w

Atomic Energy of Canada. Limited

CALCULATIONS OF FLUX SPECTRA AND

ENERGY DEPOSITION FOR FAST NEUTRONS

by

K.K. MEHTA and P.R. KRY

WMt*th«ll NoeUor Research Esloblishm«n»

Pinawo, Manitoba

S«pt«mber 1969

ÂECU3423

> • 'I ' i i -

ATOMIC ENERGY OF CANADA LIMITED

CALCULATIONS OF FLUX SPECTRA AND

ENERGY DEPOSITION FOR FAST NEUTRONS

by

K.K, Mehta and P.R. Kry

Whitesheil Nuclear Research Kstabl i shmont

Pinawa, Manitoba

September 1969

CALCULATIONS OF FLUX SPECTRA AND

ENERGY DEPOSITION FOR FAST NEUTRONS

by

K.K. Mehta and P . R . Kry

AJBSTRACr

A FORTRAN IV code NEVEMOR has been written utilizing

a multigroup-multiregion method for calculating fast neutron flux

spectra, neutron energy deposition, and foil activations due to fast

neutrons in a heterogeneous lattice cell.

Estimates are made of the effects of using group cross

sections and of homogenizatiorw Non-isotropic elastic scattering of

neutrons off light nuclei (in the laboratory' co-ordinate system) is

considered by applying transport corrections in such cases. Inelastic

scattering is handled by assuming that there is only one state to which

the target nucleus could be excited, except for uranium-238 where detailed

group-to-group cross sections are used.

Values obtained with NEVEMOR for dose rates are compared

with earlier measurements in the WR-1 reactor at low-reactor powers.

The agreement is within 5%, The contribution to the close rates of the

neighbouring fuel cells is also calculated for WR-1. Rer.ults of experiments

in the NRX and NRU reactors also agree well with the values calculated

with NEVEMOR.

Whiteshell Nuclear Research Hstab 1 ishnuT.t

Pinawa, Manitoba

September 1969

AECL-3423

Calcul des spectres de flux et du dépôt énergétique

des neutrons rapides

par K.K. Mehta et P.R. Kry

Résumé

On a écrit NEVEMOR (code FORTRAN IV), en utilisantune méthode multigroupe-multirégion pour calculer les spectresde flux, les dépôts énergétiques et les' lames activantes deneutrons rapides dans une cellule de réseau hétérogène.

Des estimations sont faites en ce qui concerne leseffets de l'utilisation de sections efficaces de groupe etde l'homogénéisation. La diffusion élastique et non-isotropique des neutrons engendrés par des noyaux légers(dans le système de coordonnées du laboratoire) est considéréeen appliquant les corrections de transport employées dans detels cas. La diffusion inélastique est contrôlée en supposantqu'il n'y a.qu'un état auquel le noyau de cible peut êtreexcité, sauf dans le cas de l'uranium 238 pour lequel on utilisedes sections efficaces détaillées, de groupe à groupe.

Les valeurs obtenues avec NEVEMOR pour les débits dedose sont comparées à des mesures effectuées antérieurementdans le réacteur WR-1 a faible puissance. L'accord est de5% au maximum. La contribution aux débits de dose des cellulesde combustible avoisinantes est également calculée pour le WR-1.Les résultats d'expériences effectuées dans les réacteursNRU et NRX sont également en bon accord avec les valeurs calculéesgrâce a NEVEMOR.

L'Energie Atomique du Canada, Limitée

Etablissement de recherches nucléaires de Whiteshell

Pinawa, Manitoba

Septembre 1969

(i)

CONTENTS

Page

1. INTRODUCTION 1

2. THE METHOD 2

2.1 Outline of the Method 22.2 Flux Calculations 52.3 Energy Calculations 102.4 Foil Activations 16

3. USE OF THE PROGRAM NEVEMOR 17

3.1 Options 173.2 Material Identification 193.3 Input Data 213.4 Output 26

4. EFFECTS OF ZONE SIZE AND SCATTERING APPROXIMATIONS 27

4.1 The Effect on the Results of theNumber of Energy Groups 27

4.2 The Effect on the Results of theNumber of Regions 32

4.3 The Effect on the Results ofTransport Corrections 35

4.4 The Effect op. the Results of UsingAveraged Inelastic Scattering Cross Sections 38

5. APPLICATIONS 43

5.1 Whiteshell Reactor No. 1 (WR-1) 435.2 NRU Reactor 525.3 NRX Reactor 53

6 REFERENCES 54

APPENDIX 1 An Outline of Input Data and Available Options 57

APPENDIX 2 Explanation of Notations 60

APPENDIX 3 Normalization Factor ANORM 67

APPENDIX 4 Simplified Flow Chart of NEVEMOR 68

APPENDIX 5 Listing of NEVEMOR 70

APPENDIX 6 Sample Output from NEVEMOR 87

Cii)

FIGURES

Page

1, Comparison of Energy Flux Spectra for Two Cases:K = 51 Groups and K = 26 Groups (for centraldosimetry hole, 1 = 1 ) 28

2, Comparison of Energy Flux Spectra for Two Cases:K = 51 Groups and K = 26 Groups (for moderatorregion, I = 24) 29

3. Comparison of Integrated Flux vs Radius forThree Cases: N = 26, 14 and 9 Regions 33

4. Comparison of Integrated Flux vs Radius forTwo Cases: Forward Scattering Applied, andForward Scattering Not Applied 37

5, Comparison of Energy Flux Spectra for Two Cases:Group-to-Group Cross-Sections used for U-238,and Averaged Cross-Sections used for U-238 (forcentral dosimetry hole, 1 = 1 ) 40

6. Comparison of Energy Flux Spectra for Two Cases:Group-to-Group Cross-Sections used for U-238, andAveraged Cross-Sections used for U-238 (for fuelregion, I = 13) 41

7a. WR-1 Fuel Cell Geometry (stainless steel pressuretube, large calandria tube) 44

7b. WR-1 Fuel Cell Geometry (stainless steel pressuretube, large calandria tube) showing Annular^Regions used in NEVEMOR 45

8. Integrated Flux, Nickel Flux, and Energy Absorbedby Hydrogen vs Radius for WR-1 Fuel Site(stainless steel pressure tube, large calandriatube) 47

9a.. Fapt Neutron Energy Histograms for WR-1 FuelSite (stainless steel pressure tube, largecalandria tube) 48

9b. Fast Neutron Energy Spectra for WR-1 FuelSite (stainless steel pressure tube, largecalandria tube) 49

(iii)

TABLESj

Page

I Comparison of Energy Transferred to VariousMaterials in the Central Dosimetry Hole forK = 51 Groups and K = 26 Groups 30

II Comparison of Various Energy Values forK = 51 Groups and K = 26 Groups 31

III Comparison of Various Energy Values forN = 26, 14 and 9 Regions 34

IV Comparison of Various Quantities for TwoCases: Forward Scattering Applied andForward Scattering Not Applied 36

V Comparison of Energy Transferred to VariousMaterials in the Central Dosimetry Hole forTwo Cases: Group-to-Group Cross-Sections usedfor U-238, and Averaged Cross-Sections usedfor U-238 39

VI Comparison of Various Quantities for Two Cases:Group-to-Group Cross-Sections used for U-238,and Averaged Cross-Sections used for U-238 42

VII Various Energy Values for WR-1 Fuel Site 50

VIII Energy Transferred to Various Materials in theCentral Dosimetry Hole of WR-1 Fuel Site 51

- 1 -

1. INTRODUCTION

Radiation dosimetry is a very complex vet important subject

for many nuclear applications, and various computer programs have been

developed for its analysis. In this report, we explain and discuss the

code NEVEMOR developed during the dosimetry program at Whiteshell

Nuclear Research Establishment.

