + B + CO* H + + C0 2

HCO+ + 0

+5.25 +5 .13 +4 .4

+ HCO + 0 + +9.4

•* CO+ + OH +6.6 + CO + OH+ 5.7

HCO+ -* CO+ + H 6.65

co+ C + + 0 8 ^ - • C + 0 + 3.35

- 1 8 6 -

MOLECULAR ORBITAL COREELAIION DIAGRAMS

While i t i s known from the thermodynamics of the CO?-H„ sys tem t h a t

t he e x i s t e n c e of a bound i n t e r m e d i a t e (H_CO_) i s p o s s i b l e , i t i s by no

means c e r t a i n ChaC Che p o t e n t i a l s u r f a c e which o r i g i n a t e s from t h e grcund

e l e c t r o n i c s t a t e s of the r e a c t a n t s l e a d s t o Che formation of t h e ground

s t a t e i n t e r m e d i a t e . For a number of ion-molecule r e a c t i o n s p r e v i o u s l y

s t u d i e d , a q u a l i t a t i v e d e s c r i p t i o n of t h e r e a l p o t e n t i a l s u r f a c e s f o r Che

r e a c t i o n has been achieved by the u s e of molecular o r b i t a l and e l e c t r o n i c 2 +

s t a t e c o r r e l a t i o n diagrams. For t he CO^-H- system, we have c o n s t r u c t e d

such d iagrams , which w i l l now be d e s c r i b e d .

For any chemical r e a c t i o n t h e dynamics of the c o l l i d i n g r e a c t a n t s

a r e determined fay the e l e c t r o n i c p o t e n t i a l energy s u r f a c e of t h e r e a c t i o n

( w i t h i n t h e framework of the Born-Oppenheimer approximation) . However,

f o r z l l b u t the s imples t r e a c t i o n s , t h e p o t e n t i a l energy s u r f a c e s a r e n o t

known i n d e t a i l ; c a l c u l a t i o n of t h e s e s u r f a c e s i s most o f t en an expens ive

and compl icated p r o p o s i t i o n , e s p e c i a l l y fo r t he mul t id imens iona l s u r f a c e s

a p p r o p r i a t e to r e a c t i o n s i n v o l v i n g many atomic c e n t e r s .

Without knowing the d e t a i l s of t h e p o t e n t i a l s u r f a c e , i t i s s t i l l

p o s s i b l e t o v i s u a l i z e the q u a l i t a t i v e f e a t u r e s of Che s u r f a c e f o r a

r e a c t i o n us ing molecular o r b i t a l (M.O.) c o r r e l a t i o n d iagrams. As a

chemical r e a c t i o n p r o g r e s s e s , t he molecu la r o r b i t a l s of the r e a c t a n t s

evo lve i n t o those of an i n t e r m e d i a t e c o l l i s i o n complex and f i n a l l y i n t o

Chose of the r eac t ion p r o d u c t s . By fol lowing the evo lu t i on of t h e s e

o r b i t a l s , i t i s pos s ib l e to a s c e r t a i n t he o v e r a l l e l e c t r o n i c energy

th roughout the r e a c t i o n In o r d e r t o d e c i d e wheCher format ion of a long

l i v e d c o l l i s i o n in t e rmed ia t e i s p o s s i b l e .

•187-

To c o n s t r u c t an M.O. c o r r e l a t i o n diagram, one f i r s t assumes a

"dynamica l ly reasonab le" c o l l i s i o n geometry wi th one o r more symmetry

e lements* The o r b i t a l s of the r e a c t a n t s , i n t e r m e d i a t e , and p r o d u c t s a r e

then i d e n t i f i e d anC resolved i n t he p o i n t group corresponding t o t h e

symmetry e lements fo r the assumed geometry . Espec i a l l y i n a low symmetry

i n t e r m e d i a t e c a s e , such as H 2C0_, t he n o d a l s t r u c t u r e of the v a r i o u s

H.O.*s p r o v i d e s usefu l c lues t o t h e e v o l u t i o n of each o r b i t a l as t h e 20 r e a c t i o n p r o g r e s s e s . The o r b i t a l energy of each o r b i t a l I s e s t i m a t e d

us ing SCF c a l c u l a t i o n s , e l e c t r o n a f f i n i t i e s , appearance p o t e n t i a l s and

p h o t o e l e c t r o n and u l t r a v i o l e t s p e c t r o s c o p y . Af te r each o r b i t a l f o r

r e a c t a n t s , i n t e r m e d i a t e and p roduc t s h a s been i d e n t i f i e d and p l a c e d

acco rd ing t o energy , o r b i t a l s of t h e same symmetry spec i e s a r e connected

( o r b i t a l c o r r e l a t i o n ) . The mixing of o r b i t a l s of t he same s p e c i e s by

nonsymmetrlc n u c l e a r motions and s p i n - o r b i t i n t e r a c t i o n s i s cons ide red

and p o t e n t i a l l y avoided c ross ings of s u r f a c e s a r e i d e n t i f i e d .

When t h e M.O. c o r r e l a t i o n has been completed, by p l a c i n g t h e e l e c ­

t r o n s of t h e r e a c t a n t s i n t he o r b i t a l s , t h e i d e n t i f i c a t i o n of e l e c t r o n i c

s t a t e s f o r each of t he spec i e s found d u r i n g the evo lu t i on of t he r e a c t i o n

i s made. By c o r r e l a t i n g the e l e c t r o n i c s t a t e s of l i k e symmetry f o r

r e a c t a n t s , i n t e r m e d i a t e and p r o d u c t s , a s t a t e c o r r e l a t i o n diagram i s con­

s t r u c t e d which i s a rough approximation t o the p o t e n t i a l s u r f a c e s

a p p r o p r i a t e t o the r e a c t i o n .

In g e n e r a l .'here i s more than one c o l l i s i o n geometry a p p r o p r i a t e t o

the r e a c t i o n (o r s e v e r a l narrowly c o n s t r a i n e d ranges of c o l l i s i o n g e o ­

m e t r i e s ) o r more than one p o s s i b l e s e t of p r o d u c t s . For each p o s s i b l e

geometry range or s e t of p r o d u c t s , a s e p a r a t e s e t of c o r r e l a t i o n s i s

r e q u i r e d .

For Che CCL-H,, system the I n t e r m e d i a t e * H^CO,, con be forced in one

of two b a s i c ways (F ig . 35) . P a r a l l e l approach by iU and CO- l e a d s t o

t h e C symmetry in t e rmed ia t e f a v o r i n g the formation of HCO^ o r HCO

( F i g . 3 5 a ) , whi le pe rpend icu la r approach of H, toward CO™ leads t o on

i n t e r m e d i a t e of C 2 „ symmetry ( F i g . 3 5 b ) . Figure l e shows a t h i r d p o s s i b l e

mode of approach, but t h i s geometry does not lead t o formation of a s t a b l e

H 2 C0 2 mo lecu la r c o n f i g u r a t i o n . These geometr ies of course r e p r e s e n t

i d e a l i z a t i o n s ; any r e l a t i v e geometry of approach i s p o s s i b l e , bu t t he se

examples p rov ide a f i r s t approximat ion u s e f u l for c o n s t r u c t i n g c o r r e l a ­

t i o n d iagrams . Once the diagram h a s been c o n s t r u c t e d . I t i s p o s s i b l e to

c o n s i d e r the e f f e c t s of geometr ic p e r t u r b a t i o n on the s t a b i l i t y of the

complex.

We begin wi th lUCOj format ion a s a C symmetry i n t e r m e d i a t e . The

m o l e c u l a r o r b i t a l c o r r e l a t i o n diagram f o r t h i s case i s shown i n F i g . 36.

The D . p o i n t group of CO- and H 2 i s used t o c l a s s i f y the r e a c t o n t

m o l e c u l a r o r b i t a l s , while the o r b i t a l s for the HCO, product a r c c l a s s i ­

f i e d accord ing to C ? v symmetry. The impor tan t elements of the o r b i t a l *

c o r r e l a t i o n are the combination of t he H~ o and o o r b i t a l s t aken In 2 g u *

banding-an t ibonding combinations w i t h the in -p lane TT and IT o r b i t a l s of 20 CO. ( F i g . 37) in a manner s i m i l a r t o the pro to type H_ + e t h y l e n e c a s e .

I n each case the in-phase combinat ion l e ads to the low energy bonding

o r b i t a l whi le the ou t -of -phase combination leads to the h igh energy a n t i -

bonding o r b i t a l conta in ing an a d d i t i o n a l node. The c o r r e l a t i o n which

-189-

(a) 1 D+ AE=-2.5eV, H _jk AE = -H.75eV> „_ J ^ „ I H-rJ * H 0

AE-+ l .8eV + Parallel Inter- »- H—C=0 nuclear Axis +

Apprcaeh

+ " V + " \ + H 0 = C = 0 —* - ^ 3 - C = 0 — * • 0 + C=0 I

Perpendicular Bisector (Energy of Intermediate Unknown)

Approach

(c) 9 0 J> H - H C+ — • • H — H - C K + — ^ H + H - C ! + | + - ^ H - . H - C ^

^ 0

XBL 749-7314

Fig . 35. Col l ir ion geonetr ies for the H2-CO_ Interoedia te complex,

a) Cs synactry intermediate; b) C,y sycnetry intermediate ;

c) a perpendicular approach leading to d i r e c t I n t e r a c t i o n .

aa|<r;(CO)

2T, UsC) 3a'(UCI 2a,(liC]

ld„llsOI 2o'(UOI IbjIliO] lirQ(lsO) } lo'llsO) la, 1 ISO)

4 t d ails in plane)

(C s)

-cf +

( C 2 v )

XBL 749-7256

Fig. 36. Molecular orb i ta l correlation diagram for fomation of HCOj4" from C02+H2» p a « l l e l internucleat axis approach.

Basis Orbitals

H2:© 0 © 0

g u

C0 2: 0 O GX0 GX0

0X0 ex© 0*3

Bonding Combinations u

© 0 i G © 0 i G

©£> C g + V 6 0 ' '

© 0 ^ 3

a*+»*(7a') Antibonding Combinations

cr g-^(l lo')

©iG^O ©IS©)

0©~ <-tr*(!2a')

] <BL 749-7227

Fig. 37. Bonding and antibonding combinations of H, and CO, orbitals to form H2C02+ molecular orbitals (labeled in parentheses).

-192-

of H,Cot, a (H_) with the l l a 1 , 7T (CO.) with 7a' and a (H-) with the

12a' orbi ta l of the intermediate. This correlation leads to an avoided

crossing of the 11a* and 7a 1 o rb i ta l s as the intermediate i s formed. The

mixing of these orbitals can be visualized as due to formation geometry

less than parallel , or as due to the asymmetrizing presence of the non-

part icipating oxygen atom. In the l a t t e r case, one can see that the node

between the 0 atom and the closest H atom (Fig. 37) contains geometric

components both parallel and perpendicular to the CO- intemuclear axis

which perturb an otherwise symmetric (approximately C„„) s i tua t ion , mix­

ing the 7a 1 and l l a 1 orbitals and leading to an avoided crossing. The

exact point of the avoided crossing and the height of any resul t ing

potent ia l energy ban ie r in the entrance channel are open to speculation.

The significant point i s that there theoretically exists a route by which

reactants in the ground s ta te may adiabatically evolve to the ground

s t a t e of the intermediate, suggesting that the potential well for forma­

tion of an intermediate complex may be accessible.

The formation of HCO, proceeds via the ground s ta te intermediate in

a simple way when the 0 (H_) electrons evolve through the 7a* s ta te of

H-CO-. The final assignment of an electron to the ls(H) orbi ta l occurs

through the transfer of a nonbonding 10a* electron which may involve a

second avoided crossing (Fig. 36} .

The M.O. correlation diagram for formation of HCO + OH i s shown in

Fig. 38. The formation of ground electronic state products from the

ground s ta te intermediate i s readily apparent. In this case, the forma­

tion of HCO over OH (see below) is explainable both on the basis of

thermodynamics (HC0+ + OH l ies some U eV below HCO + 0B +; see Table 8)

- 1 9 3 -

-10-

-12-

- 1 6 -

- 1 8 -

g -20-

»(0HH2iO) /

2o g(lsC) 3o'lllC) irtCOUfsCI l<r„ (IsO) Zn'(lsO) alOHKIsO) Ia„(ls0) la'(lsO) trlCOKHO)

i: o. (t aiis in plane) fcrt [HCO+OHJ

(Co. )

XBL749-7Z33

F i g . 38. Molecular orb lce l c o r r e l a t i o n diagram for formatim of HCff1- + OH from C0,+H 3.

and an the basis of the molecular o rb i ta l correlation. The al ternate set

of products, HCO + OH , are adiabatlcally inaccessible! and the t o t a l

energy of the f i l led molecular orbi ta ls in the HCO + OH case i s well

separated in energy from that of HCO -4- OH.

The formation of C_ H_C02 by a perpendicular approach of H- and

CO, leads to the M.O. correlation diagram shown in Fig. 39. The i n - and

out-of-phase combination of the terminal 2S oxygen orbital and the H-O

orbi ta l lead respectively to -.,e bonding 2a, and antibonding 4a.. orbi ta ls

of H„0 (since the symmetry of the intermediate and the IL,0 product are

ident ical , identification of the intermediate orbitals has been dispensed

with) . In a similar manner, combination of the in-plane TT^CO,) and

a (H_) orbi ta ls leads to the formation of a lb 2-2b„ bonding-antibending

pa i r . Combination of the CO- a and a bonding orbitals forms the

bonding and nonbonding orbitals of CO (combination leads to the local iza­

tion of the orbi ta ls ) .

Start ing with the ground s ta te react ants, one finds again that the

<J(H_) electrons in i t i a l ly correlate to a high energy orbi tal (4a.) . A

crossing of the Aa_ orbital surface by that of the 3a, orbi tal again pro­

vides a path to ground state products. However, in this case i t i s likely

that the energies of the adiabatic surfaces (noncrossing path) are closely

a i

regions of space. The experimental observation that no H20 i s formed in

the reaction (see below) may provide support for the conclusion that the

close orb i ta l spacing at the avoided crossing allows the react ants to

follow a non-adiabacic path in a large fraction of C0~ + H« collisions

occurring in a nearly perpendicular geometry.

'gg (ISO)

( C 2 v )

4o*lHaO)

2bf IrigO)

27r«|CO)

6<r»(C0)

I +O=C=0 , . . , . ~>3-C=0 ">> + CO |_H J («ins in plane) [ _ H ^ J V^ J

<C2„ a C m v )

XBL 719-7234

Fig. 39. Molecular orbi tal correlation diagran for formation, of HiO++CO from C0 2

++B 2-

He note parenthetically that a crossing of the 3a. and 4a. orbitals

is likely to occur a t a high energy. This i s suggested by the fact that

the molecule OCF is bent (OCF can be correlated with OCOH which should

have a geometry similar to OCOH„). This suggests tha_ sn H-OCO inter ­

mediate would also be bent in a low energy configuration. I t may be that

formation of H70 requires achievement of a lower energy bent inter­

mediate. Formation of such an intermediate would require some destruc­

tion of the C0? IT bonding system, entailing a significant energy of

activation.

Throughout our discussion of correlation diagrams we have dealt only

with the orbi ta l correlations, neglecting the s ta te diagrams which actually

describe the electronic potential energy surfaces. This omission i s

motivated by the fact that the orbital energies of the intermediates are

very poorly characterized. Additionally, especially in the case of the

C intermediate geometry, the low symmetry of the intermediate leads to

labeling of the electronic states as being of only two types (A , A. ) .

Thus in any s t a t e correlation diagram there wi l l be a very large number i

of closely spaced states of the same symmetry (especially in the A

case), and i t is impossible to draw any meaningful conclusion. This i s a

problem that wil l persis t throughout the further study of reactions in ­

volving many atoms and low symmetry intermediate geometries.

In summary, we have seen how the molecular orbital correlation dia­

grams for the CG„ + H_ system describe a possible low energy path to

product formation. The importance of lowered symmetry in the reaction

intermediate may determine whether mixing of orbitals of like symmetry

leads to avoided crossings with a significant enei^y gap allowing the

-197-

fortnation of a ground state intermediate. In the following section the

experimental measurements of product in tens i t ies are presented. la view

of the preceding discussion I t iB possible to rationalize the appearance + + + +

of HCO. and HCO as major products while l i t t l e or no H„0 or OH are found.

2 The exper imenta l ly determined p roduc t v e l o c i t y d i s t r i b u t i o n s f o r the

" 2 ^ H 2

l o n g - l i v e d in t e rmed ia t e complex and a d i r e c t i n t e r a c t i o n mechanism a r e

d i s p l a y e d . At a l l the i n i t i a l r e l a t i v e ene rg i e s s t u d i e d , t h e r e was

ev idence of s t r o n g chemical coup l ing between the r e a c t a n t s p e c i e s . Con-

s i s t a u t wi th the moderate depth of t he e l e c t r o n i c p o t e n t i a l w e l l , low

energy r e s u l t s d isp lay the symmetric behavior a s s o c i a t e d wi th complex

format ion whi le h igher energy d i s t r i b u t i o n s suppor t a s p e c t a t o r s t r i p p i n g

mechanism. In te rmedia te complex format ion and l i f e t i m e appea r t o be

governed by the e f f ec t i venes s w i t h which i n i t i a l r e l a t i v e t r a n s l a t i o n a l

energy i s disposed among the a c t i v e v i b r a t i o n a l modes of t h e i n c i p i e n t

complex.

DCO*

Prev ious s t u d i e s of CO- have p rov ided a l i m i t e d amount of i n fo rma­

t i o n about t h i s product , which i s t h e major r e a c t i v e c h a n n e l . Ding has

p u b l i s h e d a b r i e f d e s c r i p t i o n of t h e zero degree energy d i s t r i b u t i o n of

DCO- a s a funct ion of i n i t i a l r e l a t i v e energy . He found t h a t a t ve ry low

r e l a t i v e energy (E .-=r 0 .5 eV) t h e r e i s some sugges t ion t h a t complex

format ion may occur, whi le a t low and in t e rmed ia t e r e l a t i v e e n e r g i e s

* ( 1 - 8 eV) , v e l o c i t y d i s t r i b u t i o n s r e f l e c t a s p e c t a t o r s t r i p p i n g mechanism.

However, t h e exper imental e r r o r r e p o r t e d for the low energy r e s u l t s make

i t u n c l e a r whether t h e r e i s indeed complex formation o c c u r r i n g .

*There i s some ambiguity i n t h e s e r e s u l t s s i n c e t he r e p o r t e d energy s c a l e s ( l a b o r a t o r y and r e l a t i v e ) a r e i n c o n s i s t e n t l y l a b e l e d .

Smith and Futrell have reported the results of ion cyclotron

for H atom transfer at low trans la t ional energies (<10 eV) . These authors

report a value of k = 4x10 ° cm3/molecule-second for the HCO- formation

rate constant; this value was found to be independent of incident ion

k inet ic energy for E < 6 eV. The fact that this rate constant i s approxi­

mately one-fourth of the typical value (k = 15-20 x 10 1 0 cm3/molecule-19

second) expected from Langevin polarization theory raises a question

about the nature of the potential surface for the reactants a t impact

parameters somewhat smaller than the c r i t i c a l impact parameter for

Langevin col l is ions. While this might be viewed as evidence supporting

a moderately sized barrier to complex formation in the entrance channel

of the potent ial surface* such a proposition would be entirely specula­

t ive .

The examination of HCO_ and DC0? product velocity distributions in

our laboratory i s complicated by problems of mass analysis. There are

several d is t inc t aspects of this problem. The incident CO- Ion beam con-

13 +

tains approximately 1% C 0„ (mass 45) which i s transmitted by the momen­

tum analyzer of the ion source t ra in , though this was not found to pro­

vide significant interference. A more significant problem encountered

was transmission of nonreactively scattered CO- (mass 44) by the quad-

rupole mass f i l t e r . Although each measurement of product intensi ty

includes a background measurement which removes mass 44 whose source i s

primary beam transmission, background measurements are incapable of cor­

recting intensi t ies for nonreactively scattered CO- which i s transmitted

at a QPHS set t ing of mass 45 or 46. Since there is a relatively large

amount of inelastic nonreactively scattered C02 at a l l in i t ia l relative

energies studied, and since resolution of mass 45 from mass 44 i s very

limited with the apparatus used in these studies, DCO_ was chosen for

study at most relative energies. HCO_ was studied only at low relative

energies since use of an H~ target rather than D_ decreases the i n i t i a l

relative trans la tional energy of the reactants by a factor of one-half.

Figure 40 displays the HCO, product velocity distribution measured

in our laboratory for E . = 1.5 eV, the lowest relative energy studied.

The distribution appears quite symmetric. However, in view of the

relatively large in i t ia l beam velocity distribution (20X Beam Profi le) ,

one cannot state categorically that there i s no asymmetric component to

the map. In this figure, as well as subsequent ones, the velocity ex­

pected for a spectator stripping (SS) model i s marked with an X. This

low energy result unquestionably contains a large symmetric component

suggestive of complex formation. The intensity of the product distribu­

tion (I units) i s quite large and in fact i s somewhat larger than the

intensity of nonreactively scattered CO, at the same relative energy

(see below). This suggests that a large fraction of ion-molecule c o l l i ­

sions in this system are influenced by the chenical forces represented

by a potential energy well.

The DCO- distribution :

this taap also shows a sizeable sycoetrlc ccsponent, i t s basic nature is

asymmetric. The peak intensity fa l l s very near to the velocity expected

from a spectator stripping coll ision.

In order to establish unequivocally the stripping nature of the

product distribution at this low translations! energy, a similar nap of

-201-

the n C0 2 resulting from collisions with HD was constructed (Fig. 42) 4

Again, the velocity distribution i s quite broad with a product intensity

peak at the spectator stripping velocity. For each of these cases the

Q value of the spectator velocity i s given by the negative of the relative

energy between CO. and the 0 atom. Since the D atom comprises a larger

fraction of the total target mass in the HD case, Q appears closer to

the center of mass in the HD map, although Q i s approximately equal in

both cases.

The comparison of these two distributions provides firm evidence for

a direct interaction mechanism at relative energies as lev as 1.5-2 eV.

However, the broad extent of the product distribution suggests the con­

tinued influence of a long lived complex. One possible explanation of

these results i s chat snail impact parameter collisions lead to coopleac

formation while more grazing collisions could lead to DCO_ formation by

a stripping mechanism.

Figures 43 and 44 are DC02 intensity amps (from D,) for relative

energies of 2.9 eV and 5 eV respectively. As the relative energy i s in­

creased the distributions became increasingly asymmetric and more highly

peaked about the stripping velocity. This i s in keeping with the asstiap-

tioa that as relative translations! energy i s increased much above the

well depth. It becomes more difficult to fom a long lived eosplex and

the direct interact lea predominates.