NEVEMOR is a Fortran IV, G-level computer program, developed

with the aim of computing various quantities related to fast neution

dosimetry in a heterogeneous nuclear reactor. In NEVF.MOR, one considers

a cylindrical lattice cell (a unit cell which repeats itself periodic^ ly

in space), and divides it into homogenized annular regions. The fast

neutron spectrum is then calculated for each region. From this, the

kinetic energy transferred from fast neutrons to each material in each

region is calculated. Radioactivity induced in various fast neutron

activation detectors can also be estimated. The dose rate and the

induced radioactivity can be measured experimentally, thus providing

a check on the calculations.

NEVEMOR is primarily an extension of an Apex language

program EPITHET ' , which uses a multigroup-multiregion method for

calculating flux spectra and neutron absorption at epithermal energies.

NEVEMOR incorporates two modifications applied to EPITHET *' . The first

of these extended the energy range from epithermal to fast neutrons

(0.1 to 10 MeV, for example) by including inelastic scat teri ig in the

calculations. The inelastic scattering reaction is treated as if there

were only one possible channel for such a collision in each energy group,

for each material except uranium-238. For U-23.S a full matrix of sroup-

to-group cross sections is read in. The second major modi(ivat ion was

the inclusion of corrections for forward scattering by light nuclei for

the flux calculations. For systems with uniform spatial distribution

of the sources of neutrons (e.g. fission), i\\i> im>ih i i i .n ion has c.encial 1\

a negligible effect. But, when the sources are cui: •'•nt rated in the inner

- 2 -

regions of the system, the forward scattering*corrections tend to flatten

the flux.

2. THE METHOD

2,1 OUTLINE OF THE METHOD

A cylindrical lattice cell is divided into N arbitrarily

spaced homogenized annular regions numbered from the innermost as 1

to the outermost as N, (N < 30). The neutron energy range considered

(from 10 MeV to some lower energy) is divided into (K-l) arbitrarily

spaced energy groups numbered from the highest as 2 to the lowest as

K, (K < 51), while the first energy group consists of all neutron

energies above 10 MeV. The basic unit for calculations concerning

this system is thus a zone, or the intersection of a group and a

region.

For the first energy group, a spatial flux distribution

is read in and normalized in the program to one source neutron in this

group over the whole cell.

For all other zones, the average neutron flux for each zone

is calculated from the total number of collisions, C. ,,* in that zone,1 ,K

working from the highest to the lowest energy; thus

The number of collisions in each zone is calculated from

the numbers of neutrons entering that zone and the cross sections for

the various reactions (elastic and inelastic scattering and neutron

* See Appendix 2 for explanation of the notations.,

- 3 -

absorption). Neutrons enter a zone from three sources: slowing-down

from higher energy groups in the same region, neutron currents from

adjacent regions, and source neutrons directly from fissions (or any

other source) in that zone.

The source neutrons are automatically given the same spatial

distribution as the flux in group 1, which is given as input data.

Their energy distribution is also given as input data. The neutron

currents from adjacent regions are calculated from conservation equations

involving probabilities of escape from or collision in a zone. Th°

slowing-down from higher groups takes place by two processes: elastic

scattering and inelastic scattering.

From the average neutron flux in each zone, the ki'.etic

energy transferred per second to each material in that zone is calculated

assuming only three types of reaction: elastic scattering, inelastic

scattering and neutron absorption. The total energy given off per

second as gamma rays in inelastic scattering reactions is calculated

by summing over the contribution from each zorc% The net energy flux

out of the lattice cell is calculated from the inward and outward

neutron currents at the cell boundary. The energy removed from the

system by neutrons slowing dowi. past the lower bound of the energy range

is also calculated. The distributed energy is totalled and then balanced

against the energy which is introduced into the svstem by source neutrons,

in order to check energy conservation. Foil activations are calculated

from the average neutron flux in a zone and the input differential

absorption cross sections for the foil.

The entire output is normalized by the factor .WORM* tc

any desired number of kilowatts of U-235 fission energy produced per

centimeter thickness of the lattice cell. The value of WORM depends

upon the fact that the source spectrum is normalized to one neutron

above 10 MeV over the entire lattice cell.

See Appendix 3.

- 4 -

The following assumptions and approximations are made

in NEVEMOR:

(i) The angular distr ibution of neutrons passing through

any surface is cosine-like. This assumption is

reasonable fer a medium whose absorption cross section

is small. Also, deviation from a cosine dis t r ibut ion

is associated with small currents and thus the effects

of such deviations are se l f - l imi t ing .

( i i ) Scattering-up of neutrons in energy is negl igible ,

( i i i ) Regions are homogeneous annuli.

(iv) The lower bound of the f i r s t group is 10 MeV. This

assumption pertains only to the normalization factor

ANORM.

(v) Neutrons in a given zone have a uniform d i s t r i b u t i o n

in space, and a 1/E spectrum in energy, the spectrum

being discont inuous at the group boundar ies . The l /£

spectrum i s a carry-over from the o r i g i n a l program

EPITHET, and i s adequate for p r e s e n t purposes . As

can be seen from the output s p e c t r a , * a 1/E spectrum

is a s a t i s f a c t o r y approximation above 3 MeV. Errors

due t o dev ia t ion from 1/E below t h i s energy a re small

s ince the energy involved i s sma l l e r and the energy

groups are also getting progressively smaller.

(vi) Nuclei have negligible kinetic energy prior to collision

with a neutron.

(vii) Elastic scattering is isotropic in the laboratory

system. At the user's option, however, corrections

for forward scattering by light nuclei for up to four

materials can be automatically applied in the program.

(D, H, C, 0 are the usual nuclei for which this option

is used.) 2 Inelastic scattering, which is important

only for heavy nuclei, is isotropic in the laboratory

system.

* See Section 5.

- 5 -

(viii) There is no inelastic scattering in croup l.

(ix) For all materials except uranium-2:J8, a nucleus can

be excited to only one energy state by a neutron in

a given group. This excited state is taken as a

weighted average cf all possible states. (Alternatively,

one could choose any isotope in placp of U-238 if

necessary cross section data are provided.)

(x) For U-238, the excited states of the nucleus are not

considered directly, but rather group-to-group in-

elastic scattering cross sections arc read in.

(xi) For inelastic scattering calculations, all neutrons

in a group have the average neutron energy of that

group.

(xii) If an absorption takes place the energy transferred

as kinetic energy to the nucleus is just the energy

associated with the motion of the center of mass.

The remainder of the neutron's energy does not contri-

bute to the recoil energy of the nucleus, but eventually

appears as radiation (e.,g., gamma-ray) energy,

2.2 FLUX CALCULATIONS*

The total number of collisions in a zone is the sum of

three terras: the number of neutrons entering the ^one by slowing

down in the same 1 ion (this includes source neutrons), the number

entering through the inner surface of the region, and the number

entering through the outer surface of the region, multiplied by the

respective probabilities of collision for a neutron which enters by

one of these three methods. Hence,

* See Appendix 2 for explanation of the notations.