As ocntioned above, the internal energy associated with formation of

DCOj by a stripping ocdianism Is a function of the relative clergy of D

and CO. since the spectator D acoa i s incapable of rcaoving this relative

energy. As troftslatinnal energy is increased, eventually this internal

energy wi l l exceed the dissociation energy for DCO-. The thermodynamics

for this process are:

CO* + D2 (0 eV) - DCO* + D (- .7 eV) •*• D + D+ + C02 (+ 4.4 eV)

2 Kcal/mole) in energy above the initial react ants.

The DCO_ product will be unstable if Q ^ - AE° or

If E denotes the energy of CO. relative to the D atom,

"D^CO.

co2

"^LAB

0 _ U L U U i b LUCU HUCU Ci_ *" =—

and the spectator stripping peak i s expected to be greatly attenuated

(and show forward movement due to loss of more highly excited product)

for i n i t i a l C02 energies greater than 100 eV.

Product intensity distributions for DC0_ were examined at laboratory

energies of 100 and 125 eV. At 100 eV (8.3 eV relative energy - Fig. 45)

the stripping peak persisted, but showed a l i t t l e forward movement. At

125 eV the peak intensity had moved farther forward and intensi ty of the

DCOo product dropped by a factor of 10. This is consistent with loss of

-203-

DCO, formed by a s t r i c t spectator str ipping mechanism and s tabi l izat ion

of the detected product by forward r eco i l . This i s consistent with the

results of Ding.

At i n i t i a l laboratory energy of 150 eV no significant amount of

DC0- was detected. At this and higher energies, product s tabi l iza t ion by

forward recoil becomes improbable and formation of products in competing

reactive channels is l ikely.

COf + H 2 —•- HCOj + H (35 eV) Relative Energy = 1.5 eV

560 tn/sec

XBL 748-7117

Fig. 40. HCO iocensicy distribution tor l .S eV relative energy <H2 target).

COg + D 2 — DCOj + D (25 eV) Relative Energy = 2.03 eV

I +90°

180°

560 m/sec

Q = 0eV

) 0°

\ !0% Beam "rofile

XBL 749-7206

Fig. 41. DCO- Intensity distribution for 2 eV relative energy (D_ target). X marks spectator stripping velocity.

COf + HD —-DCOf + H (22.7 eV) Relative Energy = 1.51 eV

480 m/sec

Q'l.OeV

01.

\ 20% Beam Profile

XBL 749-7210

Fig. 42. DCO- intensity distr ibution from HD at 1.5 eV re la t ive energy. X marks spectator stripping velocity.

C 0 | + D 2 —*~ DCOg + D (35 eV) Relative Energy = 2.9 eV f+go"

180°

560 m/sec

\ 0 ° .

X5L 748-7119

Fig. 43. DCO_ intensity distr ibution from D, at 2.9 eV re la t ive energy.

-208-

CO| + D 2 — - DCO| + D (60 eV) 981

Relotive Energy = 5.0 eV

T+90 Relotive Energy = 5.0 eV

T+90

Q = OeV S\^/!~^*~-Q = -2.5 eV / [ / / S ^ ,

>s/5* y^x ^JOOI^A

1 ( / l O K 20K

ISO" I If ( 1 [ f n n '"—-N

>—J/u 20% *-*y#y Profit*

| |

\

[ f n n '"—-N

>—J/u 20% *-*y#y Profit*

1 BOO m/sec ' 1-90°

XBL 749-7207

Fig. 44. DC02 intensity distr ibution from D- at 5 eV relat ive energy. Spectator stripping peak i s becoming more pronounced.

-209-

C 0 | + D 2 — > DCOg + D (100 eV)

Relative Energy = 8.3 eV

Q = -3.2 eV,

180°

1200 m/sec

+ 90"

jo*y^\

XBL 749-7238

Fig. 45. DC0 2 ' intensity distribution from D at 0.3 eV relative energy.

- 2 1 0 -

C 0 | + D 2 — » • DCOg + D (125 eV)

Relative Energy = 10.4eV

Q= -2.5 eV.

180°

1200 m/sec

-90°

X6L749-7237

Fig. 46. DCQ,+ Intensity distribution from D, at 10.4 eV relative eaergy. Intensity peak has moved forward of the spectator stripping velocity showing forward recoil product s tab i l ­ization.

DCO* (HCO+)

The DCO product forms a second Important reactive channel In the + + •*•

C 02~ a2 s v s t e m - Wai l e DC° Intensities are typically lower than DCO'

intensities by a factor of 50, there is a sizeable amount of this product

produced in the reaction.

The DCO product distributions provide further evidence for low

energy complex formation giving way to a direct mechanism at higher

energies. The reaction forming DCO + OD is 0,7 eV exothermic, very close

to the value far formation of DCO..

Figures 47-51 show HCO and DCO product intensity maps over a range

of Initial relative energies. The HCO distribution in Fig. 47 is very

close to being symmetric while Fig. 48 showing the analogous DCO distri­

bution shows somewhat greater forward emphasis. In both cases cbe dis­

tribution is peaked at the center of mass. As the relative energy in­

creases to 8.3 eV (Fig. 49) this asymmetry becomes more marked and a for­

ward peak is present. The distribution for E . = 10.4 eV (Fig. 50) is

quite similar. The position of the peak moves steadily forward with

Increasing energy until the distribution lies entirely in the forward

direction (Fig. 51).

The movement of the product distribution with increasing energy is

most clearly viewed by examination of the zero degree scattering (center

lines) with a normalized velocity scale as shown in Fig. 52. At low

energies the distribution is quite symmetric about the center of mass

and steadily progresses toward forward scattering as the initial energy

is increased. This is further evidence of complex formation at low

e n e r g i e s w i t h a more d i r e c t i n t e r a c t i o n a t h i g h e r e n e r g i e s .

To i n v e s t i g a t e whether t h e r e i s any i s o t o p e e f f e c t wi th r e g a r d t o

HCO and DCO format ion, both HCO and DCO product i n t e n s i t i e s a t low

r e l a t i v e e n e r g i e s were measured u s i n g HD as a t a r g e t . The r e s u l t s , shown

i n F i g . 5 3 , show t h a t i n both v e l o c i t y d i s t r i b u t i o n and i n t e n s i t y t h e r e

i s no d i s c e r n i b l e i so tope e f f e c t .

To v e r i f y presence of a symmetric d i s t r i b u t i o n peaked a t t h e c e n t e r

of mass a t low e n e r g i e s , HCO c e n t e r l i n e d i s t r i b u t i o n s from H_ were

measured ( F i g . 5 4 ) . These zero deg ree s c a t t e r i n g p r o f i l e s g e n e r a l l y d i s ­

p l a y t h e symmetric behavior expec ted from l o n g l i v e d complex f o r m a t i o n .

The e x a c t mechanism of format ion of t h e DCO product has no t y e t

been c l e a r l y def ined . Using the v e l o c i t y and i n t e n s i t y d i s t r i b u t i o n s

f o r SCO ( F i g . 52) i t i s p o s s i b l e t o make some i n f e r e n c e s . At low energy

mass v e l o c i t y . The i n t e n s i t y and p o s i t i o n of t he peak a long wi th t h e low

i n t e r n a l energy a s soc ia t ed wi th complex formation suppor t t he c o n t e n t i o n

t h a t a t low r e l a t i v e energy, DCO i s formed d i r e c t l y from decay of t h e

D2CO+

At somewhat h ighe r ene rg i e s t he peak i n t e n s i t y i n c r e a s e s and moves

forward . I n t h i s i n t e rmed ia t e energy regime (E . = 4-8 eV) , t h e DCO

p roduc t appears near a v e l o c i t y c o n s i s t e n t wi th a "double s t r i p p i n g "

mechanism (V (CO ) in F i g . 52) . The p i c t u r e of the i n t e r a c t i o n i s of

CO i n t e r a c t i n g s o l e l y wi th a s i n g l e D atom whi le 0 i n t e r a c t s w i t h t h e

o t h e r D atom. While such a p rocess r e q u i r e s a r a t h e r s e v e r e l y c o n s t r a i n e d

range of c o l l i s i o n geomet r ies , i t i s n o t e n t i r e l y u n l i k e l y t h a t such an

i n t e r a c t i o n may occur .

As initial relative energy is further increased, the intensity peak

for DCO moves further forward until (E ~ 10 eV) it appears near the

Fig. 52) . In this case one imagines that DCO, is formed by a direct

interaction and later decays to form DCO + 0 (AE° = 4.5 eV) or CO- + H

(AE° -5.2 eV). Since the relative energy (10 eV) lies above that at

which DCO- formed by a strict stripping mechanism remains stable and

rationalize the production of DCO from stripped DCO..

As relative energy is increased further, there is a dramatic drop

in DCO peak intensity at high relative energy, DCO formed both by a

double stripping mechanism and by decay of DCO„ is expected to be un­

stable. For the double stripping case, the energy of the CO moiety is

28/44 of the CO^ energy and relative to the D atom.

- E a = Q = - 28/44 x 2/30 E , ^ = .0424 E ^ .

At Ey A R = 150 eV DCO formed by double stripping will be found at

Q - - 6.4 eV. If we add to this one-half the exoergicity of the reaction

(CO + D -*• DCO + + 0D AE° = .7 eV) then the internal energy of DCO is

D = - Q - &E° ss6.7 eV. o This i s equal to the dissociation energy of DCO (6.7 eV) and one expects

that DCO formed by a double stripping mechanism will disappear for

" 2 '

cion of DCO* (E a = - Q = 2/46 E ^ ) i s equal to 6.5 eV at E y j l B = 150 eV.

However, the formation of DCO + 0 from DC0_ requires 4.5 eV energy.

Since this endothermicity must be subtracted from the final internal

energy of DCO v at ISO eV In the laboratory,

U • - q - fiE° a 2 cV. o This internal energy is less than the dissociation energy of DCO by a

considerable aeounc, Ve thus expect that at 150 eV DCO forced by double

stripping wi l l be unstable vhile DCO foracd f rem decay of DCO, will

retain undlssociatcd (dissociation in the latter case occurs for E,._ > LAS

250 eV). The drop In peak intensity of DCO for E^j. > ISO eV thus pro­

vides evidence for formation of a significant osount of DCO by a double

stripping mechanism at intermediate energies. It appears that at high

energies this component of the DCO Intensity distribution disappears

with the remaining DCO being that formed by deeny of DCO,. Zt i s un­

clear whether the forward movement cf the DCO peak intensity tovard V

for DCO, i s actually due to DCOj stripping followed by DCC formation, or

i f the peak movement i s due to a forward recoil effect. The above d i s ­

cussion tends to support the latter hypothesis.

In any case, DCO formation appears to be the result of several

types of interaction mechanisms within the energy range studies. It i s

possible that several mechanisms cay work simultaneously at any given

energy. The transition between oechanises of DCO formation Is likely

a gradual one.

-215-

I COj + H 2 — - HCO* + OH (100 eV) Relative Energy = 4.37 eV

IBO*

1200 m/Me

0--0.77

XBL 749-7205

Fig. 47. BCD Intensity ducributlan froi a , *t 4.4 eV relative energy.

COg + D 2 - — DCO + + OD (52 eV) 9SZ

Relative Energy = 4.36 eV T+90"

S jS" ^-—2K -~,

/ - °K

. /° = ~3

« 1 8 0 " 1 1 1 ( > X • M 1 °°r I ) \J JJJ V S ^-20%

Beam Profile

' IOOOm/sec ' 1-90°

XBL 749-7ZC6

Fig . 48 . DCO i n t e n s i t y d i s t r i b u t i o n from D, at 4 .4 eV r e l a t i v e energy.

C0£ + D 2 — DC0+ + OD (100 eV) 104

Relative Energy = 8.3 eV * T+90*

•0 ^^ ,Q«-6 .0»V

Q = -8.0«V j//^*****^' " S^vX. \ Z \ ^ ^ v^*^eo

• ^ ^ \ \ \

^ey [ 1 i f M f §^])J^ >yyUJ I

1 1 *"~~ 0^

1 I600m/»e ' I-90*

XBL 7 4 9 - 7 2 0 4

Fig . 49 . DCO i n t e n s i t y d i s t r i b u t i o n from D, at 8 .3 eV r e l a t i v e energy; X marks spectator s t r i p p i n g v e l o c i t y of DCCf** (double s t r i p p i n g ) .

COg + D 2 —» OCO* + OD (125 eV)

Relative Energy -10.4 eV j+90'

Q=-IOeV.

1400 m/sec

20% Beam Profile

x = Vce for DCOg formation

XBL 749-7231

Fig. SO. DCO Intensity distribution from D- at 10.4 eV relative energy; X marks spectator stripping velocity of DCO2 *

- 2 1 9 -

COg + D 2 - • DCO+ + OD (200 eV) • ISO

Relative Energy = 16.67 eV . +90°

Q=-l5.5eV / 30 / \

1 / > V * > \ \ / SO /

^-Ar-100 \ \

x 180° j ' ) r 1 / s v / / A

' ) r 1 / s v / / A

1

7^20% ' Beam

Profile

1400 m/sec -90°

XBL 749-7203

F i g . 5 1 . DCO I n t e n s i t y d i s t r i b u t i o n from D, a t 16.7 eV r e l a t i v e ene rgy .

0-L 1200--

0 i 12.000--

~ 7000-

-220-

COf+ D2-»DCO*+O0

' n l * 4 - 3 6 1 '

V B S VCU \ \ . V B E * y

0 C 0 + Product Velocity * XBL749-7229

Fig. 52. DCO centerline distr ibutions from D_ as a function from long lived complex to direct interaction mechanisms.

- 2 2 1 -

C 0 | + HD — * HCO +, DCO

i 1,000- -

E r e l -- 2.22 eV Product Velocity —

XBL749-7228

Fig . 53 . HCO and DCO centar l ine d i s t r i b u t i o n s from HD shaving no s i g n i f i c a n t i sotope e f f e c t a t law r e l a t i v e energy.

COt + H, Hccr + OH 2000--

HC0+ Product Velocity BEAM

XBL749-7230

Fig. 54. HCO cencerline distributions from H_ at low i n i t i a l re la t ive energy.

i n i t i a l re la t ive energies there Is a large amount of inelas t lcal ly

scattered CO.. The distributions suggest that scattering occurs by

simultaneous direct interaction and long lived complex mechanisms.

A product map of C0_ from D„ i s shown in Fig. 55 for E , = 1.86 eV.

There i s a large component of e las t i c scattering which follows the Q = 0

c i rc le , yet in the forward hemisphere there i s a significant amount of

ine las t ic i ty displayed, even at this low relative energy. For comparison,

Fig. 56 shows the analogous experiment with Be target gas. While there

i s again a large elast ic component to the map, near the center of mass

the intensity drops, suggesting a much less inelast ic type of interact ion.

Comparison of these two distributions leads to the conclusion that even

though much nonreactive scattering occurs by a direct mechanism, the

formation of a long lived complex in collisions of CO., With D_ i s likely

responsible for the highly inelast ic CO, intensity.

The CO- distribution from D2 at E , = 3.0 eV i s shown in Fig. 57.

The relat ive inelasticity has increased and now contributes to the for­

mation of a ridge projecting back toward the center of mass. The

existence of such high inelast ici ty at this relative energy i s s ign i f i -

+ 21 more ine las t ic than the Ar -D_ resul ts at a similar energy. This

-224-

suggests e i ther that complex formation is occurring or that the large

number of additional vibrational degrees of freedom in the C0_ case are

inportant.

Figures 58-60 are maps of CO from D_ at relat ive energies of 5,

8.3, and 10.4 eV respectively. They continue to display large ine las t ic

components although the overall intensity of the maps drops off as

ccllisions occur with greater relative energy. This intensity change

is couciscant with an expected drop in to ta l cross section for C0--D

collisions as the relative energy is increased.

-225-

COj+D 2 — C0| • D2 (22.7 eV)

Relative Energy = 1.88 eV [+90°

.180°

Q-OeM

680 m/sec

80% Beam Profile

X8L 748-7118

Fig. 55. Sonreactive CO.1- intensity distribution from D, at 1.9 eV relative energy showing broad inelasticity at the center of mass velocity.

- 2 2 6 -

COg + He — - C0| + He (22.7 eV)

Relative Energy = 1.89 eV f +90°

^180"

680 m/sec

20% Beam Profile

-90°

XBLMB-7IIG

Fig. 56. Nonreactive CO„ intensi ty distribution from He at 1.9 eV relat ive energy. There i s a significant lack of intensi ty due to inelastic collisions near the center of mass veloci ty.

COg + D2 — COj + 0 2 (36 eV} Relative Energy = 3.0eV 1+90°

.180°

800 m/sec

0 = OeV

20% Beam Profile

*&. 746-71 15

Tig. 57. Honreactive C0 2 intensity distribution from D at 3 eV relative energy.

-228-

C 0 | + D 2 —•*• COg + D 2 (60 eV) Relative Energy = 5 eV »

[+90°

0 = OeV Q=-2.8eV

J80"

^20% Beam Profile

1200 m/see

XBL 749-7209

F ig . 5 8 . Honreactive CO- i n t e n s i t y d i s t r ibut ion from D_ at 5 eV r e l a t i v e energy.

COj + D 2 — - CO2 + D 2

COOeV)

Relative Energy = 8.4 eV +90'

180°

2000m/sec

-90°

20% Beam Profile

XBL 749-7202

Fig. 59. Nonreactive CO- intensity distribution from D_ at 8.4 eV relative energy.

C0£+ D 2 -*• C 0 | + D 2 (150 eV)

Relative Energy = 12.3 eV

Q = OeV

180°

1600 m/sec

0% Beam Profile

XBL 749-7235

Fig. 60. Nonreactive C0 2

+ intensity distribution from D at 12.3 eV re la t ive energy.

-231-

The CO product i s a third reactive channel which was studied at

several energies. At i n i t i a l energies below 100 eV, no significant •f

amount of CO was detected. For energies above this level, in general

the CO distr ibutions are very Bimilar to products of coll lslonally

induced dissociation which have been measured in other ion-molecule 22 +

systems. The CO product lies forward of the center of mass and has

a broad angular distribution. The overall intensity remains approxi­

mately constant as a function of relative energy.

One question which arises is whether the formation of CO occurs

by an impulsive dissociation, or whether the chemical interaction between

CO. and D_ plays n role In the dissociation. The distribution of CO

formed in collisions with He (Fig. 61) are quite similar to those from

D 2 (Fig. 62-64). This suggests that in both cases the dissociation

occurs by an impulsive collision in which the chemical nature of the

product plays a very small role. The large Q figures for the CO dis­

tribution peaks (Figures 62-64) make it highly unlikely that any H~0

target is formed. It is more probable that (H_ + 0), (H + OH) or

(H + H + 0) are formed, with each neutral product leaving the scene of

the collision taking with it a sizeable amount of translational energy,

consistent with the large -Q valueB of the CO distribution. Another

possible source of CO intensity might be dissociation of highly excited

HC0 + formed by a stripping mechanism for Q s s > B ^ ^ H o w e v e r > ± t u

impossible to confirm this mechanism for CO production.

C0|+ He-*- CO++0 + He A (125 eV) J+90'

Relative Energy - 10.4 eV

0=-9.5eV

Q=-l0.3eV.

180'

1200 m/sec

XBL749-7232

Fig. 61. CO Intensity distribution from He at 10.4 eV relative energy.

-233-

C0| + D 2 —*• C0 + + (D20) (150 eV)

Relative Energy = 12.5 eV +90°

998

Q=-IOeV-Q = -l2eV.

.180°

2200 m/sec

20% Beam Profile

XBL 749-7200

Fig . 6'2. CO i n t e n s i t y d i s t r ibut ion from D, at 12.5 eV r e l a t i v e energy.

-234-

COg + 0 2 — CO++ (D20)(200 eV) Relative Energy = 16.7 eV +90°

Q=-15eVv

Q=-9eVv

180s

2600 m/sec

100

- £ •

20% Beam Profile

Fig. 63. CO intensity distribution from D- at 16.7 eV relat ive energy.

C 0 | + 0 2 — ^ C 0 + + ( D 2 0 ) (250 eV) 1156

Relative Energy = 20.8 eV 1 T+90°

s^~ ^ J > C \ Q = -\4eV^yS A l O t J N A

Q = -l9eV^/^ Jl p° \ \ \ \ 2 0 0 V l \ . 250O w

IW \\\V a , 1 8 0 " f 1 l\ ,¥i\ H 1

• l l 11 1

0 ° f c

^ 2 0 %

1 1 !

Beam Profile

' 2600 m/sec ' 1-90°

Fig. 64. CO intensity distribution from D, at 20.8 eV relative energy.

-236-

0D+, 0 + , and H 0 +

Both OH and 0 were noted as minor products of C0„ + H, col l i s ions .

H_0 was not detected at any of the re la t ive energies studied, which i s

consistent with a possible energy barr ier in the entrance channel sug­

gested by the H O correlation diagram. + Figure 65 shows the distribution of OD from D» at a relat ive energy

of 16.7 eV and Fig. 66 the distribution for 0 from D-. Neither product

was detected for E < 100 eV. Because of the very low intensity associated

with each of these reaction products, they were not investigated to any

extent. I t i s assumed that 0 i s the product of collisional dissociation

while OH may be formed either direct ly from the H CO. intermediate or

from dissociation of highly excited HC0~ or HCO . In any case, neither

of these products has contributed to our understanding of the overall

reaction system.

I t should be noted, however, that OD i s clearly not the product of

formed by independent collisions of CO and 0 (in the form of CO-) with

separate D atoms. This possibility i s ruled out by the position of the

OD distribution- In the event of a double stripping mode of OD forma-16 , t ion, one would expect an intensity peak at V = — V where V i s the

velocity of the incident C0„. This velocity l ies behind the center of

mass where there is in fact negligible intensi ty. + 4- *

By similar reasoning the formation of 0 from excited (D„0 ) may

be ruled out since such a mechanism in which an 0 ion is stripped from

C02 as i t passes by would also lead to 0 backscattering.

COg + D 2 - * O D + + DCO (200 eV) Relative Energy = 16.7 eV .

1153

1000 m/SBC

XBL7"lfl-7ll3 F l j . 65. OD i n t e n s i t y d i s t r i b u t i o n trom D, at 16.7 eV r e l a t i v e

energy.

COg + 0 2 — " 0 + + (D2CO) (100 eV) Relotive Energy = 8.3 eV

Q=-8.0eV,

.180°

1200 m/sec •90

XBL 749-7201

Fig. 66. 0 intensity distribution from D2 at 8.3 eV relative energy.

239-

Summary of Results

As we have emphasized previously, the C0_ - H_ system can he charac­

terized as a reaction evolving through both a long lived complex and a

direct spectator stripping mechanism. The DCO- product i s predominantly

the resul t of the stripping process although complex formation apparently

plays a role for E < 2 eV. The HCO product Is formed by a complex at

low energies* and i t s forjiation at higher energies can be rationalized

using two competing stripping processes. The CO? which is nonreactively

scattered shows- large inelastici ty due to vibrational mode exci ta t ion.