- 6 -

The inward and outward neutron currents (J. . , and J, ,.) from

the zone (i,k) satisfy the neutron conservation relations, viz.,

and

*J i K = Qi h W| i, + J|-l,k wi,k "*" J i,k "I,»

[2-21

+ d,o - 0,0 r .,

The calculation of the neutron currents from these equations and the

calculation of the nine probabilities (W's) are described in detail in

Reference 1.

In NEVEMOR, Q. , is made up of three terms: elastic andl ,K

inelastic scattering contributions, and a contribution from source

neutrons. The elastic scattering contribution is described in detail

in Reference 1. The number of source neutrons in each group is input

data, which is normalized to 1 neutron above 10 MeV over the whole cell,

and is given the same spatial distribution as the input flux shape for

group 1.

Inelastic scattering is handled by two methods in NEVEMOR.

For U-238, a group-to-group inelastic scattering cross section matrix

is read in. Thus if a?, , is the inelastic scattering cross section

from group k1 to group k, and if K (K ^ K) is the last and the lowestin ID

group for which inelastic scattering cross section data are considered,

the following matrix is read in:

- 7 -

or3,3 3,4

• •

K

These cross sections must be normalized, so that

Kro . Tz. a- - a;h=k! k > it»

the to ta l inelast ic scattering cross section for group k ' . The number

of neutrons slowing down into group k from group k' due to inelastic

scat tering collisions with U-238 is

The second method of dealing with inelast ic scattering is

applicable to a l l materials . The average neutron energy, E, , , in group

k ' , i s defined by

•/En'EdE

E

dEE

loge

L ~ E k '

EK'-1EK"

E L . = = {2mS]

IVhen a neutron of a given energy excites a nucleus in an inelastic

scat ter ing reaction, there are usually several gamma rays the nucleus

might emit. If EY, EY, . . . EY are the energies of the gamma rays1 2 M

- 8 -

which could be emitted, then associated with these are the cross sectionsT T T

a , a , . . . a , for the given incident neutron energy. Thus, for every1 2 m

material, the input data comprise a cross section and a weighted, gamma-

ray energy for each neutron energy group. The cross section used for

a material j and group k1 is

The gamma-ray energy used is the average gamma-ray energy with which

the nucleus decays, i.e.,

r

For U-238, which has the group-to-group cross section matrix,

values of a. ,. are also read in. This is a total cross section for

group k1 neutrons to scatter inelastically to any lower group, even below

group K . To consider inelastic scattering for U-238 across the lowerm j

energy bound K , the program reassigns a new value to a. . ,, viz.,

The second term in the above expression is the sum of all the elements

in (k'-l) row of the matrix, i.e., it is the cross section for group

k' neutrons to" inelasticaliy scatter to any lower group above group

K . Also, all of the available neutron energy (excluding center-of-

mass energy) is assigned to EÏ .,. The assignment is done, because

for all but the lowest energy groups

I Km :

and for the lowest energy groups, if an inelastic scattering reaction

occurs, practically all of the neutron energy is converted into gamma-

ray energy.

If E^, is the initial neutron energy of a group k1 neutron,

- 9 -

its final energy after an inelastic scattering collision with a nucleus

of atonic mass A. will be*J Z

I—i A IE" •" JT^W ^ - -TT7 EJ>

12-61

The neutron is then assu d to end up in group k, if

i—i

Since a l l neutrons which undergo i n e l a s t i c s c a t t e r i n g in a group are

assumed to have the average group energy, the number of neutrons slowing

down into group k from group k ' , if condition 2.7 holds, is

4>i.*' Vi [2.8]

and I. . , = 0 if condition 2.7 does not hold.

Adding all of these contributions together gives

where q. . , , is the number of neutrons elastically scattered into

group k from group k' by the j material in region i.

An important quantity in the calculation of the nine

probabilities is the probability of production of a secondary neutron

in each zone, or, in other words, the number of neutrons in zone (i,!O

which have come from collisions in that zone divided by_ the total collisions

in that zone. The calculation of the number of inelastic scattering

reactions which result in secondary neutrons depends on the method of

handling inelastic scattering. For U-238, the number of secondary

neutrons is proportional to

\ ' (Ek-l/Ek >

See Section 2.3, equation 3.5

- 10 -

For all other materials, ET , ïs significantly greater than a typical

energy group width, so that it is assumed there is no contribution to

secondary neutrons from this method of dealing with inelastic scattering.

Also, as in Reference 1, let the number of elastic scattering collisions

which result in secondary neutrons in zone (i,k) be proportional to

N? . ,. Now, the total number of reactions or collisions with material

j in zone (i,k) is proportional to

Hence, the probability of production of a secondary neutron in zone

(i,k) is 9 j

[2.10]

As part of the optional output of NEVEMOR, one can calculate

a neutron flux energy spectrum averaged over the entire cell. This

average is weighted by the amount of a given material in each regjonsand thus the flux spectrum one calculates is the average flux spectrum

seen by the material in the entire lattice cell. Hence,

[2.11]2. Nj j Vj

2.3 ENERGY CALCULATIONS

Using the notation described in Appendix 2, the equations

governing scattering reactions' are as follows:

Conservation of Energy;

V E c s En +Ej = En + Ej + E 7

- 11 -

where EY = 0 for e last ic scat tering.

Conservation of Momentum;

EJ "" E ) » / A [3.21

and since *E. i s assumed to be zero ,

E c = ' E n / ( A + 1 ) [3.3]

Using the cosine law to transform to the laboratory systenr3 ,/ • v 1 ^

• El - 2ACoSflV. ElI A+l I

If the scattering is isotropic in the center-of-mass system, the averaget t

value of E. is• zir rzir

•E; <e / JI

A+l ' y[3.4]gA('En) I" (At-1) J _ 1

(A+l)2 L 2 A 'EnJ

where equations 3.1, 3.2 and 3.3 have been used.

The second energy of interest in a scattering reactioni i

is E . Using the cosine law to transform to the laboratory system,

•=• [ A2 + 1 "I . A2 + 1 "I .+1)Z J E'

and as before, if the scattering is isotropic in the center-of-massgsystem, the average value of En is

(4^) 13.51

- 12 -

In the case of inelastic scattering off U-238, the final

neutron enerpy is taken as the average energy of the group it scatters

into, i . e . ,

n k n k

if the neutron scatters from group k to group k'. The energy transferred

to the j material in region i by a group k neutron which inelastically

scatters to group k1 is given by

Using equation 3.5, which must be satisfied by Ë, , Ë., » and

i—i

For an absorption reaction, it is assumed that only the

center-of-mass energy appears as kinetic energy of the nucleus, the

remainder of the neutron's initial energy being converted into radiation

energy'. Thus, for an absorption reaction in group k, the energy

transferred to the j material is

- £ - * k [3.73

where equation 3.3 has been used. The energy A.ÏÏ,/(Aj + 1) is classed

under the heading "non-center-of-mass energy in absorption reactions."

The total energy transferred per second to the j material

in region i by group k neutrons is

Summation over k gives the kinetic energy transferred per second to the

j material in the i region.