CO and 0 appear to be formed by col l is ional dissociation while no

H?0 was found at any relative energy. All of these results can be

rationalized in terms of the pertinent molecular orbital correlation

diagrams.

-240-

REPFRRNCES FOR CHAPTER IV

la. H. H. Chiang, E. A. Glslason, B. H. Mahan, C. W. Tsao and A. S.

Werner. J. Phys. Chem. 75, 1426, (1971).

b. Ibid., J. Chem. Phys. 52 , 6150, (1970).

c. K. T. Glllen, B. 11. Mahan and J. S. Winn. J. Chem. Phys. 58,

5373 (1973).

d. Ibid., J. Chem. Phys. 59, 6380, (1973).

B. H. Mahan and T. M. Sloane J. Chem. Phys. 59 5661 (1973).

2. B. H. Mahan. J. Chem. Phys. 55 1436 (1971).

3. R. A. Marcus. J. Chem. Phys. 42, 2658, (1965) and references

therein.

4. J. C. Light. J. Chem. Phys. 40, 3221, (1964).

5. J. L. Franklin, et al. Ionization Potentials, Appearance Potentials

and Heats of Formation of Gaseous Positive Ions. NSRDS - NBS 26_

(1969).

6. W. R. Gentry, E. A. Gislason, B. H. Mahan, and C. W. Tsao. J.

Chem. Phys. 49, 3058 (1968).

7. F. C. Fehsenfeld, K. M. Evanson, and H. P. Broida. Rev. Sci.

Instrmn. 36, 294 (1965).

8. Ref. la.

9. Refs. 1c and Id.

10a. R. S. Hulliken. J. Chem. Phys. 3_, 720 (1935).

b. J. F. Mulligan. J. Chem. Phys. 19, 347 (1951).

c. Y. Tanaka, A. S. Jursa, F. J. LeBlanc. J. Chem. Phys. 32., 1199 (1960).

d. S. Mrozowski. Phys. Rev. 61, 730 (1941).

e. ibid., Phys. Rev. 62, 270 (1942).

-241-

G. Herzberg. Molecular Spectra and Molecular Structure. Vol. Ill

Van Nostrand Beinhold Co., New York, 1966.

0. W. Turner, C. Baker, A. D. Baker and C. R. Brundle. Molecular

Fhotoelectron Spectroscopy. Wlley-Interscience, New York, 1970.

1. F. Moran and L. Friedman. J. Chan. Phys. 42., 2391 (1965).

C. S. Matthews and P. Wat neck. J. Chen. IhyB. 51, 854 (1969).

B. II. Mittmann.H. P. Weise & A. Hlngleln. Z. fur Naturforsch.

26A, 1282 (1971).

A. Roche, H. Sutton, D. K. Bobme, H. I. Schlff. J. Chem. Phys. 55

54B0 (1971).

J. A. Burt, J. L. Dunn, H. J. HcEwan, H. H. Sutton, A. E. Roche and

H. I. Schlff. J. Chem. Fhya. 52, 6062 (1970).

A. Ding. 2. fur Saturforsch, 24A, 856 (1969).

D. L. Smith and J. H. Futrell. Int. J. Haas Spectrom. Ion Fhys. 10.,

405 (1972).

G. Gioumousis and D. P. Stevenson. J. Chen. Fbys. 29, 294 (1957).

H. B. Woodward and B. Hoffman. The Conservation of Orbital Symetry.

Academic Press, 1970.

T. F. George and B. 3. Suplinskas. J. Chen. Fhys. 54_, 1037 (1971).

M. H. Cheng, H. Chiang, E. A. Glslason, B. H. Haban, C. H. Tsao and

A. S. Herner. J. Chen. Phys. 52, 5518 (1S70).

-242-

APPENDIX A

THE MATHEMATICAL DESCRIPTION OF RANDOM PROCESSES

In s u p p o r t of the d i scuss ion of pseudorandom modulation p r e s e n t e d

i n Chapter I I , ue have c o l l e c t e d a b r i e f i n t r o d u c t i o n / r e v i e w of t he

d e s c r i p t i o n of random p r o c e s s e s . This d i s c u s s i o n i s by no means c y c l o ­

p e d i c , b u t i s aimed a t def in ing the terms used t o d e s c r i b e random

p r o c e s s e s .

A random p r o c e s s desc r ibes a system whose ou tpu t i s no t d e t e r m i n i s ­

t i c ; g iven a sample record ( t ime h i s t o r y ) of t h e r e s u l t s of a random

phenomenon, i t i s only p o s s i b l e to make p rob ab l i s t i c s t a t ement s conce rn ­

i n g t h e n a t u r e of f u t u r e sample r e c o r d s . The c o l l e c t i o n of a l l p o s s i b l e

sample r e c o r d s from a random phenomenon i s c a l l e d a s t o c h a s t i c p r o c e s s

(random p r o c e s s ) . Thus, i n s t o c h a s t i c t heo ry no d i s t i n c t i o n i s drawn

between t h e phenomenon re spons ib le fo r sample r eco rd genera t ion and the

c o l l e c t i o n of a l l such r eco rds ; t he phenomenon and i t s r e s u l t s a r e from

a s t a t i s t i c a l p o i n t of view i d e n t i c a l .

The e v e n t s of a s t o c h a s t i c p rocess a r e d e s c r i b e d by a random

v a r i a b l e , X, and the process i t s e l f i s denoted by { X ( t ) , t £ T } where

{T} i s an i n d e x s e t desc r ib ing the time v a r i a b l e , { T } can be e i t h e r a

d i s c r e t e o r cont inuous s e t , de sc r ib ing r e s p e c t i v e l y d i s c r e t e o r c o n ­

t inuous pa ramete r p r o c e s s e s .

The space of a l l p o s s i b l e outcomes of t h e p rocess i s c a l l e d t he

sample s p a c e , S:

X ( t ) C S , t C T

-243-

The c o l l e c t i o n of a l l s e t s of even ts ( p a r t i a l sample records) i s

denoted by F , the family of e v e n t s . For many p h y s i c a l p rocesses t he 1 2

sample space i s R and the family of even t s i s B , t he Bore l s e t s .

The random v a r i a b l e X i s r e a l , f i n i t e va lued and de f ined on a l l of S .

A c o l l e c t i o n of sample records of a s t o c h a s t i c p rocess i s an

ensemble. In g e n e r a l , ensemble averages of p r o c e s s p r o p e r t i e s ( s imple

and j o i n t moments) a r e no t n e c e s s a r i l y e q u a l t o t h e corresponding t ime

averaged p r o p e r t i e s .

The o u t p u t of a s t o c h a s t i c process can b e d e s c r i b e d by a p r o b a b i l i t y

l a v ( d i s t r i b u t i o n f u n c t i o n ) . This c h a r a c t e r i z a t i o n may be p resen ted i n

one of s e v e r a l ways (ensemble ave rages ) :

(1) By t h e p r o b a b i l i t y dens i ty func t i on .

x,<X(t ) < t + Ax P. (x - ) = l i m — * x- e s

1 AK*O &X A

which describes the probability that the stochastic output in a small

range surrounding the value K-C s -

(2) By the moments of the distribution, including the mean value

and autocorrelation function:

H

-244-

These are,respectively!the f i r s t simple and jo in t moments. Complete

characterization of a stochastic process requires specification of higher

moments as well.

(3) By spectral density functions which are the Fourier transforms

of simple and jo in t moments ( i . e . the power spectral density function).

in general, each of these measures varies with time. If this i s the

case, the process i s said to be nonstationary. If u and R are time

invariant the process is said to be weakly stationary, while if a l l higher

moments are also time invariant the process (and hence the distribution 3

function) are said to be strongly stat ionary. From a practical stand­point, proof of weak stationarity i s often used to justify an assumption of strong s ta t ionar i ty .

For a stationary (meaning strongly stationary henceforth) stochastic

process, i f the corresponding time averaged properties of the mean and

autocorrelation,

U (k) = lim f X. ( t)dt o

T R** C T ; k ) ° iZ T / \ M V t + T ) d

are equal to the corresponding ensemble averaged (over index k) proper­

t i e s , the process i s said to be ergodic. This i s an important requirement

for characterizing the properties of a stochastic process since i t i s

rarely pract ical to compute ensemble averaged properties. Ergodicity i s

difficult to prove. However, if a process i s self-stationary, i . e .

-245-

properties computed over short time intervals are relatively invariant

with respect to interval choice, then an assumption of stationarily and 3

ergodicity i s j u s t i f i ed .

An equivalent way of specifying the probability density function for

a process i s to use i t s probability law (or cumulative probability den­

si ty function):

P £ Uj> = Prob [X(t)-=xL]

X l P(x )dx .

Two stochastic processes are said to be identical ly distributed i f they

have the same probability lav.

The importance of the above mentioned terminology i s this : random

processes (such as m-sequences or detector outputs) are generally assumed

to be stationary and ergodic. As s t a t i s t i c a l methods are applied to more

complicated physical systems, the systems designer must remain acutely

aware of the assumptions of stationarity and ergodicity as ve i l as the

often made assumption of system l ineari ty. Thus an understanding of the

description of random processes becomes more important as more sophist i ­

cated analytical systems of measurement (such as impulse response deter­

mination) are employed. During our i n i t i a l evaluation of the correlation

TOP system we found the above concepts important and hence their pre­

sentation here.

• /

APPENDIX B

DETECTOR COIHCIDENCE ANALYSIS

I n p r e s e n t i n g t he s t a t i s t i c a l a n a l y s i s of the c o r r e l a t i o n method i n

Chapter I I , a d i s c u s s i o n of the problem of d e t e c t o r p a r a l y s i s r e q u i r e d

the e s t i m a t i o n of the p r o b a b i l i t y t h a t two i o n s a r e de t ec t ed d u r i n g a

s h o r t i n t e r v a l . We p resen t here a d e r i v a t i o n of t h i s p r o b a b i l i t y under

t he assumption of a Gaussian TOP d i s t r i b u t i o n .

We r e c a l l t h a t t he output of t h e TOF sys tem, y ( i r ) i s g iven by t he

convolu t ion of t he TOF response f u n c t i o n , h ( t ) and the inpu t modu la t ion ,

g ( t - T ) :

y(T) = h*g = / h ( t ) g ( t - x ) d t (B - l )

The p r o b a b i l i t y of co inc iden t d e t e c t i o n of t»o p a r t i c l e s du r ing any t ime

i n t e r v a l T i s desc r ibed by the a u t o c o r r e l a t i o n func t ion , R ( T ) , of t h e

system o u t p u t :

By us ing Eq. (B- l ) iu (B-2) ,

T

VT> = i f J d T ' f h ( t , ) Sft'-T')"' M(Og(t-i'«)dt - I i -a

" 5 f / h ^ ' > d t ' / MOdt / g(t ' -T , )g(c-T'+ )dr '

KyyCt) = J h C t ^ d t ' J h ( t ) d t E ( t - t ' + T ) (B-3)

where t he t h i r d e q u a l i t y follows from changing t h e v a r i a b l e of I n t e g r a '

t i o n ( T ' - ^ " * ^ ) and t h e d e f i n i t i o n of t h e a u t o c o r r e l a t i o n funct ion f o r

the i npu t m o d u l a t i o n

T

R ( t - t ' + T ) = J= I g ( - T " ) g ( t - t ' + T - T " ) d T " (B-4) (t-f+T) S ^ f

Ste rn and coworkers have eva lua ted t h i s a u t o c o r r e l a t i o n func t ion a s :

K <-0 - e " 2 o | T ' (B-5)

where m i s t he ave rage zero c ross ing r a t e of t h e modulation f u n c t i o n .