- 13 -

The total non-center-of-mass energy lost every secondin absorption reactions is

[3.9]

The total neutron energy converted to gamma-ray energy

every second by inelastic scattering is

i,jfk L '»k • i»J Ji^ i»'* •»J<

Here, the contribution, F. . . , made by U-23n is expressed as1 >3 t*

V N „' .e y ,1ui k.k j,k,k

where E! . , , is calculated using equation 3.5.

One other calculation is made concerning slowing-down,

and that is the energy per second which is taken out of the system by

neutrons slowing down past the lower energy bound of the system. As

the group-to-group inelastic scattering cross sections do not extend

below the lowest energy group, this method of dealing with inelastic

scattering does not consider any neutrons slowing down past the lower

energy bound. However, the other method calculates the average

neutron energy after an inelastic scattering reaction in zone (i,k)

and if this is below the energy range, then this energy is considered

lost to the system.. Therefore, the energy lost to the system by this

type of reaction is

= S itkN

I• *J

if 'E' < E,, where equation 3.5 is used to calculate E .

Neutrons also slow down past the lower energy bound of

the system due to elastic scattering collisions. The average energy

loss per second due to neutrons in group 1 slowing down past the lower

energy bound (E..) due to such collisions with the j material in zone

(i,D is

13.10]

[3.11]

[3.12]

- 14 -

:;, -s: dE

(for E, < EK tec. )1 K j

since h(Ev + a.E) is the average final energy with which such neutronsK jleave the system. Integrating,

\ i EKilEK

if Ex

and , , , = o >f Ei > —r

The calculation of the average energy loss per second due to neutrons

in group k (upper energy bound E, A, lower energy bound E,) slowing

down past the lower energy bound of the system by means of elast ic

collisions with the j material in region i , must be broken up into

two cases:

Case I

»-l >

i.j.k

t. N . a. ,.

V. N• i»)

2(1- « ) log (Ej • '

Ek+ a. E

JL + « : * - 2 * !k LK

dE

E

[3.13]

[3.14]

Case II

N

i - l

1 V F log (E. /E

i i l2 ( 1 - ^ )loge

EK~

(1-oME

K

X _ _ L \ - « 2 ( E ,Ek W J M

dEE

[3.15]

- 15 -

As can be seen from Table VII (page 50), the total energy

lost due to neutrons slowing down past the lower energy bound of the

system amounts to about 3% of the total input energy. This energy

could be distributed over various materials according to their mass

number and their macroscopic elastic cross section, say, at 0.1 MeV.

There is one other energy loss to the system and this

is the loss due to neutron leakage from the outer boundary of the

lattice cell. The gross energy fluxes into and out of the cell due to

group k neutron currents are:

" JN,k

The difference between these two fluxes gives the net energy flux

out of the cell every second.

The final distribution of neutron energy is then checked

against the total energy introduced into the system each second by

source neutrons.

For all groups but the first, the energy introduced per

second by source neutrons is S.E . The energy introduced into the

system by group 1 neutrons is calculated by replacing E,, by Ej in

equation 3.13 as this would then give the average energy of the neutrons

which have slowed down past the upper bound of the energy range. Thus,

is the average energy introduced into the system by group 1 neutrons.

- 16 -

2,4 FOIL ACTIVATIONS

Foil activations are calculated quite readily in NEVEMOR

because the neutron flux spectrum in each region is available.

Thus, i f

A ^ A&. . =rr p F- & * log U 4- 2 (A. 0"- . [4.1]

I,J — i j ,1 e ^,2 n f k j , k

then (a. . 10~21*) is the number of atoms activated per foil atom present

per second of irradiation time, where 4> is in cm 2 sec 1 and a is in

barns. \i£\ is the highest energy for which group 1 absorption reactions

are considered. Converting this to disintegrations per second per

milligram of sample per minute of irradiation, the activation becomes

•2* v x 10*3x 6.023 x 10

* (0.025)AT

when the irradiation time is short compared to the half-life of the product

nucleus. Here v is the isotopic abundance, A is the atomic mass of the

foil material atoms, and T is the half-life of the activated isotope.

The activation is also expressed in terms of an effective

flux, <ï>, or more precisely, a fission-spectrum integral flux. ^ If

a is the mean activation cross section for neutrons possessing a Cranberg

prompt fission-neutron energy spectrum, then

- " * ' • ' [4.31

Thus, 4> is calculated from a. . and an input value for a.1 » J

- 17 -

3. USE OF THE PROGRAM NEVEMOR

3.1 OPTIONS

Each problem run in NEVEMOR is controlled by the first

card in the data deck, which contains 40 two-digit integer variables,

forming an array called OPTION. Appendix 1 briefly summarizes what

will be discussed in this section, namely, what each of these 40

variables does.

QPTION(l) controls the input of data for each problem.

A 0 terminates the program. A 1 causes the energy data to be bypassed

so that only the geometry data mujt be read into the program (and possibly

the activation foil data). A 2 reverses this situation by causing the

geometry data to be bypassed, A 3 causes the program to read in both

energy and geometry data. A 4 causes the program to bypass reading

these data, ai well as all the calculations. This last option is

useful because one must specify all the output one wants, which is

impossible with just 40 options. Thus in effect, this option, allows

one to obtain more outputs.

OPTION(2) controls the corrections for forward scattering

by light nuclei. If it is 1 the transport corrections are applied.

If it is 0, they are not.

OPTION(3) controls the output of the data used in the

problem. A 0 suppresses this output; a 1 causes only-the geometry data

to be printed out; a 2 causes only the energy data to be printed out;

while a 3 causes all the data to be printed out.

OPTION(4)9 if 1, causes the program to read in a spatial

neutron flux distribution for group 1, while if 0 causes this distribution

to be automatically set uniform over the whole cell.

OPTION(5) controls the calculated neutron flux output.

- 18 -

A 0 suppresses it. A 1 suppresses the output of neutron flux energy

spectra. A 2 causes neutron flux spectra (per unit energy) to be printed

out for at most six regions. A 3 causes neutron flux spectra (per unit

lethargy) to be printed out for at most six regions. A 4 causes both

types of spectra to be printed out for at most six regions.

OPTION(6) to OPTION(11) specify the regions for which

the flux spectra of OPTION(5) are printed out.

If OPTION(12) is 0, the integrated neutron flux in each

region is not calculated, but if it is 1, this flux is calculated and

printed out as a function of radius.

OPTION(13) to OPTION(15) specify the reference numbers of

those materials for which the weighted average of the neutron flux

spectrum over the cell is calculated and printed out.

OPTION(16), if equal to 1, causes the total energy transferred

to the materials in the lattice cell to be compared with the energy losses

from the system. A 0 suppresses this output.

OPTION(17), if 1, causes the final distribution of neutron

energy to be compared with the initial input energy. A 0 suppresses

this comparison. This option checks energy conservation in the system.

OPTION(18) to OPTION(23) specify the regions for which

the energy transferred per second and the energy transferred per gram

per second are printed out for each material in the region.

OPTION(24) to OPTION(27) specify the reference numbers of

the materials for which the total energy transferred per second through-

out the whole cell is calculated and printed out.

OPTION(28) and OPTION(29) specify the numbers of two regions

which define the boundaries of an annular portion of the lattice cell

for which the total neutron energy transferred per second to all materials

is calculated. The two regions are included in this portion.

If OPTION(30) is 0, the program automatically starts a new

problem so that the activation foil data are not required as input.

- 19 -

When this option is non-zero, its value, Nlf is the number of regions

in which the first foil material appears, (N'^9). The next N] options

then specify these regions. OPTION (SHNj), if 0, sends the program to

a new problem, or specifies the number of regions, N2, the second foil

material appears in, (N^S-Ni). This sequence continues to OPTION(39),

which must either be the last region to contain the last foil material,

or be 0.

OPTION(40) suppresses the output of foil cross sections

if it is 0, and causes this print-out if 1.

3.2 MATERIAL IDENTIFICATION

Up to twenty materials can be handled by NEVEMOR. Each

material is arbitrarily assigned a two-digit number between 1 and

20 inclusive, and all data pertaining to this material are referenced

by this number. MPJ* is a reference number of an activation foil

material, and is non-zero only if it is also a reactor material, in

which case MPJ is equal to the reference number of that material.

The inclusion of a preceding digit enables one to determine

how the material shall be handled in the calculations. This three-digit

identification number is the one read in as MRC(I,J). Thus, the first

digit indicates how to treat the material, and the last two give the

reference number for all pertinent data for that material.

There are four choices for the first digit of a material

identification number. A 0 indicates that the material is to be treated

as a normal constituent of the reactor affecting slowing-down of neutrons

and absorbing fast-neutron energy. A 1 indicates that the material does

not affect eleastic scattering, but that it does absorb energy. This

option is useful for small numbers of heavy atoms for which inelastic

scattering is more important than elastic scattering. Some computing

* See Section 3.3.D

- 20 -

time is saved by use of this option. A 2 indicates that the material

does not contribute to s lowing-dovm of neutrons, but it does absorb energy.

This option saves computing time, but eliminates the usefulness of

energy conservation as a check on the calculations. The option is useful

for calculating the energy transferred per gram to small amounts of a

given material, in different parts of the lattice cell. A 3 indicates

that the material is to be treated as a normal constituent of the reactor,

but in addition the inelastic scattering matrix of group-to-group cross

sections has been assigned to this material. The reference number of

this material must be equal to IMAT.

The full complement of 20 materials can only be used if

one does not use the option of correcting for forward scattering by

light nuclei. This correction introduces 4 new materials which occupy

the reference numbers 17, 18, 19, and 20, corresponding to the materials

occupying the reference numbers 8, 9, 10, and 11, respectively. As

explained in Reference 2, these new materials affect only the spatial

scattering, and not the slowing-down calculation, of the materials that

they are related to. For example, if one wishes to correct for forward

scattering by hydrogen, one could assign its reference number to be 9

and the program would then set up a fictitious material with reference

number 18, which would affect only the assumed isotropic elastic scattering

enough to correct, for the forward scattering by hydrogen nuclei. Therefore,

if one wants to correct for forward scattering by light nuclei for up

to four materials, one assigns these materials the identification numbers

008, 009, 010 and/or Oil; and then one takes the option of including

transport corrections.* One must not, then, assign any data to reference

numbers 17 through 20, as these will be occupied by the new materials.

In other words, NMAT < 16 if transport corrections are applied.

* See Section 3.1.

i l -

3.3 INPUT DATA*

The input data required by NEVEMOR consist of 4 sets

of data cards: Options, Energy, Geometry, and Activation

Foil Detector.

A. The "Option" section consists of one card and contains

40 variables which control the program as mentioned

earlier. Its description is as follows:

OPTION (I) (1 = 1,40)12

fl. ENERGY DATA

This section requires OPTION(1) to be set equal to

2 or 3. The first card contains an arbitrary description

of the energy data, e.g., "51 GROUP HNERGY DATA FOR

NINE MATERIALS INCLUDING INELASTIC MATRIX FOR U-238".

Subsequent cards contain information as to the number

of energy groups, energy bounds of these groups, and

the source spectrum which enters the system. It also

contains cross sections for various reactions of neutrons

with all the reactor materials of interest as well as

gamma-ray energies associated with inelastic scattering

and their respective probabilities. The description

and the list of data cards for this section are as

follows :

(i) TITE(I) (1=1,20)A4

This section contains an arbitrary alphameric description

of the data.

( i i ) EL(1), VK(1), KLM, KIN, IMAT, NMAT, NSOPF10.5 F9.7 13 13 13 13 13

* See Appendix 1 for an outline of this section.

- 22 -

EL(1) is the lower bound of group l, (MeV).

VK(1) is the width of group 1 for absorptions,

i.e., absorptions are considered to take

place only up to a neutron energy of

VK(1)EL(1). VK(1) = 1 is allowed.

KLM is the number of energy groups used,

(KLM<60).

KIN is the lowest and the last group for which

group-to-group inelastic scattering cross

sections are given (O^KIN^KLM).

IMAT is the two-digit reference number for the

material which is to be assigned the group-

to-group inelastic scattering cross sections.*

NMAT is the number of materials for which cross

section data are to be given, (NMAT,.<20) .*

NSOR is the number of energy groups which

virgin fission neutrons or source neutrons

enter, (QsNSORsJCLM).

(iii) EL(K) (K=2,KLM)F10.5

EL(K") is the lower energy bound of group K, (MeV).

(iv) Cross section data for materials . This section

is repeated NMAT times.

(SUBST(MPR(M),L),L=1,4), MPR(Mj), AMASS(MPR(M))A4 12 F8.4

SIGA(MPR(M),K) (K=1,KLM)F10.5

SIGE(MPRO0,K) (K=1,KLM)F10.5

SIGI(MPR(M),K) (K=1,KLM)F10.5

EGAMACMPRCM^K) (tel.KLM)F10.5

* See Section 3.2.

SUBST(MPR(M),L) is an arbitrary alphameric

description of the material, (usually i t s

name),

MPR(M) is a two-digit reference number for tiie

material.*

AMASS(MPR(M)) is the atomic mass of the nuclei of

the material, (in units of neutron mass]»

SIGA(MPR(M),K) is the differential absorption cross

section of the material, (barns).

SIGE(MPR(M),K) is the differential elastic scattering

cross section of the material, (barns).

SIGI(MPR(M),K) is the differential inelastic scattering

cross section of the material as described in

Section 2.2,(barns).

EGAMA(MPR(M),K) is the gamma-ray energy associated

with inelastic scattering of group K neutrons

as described in Section 2.2, (MeV).

Each subsection starts on a new card.

(v) This section requires NSOR > 0o

SOURCE(K) (K=1,NSOR)F10.5

SOURCE(K) i s the number of source neutrons en te r ing

the system in group K,

(v i ) This s e c t i o n r equ i re s KIN > 2.

SIGIN(I) . ( I = l , KIN(KIN-l)/2)F10.5

The a r ray SIGIN** i s the mat r ix of group- to-group

ine l a s t i c scat ter ing cross sections in the order:

a , fl , a , . . . . o - ' „ , rr , a-1 , . . . .2»2 2>3 2,k 2 ' m * ' 3 3 j L |

3' m •*"• 4'Km m m

* See Section 3.2.