Using t h i s e x p r e s s i o n and an assumption of a Gaussian response func t ion

(not an unreasonab le approximation) t

h(t) = A e - ^ S A 2 < B - 6 >

we can e v a l u a t e t he ou tpu t a u t o c o r r e l a t i o n func t ion a s :

; f . - C t - y 2 / . 2

d t , f e - ( t - t o ) 2 / a 2

e-2m|t-f-B (T) + A 2 f - - ( ' - O / a - • f . - ( " J / a _ - 2 m | t - t ' + t ] d t (B-7)

*T. E. S t e m , A. B laqu ie re and J . Va la t , J . Huc lea r Energy A/B 16_ 499 (1962) .

In a t y p i c a l TOF c o r r e l a t i o n experiment t h e wid th of the TOF func t ion i s

gene ra l l y much g r e a t e r than the width of a u n i t modulation pu l se

( t y p i c a l l y by a f a c t o r of 10-25 for a r e a s o n a b l e l eng th f l i g h t pa th ) :

>»k Using t h i s assumpt ion, we approximate t h e o v e r l a p i n t e g r a l

/h ( t ) e - H ^ I (B-8)

by h ( t ' - T ) * l /m . This approximation fo l lows from the f a c t t h a t t h e

smoothly v a r y i n g response func t ion , h ( t ) , w i l l have an approximately con­

s t a n t v a l u e , h ( t f - T ) over the t ime i n t e r v a l where t he modulat ion a u t o ­

c o r r e l a t i o n func t ion i s nonzero; t h e a u t o c o r r e l a t i o n funct ion i s a p p r o x i ­

mated a s a r e c t a n g l e of h e i g h t 1 and wid th 1/m ( F i g . B - l ) .

Thus

^l. f e - ( f - t 0 ) 2 / a 2

e - ( t ' -T-t o ) 2 /a 2

ID J

m J a 2 (2y 2 -2yT+T 2 ) fly (y = t '-t o)

s A ^ e - T 2 / 2 a 2 f e - 2 / a Z ( y - 1 / 2 ) 2

m J dy

h(t) = Ae- ( , - , ° , 2 / ° 2

-2m|t-t '+ T |

X8L 749-7313

Fig. B-1. Estimating the overlap Integral of the TOF distribution function, h(t) t and the modulation autocorrelation function, R (t) .

R (x) ^ *i e-^2/2a2 ^[^7 - , , - - (B-9)

which i s the desired result for the output autocorrelation. As expected,

this expression is proportional to the square of the scattered s ignal , A,

and depends exponentially on the coincidence interval, T.

Using the values,

E^CT) - 10 J e " W J U " « (B-10)

Evaluating the probability of 2 detector events occurring in 5 usee (the

approximate detector deadtime), we note that the exponent in Eq. (B-10)

will be small (^.05) so that the exponential factor is = equal to 1.

To measure the tota l probability we integrate Eq. (B-10) ,

5 usee 5 2 "* ^ s e c

P - 1 0 3 / e - (T/10- ysec) d T = ; 1 0 3 j dx 0 0

Thus the probability of coincident detection occurring within a 5 usee

interval i s 0.5%. This shows that , given a sufficiently long f l ight path

-251-

and broad modulation bandwidth, deadtime losses of detector signal should

not pose a significant problem in TOP impulse response measurements by

the correlation method.

-252-

APPENDIX C

/ * » » i'OF CORRELATION PROGRAM MONITOR / EDITOR LISTING COMPILED BY / MACHO-B COMPILER

CAF=600 7

00000 0000 0000 00001 3040 DCA SAVEAC 00002 7004 RAL 00003 S005 JMP .1-2 00004 0000 0000 / SAVE FOR ODT LINK 00005 3041 DCA SAVEL 00006 5577 JMP I C400

00020 00021 00022 00023 00024 00025

00026 00027 00030 00031 00033 00033 00034 00035 00036 00037 00040 00041 00042 00043 00044 00045 00046 00047

7300 1041 7010 1040 6001 5400

7000 5026 1000 1074 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000

CLA CLL /RECOVER VALUES BEFORE INTERRUPT TAD SAVEL /AND PROCEED FROM THERE RAR TAD SAVEAC ION JMP 1 0

WAIT,

BIN1A. NBJNIA. THIRD* NBINNO. BINNO. COUNT. INDEX. ADDR. SAVEACj SAVEL. SCANNO. SEGNO. INSTR. HOLDL. HOLDS. CUHADD.

NOP JMP .-1 1000 1074 0 0000 0000 0000 0000 0000 0000 0000 0 0 0 0 0 0

/ ADDRESS OF BIN1 / ADDRESS OF NB1N1

- 2 5 3 -

00101 0001 0001 ooioa 0000 0000 00103 0006 0006

/ CLOCK CODE HERE / DELAY CODE HERE / I PLACES ROTATE FOR DISPLAY / SETUP C*300) HERE

00200 6007 START1. CAF 00201 7300 CLA CLL 00202 4777 JMS D02ER0 00203 3000 3000 / CLEAR DISE 00204 3035 3035 00205 4.777 JMS DO ZERO 00206 1000 1000 / CLEAR ACCl 00207 1167 1167 00210 6337 6337 / CLEAR 01/Ei 00211 4776 JMS TYFX 00212 0233 MESS1 00213 4775 JMS ZDATA 00214 7300 CLft CLL 00215 1101 TAD 101 / SET CLOCK 00216 6336 6336 00217 7300 CLA CLL 00220 1102 TAD 102 / SET DELAY 00221 6332 6332 U0222 7300 CLA CLL 0OE23 1270 TAD A / LOAD CUI 00224 6331 6331 00235 4774 JMS WAITER 00226 7300 CLA CLL 00227 1271 TAD B 00230 6331 6331 00231 6001 ION 00232 5026 JMP WAIT 00233 4007 HESS1* TEXT * G 00234 1737 0-00235 4000 •

00270 00271

3500 7500

A, 8,

3500 7500

/Cfcl CODE / CWI CODE . . . T U R N ON DATA BREAK

l | > j O U U U U s | U u ( > l U U O U ^ U l b U > I U U t > ) C ] O U > j U U ( i . ' U U > ' O U U U O » ' U u u O u U 3 t / t f c - - j co* -oooo>ooo» is -0 ' - uiow«- , »-OLntnOi -» -o*^ ( 1 nc j 1 fc '0^ -JC* )C j« - tJ to to* -OOf f»

i O 3 Ifl W W li 'Z Ti N N N

g n c H I K P I l is igBSHsEiNgggSPsgggggegNSIg

3 0 " •"* I

• T3 TO K 1 m m m m 1 o <n - S H 3 10 H

X6i » » » » » - B O E O S S

- ! H i-i H - ) H W [O *- •- CO

p i j H o n SSM — PI c CO H H Z t l

-255-

00356 3000 BUFF* 3000 00357 0077 X2, 0077 00360 0000 DEP. 0000 00361 0000 GET, 0000 00362 0000 SETX. 0000 00363 0000 RATI. 0000 00364 0000 RAT2, 0000 00365 0000 ROT1. 0000 00366 OL'OO ROT2. 0000 00367 CO 14 TBELV. 0014 00370 0000 TEMPI. 0000 00371 7700 XI. 7700 00372 7742 KX. 7742 00373 4000 NEG. 4000

/ THE DAISY CHAIN INTERRUPT PROCESSOR

00374 0513 00375 2400 00376 1200 00377 2407

00400 6031 00401 7410 00402 521S 00403 6334 00404 7410 00405 5325 00406 5207 00407 6041 00410 5213 00411 6042 00412 5020 00413 7300 00414 5024 00415 6036 00416 6046 00417 6041 00420 S217 00421 6042 00422 1377 00423 7510 00424 5242 00425 3240 00426 1240 00427 1376 00430 7700

KSF / KEYBOARD FLAG? SKP / NO JHP KEYFLG / YESi SERVICE IT 6334 / GO TO OVERFLOW SERVICE ROUTINE SKP JHP 525 JHP UNDEF / UNDEFINED FLAB TSP / CHECK PRINTER FLAG JHP .+3 6042 „r / TCF JHP BACK CLA CLL JHP 24

ACCEPT INPUT CHARACTER AND ECHO

/ TRIM CHAR.

KRB TLS TSF JMP .-1 TCF TAD (-301 SPA JHP QM / NOT A VALID CHARACTER DCA OFFSET TAD OFFSET TAD C-32 / VALID CHARACTER? SMA CLA

-256-

00431 5343 JMP QM / NOT VALID 00438 1260 TAD SLIST 00433 1840 TAD OFFSET / CALCULATE ACTION LIST 00434 3841 DCA 1MSTRR POINTER 00435 1841 TAD 1NSTRR 00436 3S41 DCA INSTHR 00437 5641 JAV I INSTHR 00440 0000 OFFSEI. OUOO 00441 0000 INSIKK. OHOU 0044* 7 j<Ju n-;« CLA CLL 004414 ''• '/ '(D JHS TYPA 00444 0446 MQM 0G445 5020 JMP BACK 00446 4077 M9M. TEXT " ? 00447 3740 *-00450 0000 •

*460

00460 0461 SLIST. 0461 / ADDRESS OF FIRST POINTER 00461 7000 7000 / ODT 00468 8600 8600 / CLASSICAL TOF 00463 8680 8680 / CORRELATION TOF 00464 8760 8760 / DISPLAY 00465 0448 QM / E 00466 0448 QM / F 00467 0448 QM / G 00470 0448 QM / H 00471 0448 QM / I 00478 0448 QM / J 00473 0448 QM / K 00474 0448 QM / L 00475 0448 QM / a 00476 0448 QM / N 00477 0448 QM / 0 00500 0448 QM • P 00501 0448 QM / Q 00S08 0442 QM R 00503 0200 START 1 / S 00504 0448 QM / T 00505 0688 SCAN / U 00506 0448 QM / V 00507 0448 QM / la 00510 0448 QM / X 00511 0442 QM / Y 00518 0448 QM / Z

-257-

/ WAITS FOR PHNG CODE TO MOVE / THROUGH THE DELAY LIME

00S13 OOOO WAITER. OOOO 00514 7300 CLA CLL 0051S 3321 OCA TOAD 00516 2321 I S i TOAD 00517 5316 JMP . - 1 00 520 5713 JHP I WAITER 00521 OOOO TOAD, 0000

/ OVERFLOW SERVICE ROUTINE

00525 6002 10F 0 0 5 2 6 7300 CLA CLL 0 0 5 2 7 1335 TAD 0 0 5 3 0 6331 6331 00531 6 3 3 7 6337 00 532 7300 CLA CLL 0 0 5 3 3 5 7 3 4 •MP I 00534 063ft iCAM 0U535 2400 EAJ &4UO

O0S75 1200 00576 7746 00577 7477

*60C 00600 OOOO NTOTAL/ OOOO 00601 7300 CLA CLL 00602 1031 TAD NBIN1A 00603 1035 TAD COUNT 00604 1432 TAD I THIRD 00605 3033 DCA NBINNO 00606 1037 TAD ADDR 00607 6211 6211 00610 3100 DCA 100 00611 1500 TAD I 100 00612 6201 6201 00613 1433 TAD I NBINNO 00614 3433 DCA I NBINNO 00615 2 0 3 3 ISZ NBINNO 00616 7004 RAL 00617 1433 TAD I NBINNO 00620 3433 DCA I NBINNO 00621 5600 JMP I NTOTAL

-258-

00622 7300 SCAN, CLA CLL 00623 1777 TAD EX 00624 6331 6331 00625 7300 CLA CLL 00626 1267 TAD F 00627 3032 DCA THIRD •0630 1256 TAD CUD 00631 3257 DCA DUM 00632 1265 TAD K4 00633 3263 DCA INDX 00634 3255 NEXTK. DCA TEMP 00635 1264 TAD K3 00636 3266 DCA TIMES 00637 1657 TAD 1 DUM 00640 3255 DCA TEMP 00641 1255 GENERj TAD TEMP 00642 4273 JUS TEST 00643 2255 ISZ TEMP 00644 2266 ISZ TIMES 00645 5241 JMP GENER 00646 7000 NOP 00647 2032 ISZ THIRD 00650 2257 1SZ DUM 00651 2263 ISZ INDX 00652 5234 JMP NEXTK 00653 4776 JMS SIGNAL 00654 5775 JMP SETUP 00655 0000 TEMP. 0000 00656 0660 DUD. L01K 00657 •000 DUB. 0000 00660 2000 L01EC 2000 00661 4000 MID1K. 4000 00662 6000 HIIK, 6000 00663 0000 INDX. •000 00664 6000 K3. 6000 00665 7775 K4. -3 00666 0000 TIMES. 0000 00667 0670 F. AO 00670 0000 AO. 0 00671 0024 Al. 24 00672 OOSO A2> 50

00673 0000 TEST. 0000 00674 3037 DCA ADDK 00675 1320 TAD BITSTR 00676 3321 DCA BIT 00677 3035 DCA COUNT 00 700 1317 TAD Kl 00701 3036 DCA INDEX

/ TRANSFORMATION ROUTINE

-259-00702 1037 00703 0321 00704 7740 0070S 4774 00706 4200 00707 2035 00710 2035 00711 1321 00712 7010 00713 3321 00714 2036 00715 5302 00716 5673

00717 7766 Kl» 00720 1000 BITSTR, 00721 0000 BIT.

TAD ADDR AND BIT SZA CLA CLL JHS TOTAL JMS NTOTAL 1S2. COUNT ISZ COUNT TAD BIT HAH DCA BIT ISZ INDEX JMP TEST1 JMP I TEST

7766 1000 0000

00774 2200 00775 0300 00776 2223 00777 0535

*I000 01000 0000 BINlj 0 /DP AC 01001 0000 0 01002 0000 0 01003 0000 0

/BJN3. T0..BIN30. AND NBIN1 TO NBIN30 FOLLOb

01200 0000 TYPX, 0 01201 7300 CLA CLL 01202 1600 TAD I TYPX 01203 3214 DCA TYPNT 01204 2200 ISZ. TYPX

01205 1614 TYPXlj TAD I TYPNT 01206 7002 7002 01207 4215 JMS TYPY 01210 1614 TAD I npNi 01211 2214 ISZ TYPNT 01212 4215 JMS TYPY 01213 5205 JMP TYPXl 01214 0000 TYPNT*

01215 0000 TYPY, a 01216 02 34 AND IK77 01217 7450 SNA 01220 5600 JMP I IfpX 01221 1235 TAD l'hM37 01222 7440 SUA 01223 522 7 JMP TYPY1 01224 1236 TAD TK2 1 5 01225 4242 JMS TLSX 01226 1237 TAD TK.012: 01227 7510 1YPY1. SPA 01230 1240 TAD TK100 01231 1241 TAD TK237 01232 4242 d«S TLSX 01233 S615 J.'P I TYPY 01234 00 77 TK77> 7 7 01235 7741 TKM37* -37 01236 0215 TK21 5» 215 01237 7653 Th«125» -125 01240 0100 TKIOO, 100 01241 0 2 3 7 TK237. 237

01242 0000 TLSX. 0 01243 6046 TLS 01244 6041 TSF 01245 5244 JBP 01246 6042 TCF 01247 7200 CLA 01250 5642 JMP I TLSX

/ D/A DISPLAY CCNTHOLJ X AXIS AUTOMATICALLY SCALED DYL=6063 D A L = 6 0 5 3 D1X=6054

*1600

01600 7300 DISPLA. CLA CLL 01601 3266 DCA N 01602 1264 TAD STAHT2 01603 7041 CIA 01604 1265 TAD ST0F2 01605 32 72 DCA DIFF 01606 12 72 TAD DIFF 01607 7004 KAL

- 2 6 1 -

0 1 6 1 0 7 4 3 0 S&L 0 1 6 1 1 5 2 1 4 JMP . • 3 0 1 6 1 3 2 2 6 6 ISZ N 0 1 6 1 3 5 S 0 7 JMP . - 4 0 1 6 1 4 7 2 0 0 CLA 0 1 6 1 5 1 2 6 4 STAR. TAD STAhT2 0 1 6 1 6 3 2 6 7 DCA XN 0 1 6 1 7 7 2 0 0 HET. CLA 0 1 6 3 0 1 6 6 7 TAD 1 XN 0 1 6 2 1 6 0 6 3 DYL / C 6 0 6 3 ) LOAD 0 1 6 2 2 7 2 0 0 CLA 0 1 6 2 3 1 2 6 4 TAD STABT2 0 1 6 2 4 7 0 4 1 CIA 0 1 6 2 5 1 2 6 7 TAD XN 0 1 6 2 6 3 2 7 0 DCA XAXFS 0 1 6 2 7 7 1 0 0 CLL 0 1 6 3 0 1 2 6 6 TAD N 0 1 6 3 1 7 0 4 0 Crtfl 0 1 6 3 2 3 2 7 1 DCA NN 0 1 6 3 3 1 2 7 0 TAD XAXFS 0 1 6 3 4 2 2 7 1 S K I P . ISZ NN 0 1 6 3 5 5 2 6 1 JHP ROT 0 1 6 3 6 6 0 5 3 DKL / C6053J LOAD 0 1 6 3 7 6 0 5 4 DIX / « 6 0 5 4 > INTEi 0 1 6 4 0 5 2 4 2 JHP . + 2 0 1 6 4 1 7 7 6 0 7 7 6 0 0 1 6 4 2 7 2 0 0 CLA 0 1 6 4 3 1 2 4 1 TAD . - 2 0 1 6 4 4 3 2 5 1 DCA . + 5 0 1 6 4 5 2 2 5 1 ISZ . + 4 0 1 6 4 6 5 2 4 5 JMP • - 1 0 1 6 4 7 7 2 0 0 CLA 0 1 6 5 0 5 2 5 2 JMP . + 2 0 1 6 5 1 0 0 0 0 0 0 0 0 / INDEX 0 1 6 5 2 1 2 6 S TAD sToPa 0 1 6 5 3 7 0 4 1 CIA 0 1 6 5 4 1 2 6 7 TAD XN 0 1 6 5 5 2 2 6 7 ISZ XN 0 1 6 5 6 7 4 4 0 -S2A 0 1 6 5 7 5 2 1 7 JMP HET 0 1 6 6 0 5 2 1 5 JHP STAB 0 1 6 6 1 7 1 0 0 HOT. CLL 0 1 6 6 2 7 0 0 4 RAL 0 1 6 6 3 5 3 3 4 JHP SKIP 0 1 6 6 4 3 0 0 0 START2. 3 0 0 0 0 1 6 6 5 3 0 3 5 S T 0 P 2 . 3 0 3 5 0 1 6 6 6 0 0 0 0 N. 0 0 0 0 0 1 6 6 7 0 0 0 0 XN. 0 0 0 0 0 1 6 7 0 0 0 0 0 XAXFS. 0 0 0 0 0 1 6 7 1 0 0 0 0 NN. 0 0 0 0 0 1 6 7 2 0 0 0 0 D I F F . 0 0 0 0

» AXIS b'lTH CONTENTS OF XN

-262r

*2200

02200 0000 TOTAL. 0000 02201 7300 CLA CLL 02202 2200 152 TOTAL 02203 1030 TAD BINIA 02204 103S TAD COUNT 02205 1432 IAD I THIKD 02206 3034 OCA BINND 02207 1037 TAD ADDS 02210 6211 6211 02211 3100 DCA 100 02212 1500 TAD I ioo 02213 6201 6201 02214 1434 TAD I BINNO 022 IS 3434 DCA I BINNO 02216 2034 ISZ BINNO 02217 7004 HAL 02220 1434 iALi I ut *ii: • • ; ^ : ' l 3434 n:n 1 lilW 02222 56U0 JIW 1 TOTAL

02223 0000 SIGNAL, 0000 02224 7300 CLA CLL 02225 1377 TAD C-36 02226 3036 DCA INDEX 02227 1030 TAD BIN1A 02230 3034 DCA BINNO 02231 1031 TAD NB1N1A 02232 3033 DCA NBINSO 02233 1433 DSUB, TAD I NBINNO 02234 7041 CIA 02235 1434 TAD I BINNO 02236 3434 DCA I BIMNO 02237 7004 HAL 02240 3257 DCA KEEH 02241 2033 ISZ NB1NN0 02242 2034 ISZ IJINNO 02243 1433 TAD I MBINNO J2244 7040 CriA 02245 1434 TAD 1 BINNO 02246 1257 TAD KEE.° 02247 3434 1JCA I BINNO 02250 7100 CLL 02251 3257 DCA KEEH 02252 2033 152 NBINNO 02253 2034 ISZ BINNO 02254 2036 ISZ INDEX 02255 5233 JMP DSOB 02256 5623 JflP 1 5IGNAL 02257 0000 KEEP, 0000

-263-

02377 7742

02400 0000 ZDATA. 0000 02401 6211 6211 02402 420 7 JriS DOZERO 02403 2000 2000 02404 7777 7777 02405 6S01 6201 02406 5600 JMP I ZDATA

02407 0000 DOZERO. 0000 02410 7300 CLA CLL 02411 6214 6214 /RDF 02412 3242 DCA DATAF 02413 6201 6201 02414 1607 TAD I DOZERO 02415 3237 DCA FIRST 02416 2207 ISZ DOZEttO 02417 1607 TAD 1 DO ZERO 02420 32*0 DCA LAST 02421 1240 TAD LAST 02422 7040 CMA 02423 1237 TAD FIRST 02424 3241 UCA l.MDEAZ 02425 1242 I4L' JJH if-.e 0242 6 7640 St.1 (;Lft -Mlf.i'i 6211 6211 •".'•!£ 30 36:17 DCA I FIRST 02431 2237 ISZ FIRST 02432 7000 SO? 02433 2241 ISZ INDEXZ 02434 5230 JMP .-4 02435 2207 ISZ DOZERO 02436 5607 iMP I DOZERO 02437 0000 FIRST. 0000 02440 0000 LAST. 0000 02441 0000 INDEX2. 0000 02442 0000 DATAF. 0000

/ CLASSICAL TOF MODE

0 2 6 0 0 7 3 0 0 CLA CLL 0 8 6 0 1 1 2 1 0 TAD XK1 0 2 COS 3 6 1 1 DCA I X A l 0 2 6 0 3 1 2 1 2 TAD XK2 0 2 6 0 4 3 6 1 3 DCA I XA2 0 2 6 0 S 1 2 1 2 TAD XK2 0 2 6 0 6 3 6 1 4 DCA I XA3 0 2 6 0 7 5 7 7 7 JMP S T A R T 1 0 2 6 1 0 7 7 0 0 X K 1 , 7 7 0 0 0 2 6 1 1 0 2 7 1 XA1> 0 2 7 1 0 2 6 1 2 7 0 0 0 XK2> 7 0 0 0 0 2 6 1 3 0 6 5 3 XA2j T E H P - 2 0 2 6 1 4 0 7 0 6 XA3» T E S T 1 + 4