** See Section 2.2 and Appendix 2 for notations.

- 24 -

C. GEOMETRY DATA

This s e c t i o n requires OPTION(1) t o be s e t equal

to 1 or 3. The f i r s t card contains an arbi t rary

description of the geometry data, e .g . , "TRANSPORT

CORRECTION APPLIED TO WR-1 GEOMETRY". This section

contains information regarding the number of

annular regions, boundary condition and normalizing

reactor power density. It also l i s t s the outer

radii of a l l the regions, the atomic, densit ies

and the identif icat ion numbers of all the materials

in various regions, and the spat ia l dis tr ibut ion

of input neutron flux. The description and the

l i s t of data cards far this section are as follows:

(i) TITG(I) (1=1,20)

A4

This section contains an arbitrary alphameric

description of the data.

( i i ) N, COJ ENORM

13 F8.6 E14.7

N is the number of annular regions, (O^N^SO).

COJ is the albedo at the boundary of the

la t t ice c e l l , (if COJ<0.001, COJ i 1.)

ENORM is the number of kilowatts of U-235

fission energy produced per centimeter

thickness of the l a t t i ce c e l l . All outputs

are normalized to this number.( i i i ) JL(I) (1=1,N)

13

JL(I) is the number of materials in region I.

If JL(I)>100, then region I has the same

materials and atomic densities as region

(JL(I)-IOO).

- 25 -

(iv) R(I) (1=1,N)F7.4

R(IJ is the outer radius of region I, icmj,

(v) This section is repeated for all regions (I=1,N).

MRC(IfJ), DENS(I,J) (J=1,JL(I))13 F11.9

MRC(I,J) i s t h e t h r e e - d i g i t i d e n t i f i c a t i o n number

of t he J ' m a t e r i a l in reg ion ' , *

DENS(I,J) i s the atomic d e n s i t y of t h i s m a t e r i a l

in reg ion I .

( v i ) T h i s s e c t i o n r e q u i r e s OPTION!4) = 1.

FIN ( I ) (1 = 1,MF7.4

FIN ( I ) i s the neu t ron flux above 10 MeV in region 1

D. ACTIVATION FOIL DATA

This s e c t i o n r e q u i r e s OPTION! M)} t o have a non-nero

v a l u e , and con t a in s i n f o n n a t i o n r e g a r d i n g

a l l t h e f o i l d e t e c t o r s t o be p laced w i t h i n the

r e a c t o r l a t t i c e c e l l . I t c o n s i s t s of t he names and

t h e r e f e r e n c e numbers of the f o i l m a t e r i a l s , t h e i r

n e u t r o n a b s o r p t i o n c r o s s s e c t i o n s , h a l f - l i v e s of

t h e a c t i v a t e d i s o t o p e s , e t c . The d e s c r i p t i o n and

t h e l i s t of da t a ca rds fo r t h i s s e c t i o n a r e as

f o l l o w s :

( i ) ( A L P ( I ) , I = 1 , 9 ) , MPJ, CROSS, TAU, A, AI.

A 4 1 2 F i l ) . S H 1 4 . 7 F 9 . S F 9 . " 7

ALP(I) i s an a rb i t r a ry alphameric descr ip t ion of

the foil ma te r i a l .

MPJ i s the two-digit reference number of the

fo i l ma te r i a l .*

CROSS is the mean absorption cross sec t ion of

the material for neutrons poss- '^iny. a

* See Section 3.2.

- 26 -

Cranberg prompt fission-neutron energy

spectrum, [barns).

TAU is the ha l f - l i fe of the activated species,

(seconds).

A is the atomic mass of the foi l material.

AL is the fractional isotopic abundance,

( i i ) This section requires MPJ=0.

SIGAF(K) (K=1,KLM)F10.5SIGAF(K) is the differential neutron absorption

cross section for the foil material.

Up to five different foil materials can be treated by

NEVEMOR. Sections (i) and (ii) are then repeated the corresponding

number of times.

3.4 OUTPUT

The output of NEVEMOR is very flexible, thus, any or all

the quantities, e.g., fluxes, spectra, energy transferred,

calculated by the program can be output. The choices are

made by the use of the option section. In addition, any

input data can also be output. Following is the list of

possible outputs:

(i) flux spectra (per unit energy and/or unit lethargy)

for at least six regions

(ii) integrated flux (over the entire energy range) vs.

radius

(iii) weighted flux spectra for at least four materials

(iv) total energy transferred to all the materials in

the entire cell

(v) energy flowing out of the cell boundary

(vi) total energy lost due to neutrons slowing down past

the lowest energy bound of the system

(vii) total energy input into the system dut- to source

neutrons

(viii) energy converted intc gamma-ray energy associated

with inelastic scattering

fix) non-center-of-mass* energy in absorption reactions

(x) energy per gram transferred and energy transferred tc

each material for at least six regions

(xi) total energy transferred to at least four materials

(for the entire eel 1)

(xii) total energy transferred within an annulus defined

by two regions

(xi i i activities and effective flux for at least five foil

detectors in various regions

(xiv) any energy, geometry,- or activation foil input data

4. EFFECTS OF ZONK SIZF. AVO SG\TTliRl\G APPROXIMATIONS

4.1 TIE EFFECT!' ON Till: RESULTS 0l: Till. NUMHLU Oi: HNT.RGY URiDPS

Since group cross sections are used in \TVHMOR, there

are always present inherent errors in the calculated values of various

quantities. By increasing the number of groups, and thus decreasing

the size of each group, indefinitely, these errors can be made very

small. However, in practice, the computer time and the computer memory

needed limit this process. The choice of 60 groups in NHVMMOK is a

compromise between these situations.

To estimate the errors due to a finite number of energy

groups (K), two computer runs were made using IVh 11 es!uj 1Î Reactor No. 1

* See Section 2.3.

- 28 -

(A*M xn~U

V)

Il

o

o

»

«24-1O

I-H

X O3 X

Où O

u eV -Hw o-a

CO C

0J

8OU

3

84

10

zoX

10'"-

51 GROUPS

26 GROUPS

ID

NEUTRON ENERGY (M«V)

10

FIGURE 2: Coraparison of Energy Flux Spectra for Two Cases: K - 51 Groups and K = 26 Groups(for moderator region, I -- 24)

- 30 -

TABLE I

.COMPARISON OF

ENERGY TRANSFERRED TO VARIOUS MATERIALS* IN THE CENTRAL DOSIMETRY HOLE

FOR K = 51 GROUPS AND K = 26 GROUPS

Mate r i a l

Hydrogen

Deuterium

Carbon

Oxygen

Aluminum

Iron

Zirconium

Uranium-235

Uranium-238

51 Energy Groups 26 Energy Groups

2.569+

0.884

0.0398

0.0242

0.00829

0.00208

0.00127

0.000216

0.000227

2.571

0.886

0.0397

0.0244

0.00830

0.00209

0.00127

0.000217

6.000227

Difference (%)

+0

+0

-0

+0

+0

+0

0

+0

0

.08

.23

.25

.83

.12

.48

.46

Negligible amounts of various materials were placed in the central

hole (which is empty otherwise) to calculate the energy transferred.

+ All energies given in watts/gram.

- 51 -

TABLE II

COMPARISON OF VARIOUS ENERGY VALUES FOR K = 51 GROUPS AND K = 26 GROUPS

51 Energy Groups 26 Energy Groups Difference

Outward energy flowthrough ce l l boundary'

Energy lost throughlower energy bound

Energy t rans fe r red t omaterials in the entire cell:

HydrogenCarbonU-235U-238

Energy transferred tomaterials outside pressuretube

Computer memory' used

Computer time

8.839t

0.759

16.950

106K

65.17sec

8.921

0.758

17.047

88K

50.69sec

+0.93

-0.13

2.1430.5050.001100.0485

2.1450.5050.00110 .0.0486

+ 0.0900

+ 0.21

+ 0.57

+ All energies given in watts.

- 32 -

(WR-1) geometry data;* one with K = 51, another with K = 26. Except

for group 1, the groups in the latter case were made up by merging two

adjacent groups of the first case. Averaged inelastic cross sections,

instead of group-to-group matrix, are used for U-238 for both the cases.

Output energy spectra for these two cases are compared

in Figures 1 and 2 for two spatial regions. It can be seen from these

that the spectra are very similar for the two cases. It can also be

seen from Tables I and II that all the calculated energy values are the

same within less than one percent.

Thus, it can be concluded, at least for WR--1 geometry,

that for the case of K = 51, the error introduced due to finiteness

of the energy groups is negligible. Alternatively, hardly any advantage

can be gained by increasing the numbers of energy groups to more than

SI.

4.2 THE EFFECT ON TIE RESULTS OF THE NUMBER OF REGIONS

Since NEVEMOR homogenizes each region, inherent errors

in the calculated values of the various quancities are unavoidable.

The magnitude of these errors will depend upon the geometry of the

system and also upon the number of spatial regions the system is divided

into. There may exist an optimum region dimension as suggested by

Askew 5 . The program at present uses a maximum of 30 regions.

To estimate the effects of the number of regions (N),

three computer runs were made using WR-1 geometry data*, with N = 26,

14 and 9 (the number of fuel regions was 8, 4 and 2, respectively).

In all the cases, the region boundaries were the natural boundaries

dictated by the geometry of the fuel channel. The group-to-group

inelastic cross section matrix is used for 0-238 for all the cases.

* See Appendix 6 for geometry data.

- 33 -

,13

(M

eu• s .

cX_lIL

ZOCEh-

UJ

Z

r

—OCD• • •

I

T 1

i i

"1 1 1 1—

\

I i i 1

1

O

•

T

IM -

N -

H'-

\

1

! •

14

9

1

!

•

1

T

-

10 12

RADIUS (cm)

FIGURE 3: Comparison of Integrated Flux vs Radius for Three CasesN = 26, 14 and 9 Regions

- 34 -

TABLE I I I

COMPARISON OF VARIOUS ENERGY VALUES FOR N 26, 14 AND 9 REGIONS

Total energy transferred(watts]

Energy transferred to materialsin central hole (watts/gram)

N = 26

20.388

N = 1 4

20.440

Total energy transferred(watts)

N = 9

20.610

HydrogenDeuteriumCarbonOxygenAluminumIronZirconiumUranium-235Uranium-238

2.5550.8820.03950.02440.008260.002070.001260.0002160.000226

2,4440.8470.03790.02340.007920.001990.001200.0002070.000217

2.2690.7870.03520.02170.007360.001850.001120.0001920.000201

HydrogenCarbonU-235U-238

2.13200.50250.001090.0484

2.12350.50220.001060,0470

2.1760.51640.001010.0444

Energy transferred tomaterials outsidepressure tube

16.942 17.025 17.172

Various outputs are presented in Table I I I .

The to ta l energy transferred to materials in the cell is about the

same for a l l the cases. (This i s because albedo a = 1.) As can be

seen from Figure 3, the integrated flux in the central hole is

decreasing as the mesh gets coarser, and this fact is also reflected

in the amounts of energy transferred to various materials (see Table I I I ) .

I t may be concluded, at least for WR-1 geometry, that as

the number of regions is increased the dose ra te approaches a certain

value, and that 26 regions yield resul ts suff ic ient ly close to th i s

value.

4.3 THE EFFECT ON THE RESULTS OF TRANSPORT CORRECTIONS

The assumption that e l a s t i c scat ter ing is isotropic in the

laboratory coordinate system is adequate for scat ter ing of neutrons off

heavy nuclei (A >> 1). In such cases the laboratory and the centre-of-

mass coordinate systems are close to being iden t i ca l . But as the mass

of the struck nucleus decreases, the assumption becomes less sa t i s fac tory ,

and forward sca t te r ing by l ight nuclei cannot be ignored. In NEVEMOR,

forward sca t t e r ing due to hydrogen, deuterium, carbon, and oxygen is

considered by applying transport corrections.

To estimate the error involved in not considering forward

scat ter ing due to l ight nucle i , two computer runs using WR-1 geometry

data* were made; one with t ransport corrections applied, and the other

without any transport correct ions . For both cases the group-to-group

ine la s t i c cross sections for U-238 were used. From Table IV, i t i s seen

that the t o t a l energy transferred to a l l the materials in the ce l l is

not affected. (This is because albedo a = 1.) Since the neutron sources

( f i s s i l e material) are concentrated in the inner regions of the c e l l ,

* See Appendix 6 for geometry data.

- 36 -

TABLE IV

COMPARISON OF VARIOUS QUANTITIES FOR TWO CASES: FORWARD SCATTERING

APPLIED,, AND FORWARD SCATTERING NOT APPLIED

Forward Scat,Considered

Forward Sca t .Not Considered

Difference (%)

Total energy t ransfer red(watts)

20.388 20.238 -0.74

Outward energy flow throughcell boundary (watts)

8.842 8.041 -9.1

Energy transferred to hydrogen(watts/gram)

Region No.

-

= 1

6

13

24

26

Effective nickel-flux(1013n/cm2.sec)

Region No. ,1

13

26

2.555

2.601

2.136

0.553

0.454

2.694

2.738

2.252

0.531

0.417

+ 5.44

+5.27

+ 5.43

-3.98

-8.15

0.910

0.790

0.134

0.942

0.818

0.124

+3.52

+3.54

-7.46

- 37 -

S t o 1 3

u-vc

OCE

ID

n 1 r ] T

FORWARD SCATTERING APPLIED

G FORWARD SCATTERING NOT APPLIED

10I2L5 S 7

RADIUS (cm)

_L I L8 9 10 12

FIGURE 4: Comparison of Integrated Flux vs Radius for Two Cases:Forward Scattering Applied and Forward Scattering Not Applied

- 38 -

the effect of forward scattering is to enhance the neutron flux in the

outer regions while depressing it in the inner regions (See Figure 4).

This fact is also reflected in the value of the eiu-rgy flow out of the system

at the outer boundary of the cell. The effective nickel-flux and the energy

transferred to various materials, e.g., hydrogen, in different parts

of the cell indicate the same conclusion.

4.4 TIP; EFFECT ON THE RESULTS OF USING AVERAGE!) INELASTIC

SCATTERING CROSS SECTIONS

An incide.it neutron of a given energy excites various

nuclear levels of the target nucleus with different probabilities

through inelastic scattering collision. Subsequently, scattered

neutrons would have an entire spectrum of energy. Thus, for a

rigorous treatment of the slowing-down of neutrons, group-to-group

inelastic cross section matrices should he used (see Section 2.2),

Since these cross sections are cumbersome, such a matrix is used only

for U-238 in NEVEMOR, U-238 being the most important of all the reactor

materials as far as inelastic scattering of neutrons is concerned.