/ CORRELATION TOF MODE

0 2 6 2 0 7 3 0 0 CLA C L L 0 2 6 2 1 1 2 3 0 TAD YK1 0 2 6 2 2 3 6 3 1 DCA I YA1 0 2 6 2 3 1 2 3 2 TAD YK2 0 2 6 2 4 3 6 3 3 DCA I YA2 0 2 6 2 5 1 2 3 4 TAD YK3 0 2 6 2 6 3 6 3 5 DCA I YA3 0 2 6 2 7 5 7 7 7 JMP S T A R T 1 0 2 6 3 0 7 5 0 0 Y K l j 7 5 0 0 0 2 6 3 1 0 2 7 1 YA1» 2 7 1 0 2 6 3 2 4 7 7 6 YK2> 4 7 7 6 0 2 6 3 3 0 6 5 3 Y A 2 j T E M P - 2 0 2 6 3 4 4 2 0 0 Y K 3 , 4 2 0 0 0 2 6 3 5 0 7 0 6 YA3»

• 2 7 0 0

T E S T 1 + 4

/ C L E A R

0 3 7 0 0 4 7 7 6 JMS DOZERO 0 2 7 0 1 1 0 7 4 1 0 7 4 0 2 7 0 2 I 1 6 7 1 1 6 7 0 2 7 0 3 5 7 0 4 JMP I • + 1 0 2 7 0 4 0 2 1 2 0 2 1 2

/ ION BEFORE DISPLAY

0 2 7 6 0 6001 ION 02761 5762 JMP 0 2 7 6 2 1600 1600 0<=776 240 7 0 2 7 7 7 0200 00177 0400

- 2 6 5 -

Vartable Address Assignments

A 0 2 7 0 LAST 2 4 4 0 T K 2 3 7 1 2 4 1 ADDS 0 0 3 7 L 0 1 K 0 6 6 0 T K 7 7 1 2 3 4 A 0 0 6 7 0 MESS1 0 2 3 3 T L S X 1 2 4 2 A l 0 6 7 1 MID1K 0 6 6 1 TOAD 0 5 2 1 A 8 0 6 7 2 M M 0 4 4 6 TOTAL 2 2 0 0 B 0 2 7 1 A' 1 6 6 6 T » E L l / 0 3 6 7 BACK 0 0 2 0 sinm 0 0 3 3 T VPNT 1 2 1 4 B1MNO 0 0 3 4 ••:• >U1A 0 0 3 1 TYPX 1 2 0 0 B I N 1 1 0 0 0 - . S ? o: -. TYPX1 1 2 0 5 B I N 1 A 0 0 3 0 rtEXTK 0 6 3 4 TYPY 1 2 1 5 B I T 0 - 9 1 MM 1 6 7 1 nv i i 1 2 2 7 B I T S T H 0 7 2 0 !) TOTAL 0 6 0 0 UNDEF 0 4 0 7 B U F F 0 3 5 6 O F F S E T 0 4 4 0 » A I T 0 0 2 6 COUWT 0 0 3 5 tiM 0 4 4 2 w A I T E R 0 5 1 3 CURADD 0 0 4 7 R A T I 0 3 6 3 AAXFS 1 6 7 0 DATAF 2 4 4 2 R A T 2 0 3 6 4 XA1 2 6 1 1 DEP 0 3 6 0 HET 1 6 1 7 AA<s 2 6 1 3 D 1 F F 1 6 7 2 ROT 1 6 6 1 XA3 2 6 1 4 D I S P L A 1 6 0 0 R 0 T 1 0 3 6 5 XK1 2 6 1 0 D I X 6 0 5 4 R 0 T 2 0 3 6 6 XK2 2 6 1 2 DOZEHO 2 4 0 7 SAUEAC 0 0 4 0 X.M 1 6 6 7 0 S U B 2 2 3 3 SAVEL 0 0 4 1 X I 0 3 7 1 DUD 0 6 5 6 5AX 0 3 1 7 X 2 0 3 5 7 DUM 0 6 5 7 SCAM 0 6 2 2 YAl 2 6 3 1 DXL 6 0 5 3 SCANNO 0 0 4 2 YA2 8 6 3 3 O I L 6 0 6 3 SEGNO 0 0 4 3 YA3 8 6 3 5 E X 0 5 3 5 S E T U P 0 3 0 0 VK1 8 6 3 0 F 0 6 6 7 SETX 0 3 6 2 YK2 3 6 3 2 F I R S T 2 4 3 7 S I G N A L 2 2 2 3 YK3 2 6 3 4 BENEK 0 6 4 1 S K I t ' 1 6 3 4 ZDATA 2 4 0 0 S E T 0 3 6 1 S L I S T 0 4 6 0 ZErtO 0 3 4 5 H I 1 K 0 6 6 2 S f A r i 1 6 1 5 HOLDL 0 0 4 5 i T A R T l 0 2 0 0 HOLDS 0 0 4 6 S I A R T 2 1 6 6 4 INDEX 0 0 3 6 STOPH 1 6 6 5 INDEXZ . 2 4 4 1 TEMP 0 6 5 5 IMDX 0 6 6 3 I S i t f l 0 3 7 0 IMSTft 0 0 4 4 T E S T 0 6 7 3 1NS1KE ! 0 4 4 1 TESri 0 7 0 2 K E E P 2 2 5 7 T H I R D 0 0 3 2 KEYFLG 0 4 1 5 T I K E S 0 6 6 6 KX 0 3 7 2 TKM125 i 1 2 3 7 K l 0 7 1 7 T K M 7 1 2 3 5 K 3 0 6 6 4 T K 1 0 0 1 2 4 0 K 4 0 6 6 5 T K 2 1 5 1 2 3 6

-266-

BIBLIOGRAPHY: TOF CORRELATION SPECTROSCOPY

I_. Theory of Correlation Detection

1. T. E. Stern, A. Blaquiere, and J. Valat. J. Nuclear Energy A/B 16,

499 (1962).

2. F. Hossfeld, R. Amadori and R. Scherm. IAEA, Proceedings of the Panel,

Conference on Instrumentation for Neutron Inelastic Scattering Research,

Vienna, 1970, p. 117.

3. W. Reichardt, F. Gompf, K. U. Beckurts, W. Glaser, G. Ehret and G.

Wilhelmi, Ibid., p.147.

4. R. VonJan and R. Scherm. Nuc. Instr. Hath. 80, 69 (1970).

5. C. Visser, J. Wolleswinkel and J. Los. J. Phys. E 3, 483 (1970).

6. F. Hossfeld and R. Amadori. On Pseudorandom and Markov Sequences

0ptini*2inR Correlation TOF Spectrometry. AEC-JUL-684 FF.

(Very complete list of references—avail, "jle from NTIS.)

7. J. F. Colwell et al.. Nucl. Instr. Meth. 76_, 135 (1969); Nucl. Instr.

Meth. 77, 29 (1970).

8. D. L. Price and K. Skold, Nucl. Instr. Heth. 82, 208 (1970).

9. P. Pellionisz, Nucl. Instr. Meth. 92, 125 (1971).

10. K. Weise, Nucl. Instr. Meth. 9S_, 119 (1972).

11. J. Pearce, Nucl. Instr. Meth. 103, 435 (1972).

12. C. J. Macleod, Int. J. Control 14_, 97 (1971).

-267-

II. Correlation and Random Processes

1. Hewlett Packard Journal, Nov. 1969. (Good Introduction.)

2. J. S. Bendat and A. G. Piersol. Measurement and Analysis of Random

Data. Wiley and Sons, 1966.

3. G. A. Korn. Random Process Simulation and HeaBurements. McGraw-

Hill, 1966.

4. Y. W. Lee Statistical Theory of Communication. Uiley, 1960.

(Very good.)

5. E. Parzen. Stochastic Processes. Holden Day, 1962.

6. P. Kindlemann and E. B. Hooper, Rev. Sci. Instrum. 39, 864 (1968).

7. R. Asch and H. C. Ford, Jr. Rev. Scl. lustrum. 44. 506 (1973).

III. Random Sequences and Generation

1. W. Davies, Control. June 1966, p. 302.

2. F. Bossfeld, S. Amadorl, op. dt. AEC-JDL-684-FF.

3. T. E. Stern and B. Frledland. IRE Trans. Info. Theory IT-S 114 (1959).

4. E. Denert et al.. Hud. Instr. Heth. 91, 327 (1971).

5. G. Wilhelmi and F. Gompf, Hucl. Instr. Heth. 81, 36 (1970).

6. J. Bavel, J. Pays. E 6, 495 (1973).

7. A. C. Davies IEEE Trans. Comput. C20, 270 (1971).

8. H. Zierler. J. Soc. Indust. Appl. Math. .7, 31 (1951).

-268-

Experigental Application of correlation Detection. (See also sany

papers in Section 1.)

Heucron Hoise. WaveB. and Pulse Propagation. U5AEC 1967:

R. Uhrig, H. Ohanian; p. 31S

P. Mayer, E. Garells: p. 333

H. Hara, N. Suda: p. 247

Fourth IAEA Symposium on Heutron Inelastic Scattering. Vol. II,

Copenhagen 1968.

L. Pal et al.: p. 407

F. Gompf et al.: p. 417

V. Hirschy and J. Aldrldge, Rev. Sci. Instr. 42., 381 (1971).

Y. Hurata and A. tzuai, tfucl. Instr. Heth. 87, 261 (1970).

J. Gordon et al., Phys. Lett. 26A, 122 (1968).

K. Skold, Nuc. Instru. Heth. 63, 347 (1968).

K. Skold, Ibid. 63, 114 (1968).

A. Virjo, Ibid. 63, 351 (1968).

F. Bezel and P. Pelltools:. Ibid. 99, 613 (1972).

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ACKNOVLEDGHEHTS

There have been many people who have contributed to the work

described within this thesis. It is a pleasure to acknowledge their

contributions.

It has been a priveledge to work with Professor Bruce Mahan. His

thorough scientific knowledge, independent thought, and resourcefulness

were a constant source of support. While fostering independence in the

work of his associates, he was a leader in che true sense, providing

invaluable advice and caking an active part in the formulation of both

theoretical and experimental ideas.

Thanks to Dr. Keith Gillen and Dr. John Winn for their experimental

Insights and frequent discussions. To Jin Fair, thanks for assistance

in measuring cine of flight distributions with his hard von beam

apparatus. To Ralph Terkovitz, thanks for assistance in implementation

of minicomputer programs.

Thanks to the folks in the Electronics Shops for invaluable dis­

cussion and electronic construction. Hast prominent were Tan Merrick,

Steve Smirega and Phil Eggara.

Thanks to Shirley Ashley for her superior organizational abilities

in preparing the thesis and to Kelly Bamllovic for an excellent typing

job. Thanks also to Hancy Monroe for her unexcelled figure design and

execution.

Special thanks to Professor Howard Shugart for his careful reading

and comments an the thesis, and to all those in the Departcent of

Chemistry and the Inorganic Materials Hesearch Division who

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provided so much support.

This thesis is dedicated to my wife, Patte, whose continual

support and encouragement were so vital in oft-occurring times of

adversity when the easy answer was "throw in the towel".

We gratefully acknowledge the financial support of the U. S.

Atomic Energy Commission (through LBL) under whose sponsorship this

work was undertaken, and support from a national Science Foundation

Tralneeehip.

This thesis is dedicated with the hope that science may continue to find a place for generalises within its ever expanding and more specialized framework.