Computer runs were made using KR-1 geometry data* to estimate

errors involved in using averaged cross sections instead of the group-

to-group matrix for U-238. Output energy spectra for these two cases

are compared in Figures 5 and 6 for two sp;i ial regions. The two spectra

are similar except in the region of 0.5 to 1.5 MeV. Also, it can

be seen from Tables V and VI that all the energy values are the same

within less than one percent for the two cases.

Thus, the errors involved in using averaged cross sections

for U-238 in NEVEMOR are small. Since the inelastic scattering cross

section is much larger for U-238 than for any other reactor material,

* See Appendix 6 for geometry data

- 39 -

it cna be concluded that errors due to averaged cross sections for

all other materials are negligibly small.

TABLE V

COMPARISON OF

ENERGY TRANSFERRED TO VARIOUS MATERIALS IN THE CENTRAL DOSIMETRY HOLE

FOR TWO CASES: GROUP-TO-GROUP CROSS SECTIONS USED FOR U-238, AND

AVERAGED CROSS SECl IONS USED FOR U-238

Material

Hydrogen

Deuterium

Carbon

Oxygen

Aluminum

Iron

Zirconium

Uranium-235

Uranium-238

Inelastic ScatteringMatrix Used

2.555+

0.882

0.0395

0.0244

0.00826

0,00207

0.00126

0.000216

0.000226

Averaged CrossSections Used

2.569

0.884

0.0398

0.0242

0.00829

0.00?08

0.00127

0.000216

0.000227

Difference (%)

+ 0.5S

+ 0.23

+ 0.76

-0.82

+ 0.36

+ 0.48

+ 0.79

0

+ 0.44

t All energies given in watts/gram.

GROUP-TO-GROUP MATRIX (5IGIN) USEO

O AVERAGEO CROSS SECTIONS USED

I

o

1010

NEUTRON ENERGY (K'eV)

FIGURE 5: Comparison of Energy Flux Spectra for Two Cases: Group-to-Group Cross-Sections usedfor U-238, and Averaged Cross-Sections used for U-238 (for central dosimetry hole, I

10GROUP-TO-GROUP MATRIX (S 16 IN) USEO

O ÛVERÛGED CROSS SECTIONS USED

i—

10'PL. _

NEUTRON ENERGY (MeVI

FIGURH Comparison of Energy Flux S p e c t r a for Two C a s e s : Group- to-Group C r o s s - S e c t i o n s usedfo r U-258, and Averaged C r o s s - S e c t i o n s used fo r II-238 ( f o r fuel r e g i o n , I = 13)

- 42 -

TABLE VI

COMPARISON OF VARIOUS QUANTITIES FOR TWO CASES: GROUP-TO-GROUP CROSS

SECTIONS.USED FOR U-238, AND AVERAGED CROSS SECTIONS USED FOR U-238

Total energy transferred

Outwardthrough

energy flowcell boundary

Inelastic ScatteringMatrix Used

20.388+

8.842

Averaged CrossSections Used

20.404

8.839

Difference (%)

+0.08

-0.03

Energy los t through 0.756lower energy bound

Energy t ransfer red to mater ia lsin the en t i r e c e l l :

Hydrogen 2.132

Carbon 0.503

U-235 0.00109

U-238 0.0484

Energy Transferred to mater ials 16.942outside pressure tube

Effective Ni-flux(1013n/cm2 .sec):*

Region No. 1

6

24

Computer memory used

Computer time (sec)

0.910

0.933

0.165

106K

72.53

0.759

16.950

+0.40

2.143

0.505

0.00110

0.0485

+0.52

+0.40

+0.92

+0.21

+0.05

0.908

0.931

0.165

104K

65.12

0

0

0

-

_

t All energies given in watts.

- 43 -

5. APPLICATIONS

NEVEMÛR can be used to calculate the fast neutron flux

spectrum and energy transferred from fast neutrons to various materials

in any cylindrical system or approximation thereto. Besides minor

limitations due to various assumptions*, the validity of the calculated

values depends upon two important conditions. Firstly, the system

should be such that homogenization in annular regions does not take the

problem too far away from reality. Secondly, it should be possible

to specify the conditions at the outer boundary of the cell, viz., albedo

and/or incoming neutron currents at the boundary. If the cell geometry

repeats itself periodically to large distances, one can assume albedo

(a) equal to unity. Here large distance means more than three times

the slowing-down distance of the fast neutrons, (about 11 cm in heavy

water).

5.1 WHITES!ELI REACTOR NO. 1 (WR-1)

WR-1 core has a hexagonal lattice with a pitch of 23.5 cm.

Each fuel cell is cylindrical with an effective radius of 12.3359 cms, and its

details are shown in Figure 7u. For such a geometry, homogenization is a

satisfactory approximation, and if the cell under consideration is not at the

periphery of the core, albedo can be assumed to be unity with negligible error

in the results. The energy range from 10 MeV to 0.1 MeU is divided into 50

groups, while neutrons with energy more than 10 MeV belong to group 1.

Various differential neutron cross section data (see Appendix 6) are

derived from References 6 - 12. The fuel cell is divided into 26 annular

regions. See Figure 7b and Appendix 6 for geometry data. For this case,

the transport correction for light nuclei is applied, and the group-to-

group inelastic cross section matrix for 11-238 is used. The results

* See Section 2,1.

- 44 -

Nota ; All diminuons In cmRadii art mtoturti from bundltctntrt ocipt «h«ri otturmit indicated

FIGURE 7a: WR-i Fuel Cell Geometry (stainless steel pressure tube,large calandria tube)

- -45 -

FIGURE 7b: WR-1 Fuel Cell Geometry ( s t a i n l e s s s t e e l p ressure t u b e ,large c a l a n d r i a tube) showing Annular Regions used inNEVEMOR

- 46 -

are normalized to 1.0 kW power produced per 1 cm thickness of the cell

and are presented in the following graphs and tables.

The effective nickel-flux and the integrated flux vs average

radius are presented in Figure 8. Figure 9a shows the histograms of

neutron flux vs energy (group) for the central dosimetry hole, and the

moderator region. Figure 9b shows the same spectra except that here

the ordinate is flux per unit energy obtained by dividing the corresponding

values of Figure 9a by width (AE) of the associated energy group.

Except for those in Figure 9a, all energy spectra in this report are

of the latter type. The dip present in both the spectra at about 0.4 MeV

is due to resonance in the elastic scattering cross section of oxygen

and to a lesser extent of iron.

Table VII lists results of various energy calculations.

Here the 'Total energy input1 is the energy introduced by fast neutrons

from fission into the system. The 'Total final energy' is made up of

all the eventual distributions of the neutron energy, and its equality

to the input energy suggests that the calculations are at least self

consistent. The 'Total energy transferred' is the fast neutron energy

transferred to all the materials in the entire cell. As seen from

Table VII, the majority of the energy is transferred to materials outside

the pressure tube. NEVEMOR also calculates the neutron energy leaving

the cell through the outer boundary. Since albedo is assumed to be unity,

the incoming energy flux at the cell boundary is then equated to this

outgoing energy flux. The 'Energy lost through lower energy bound'

(0.756 watts), for WR-lt amounts to about 3% of the 'Total energy input'.

This energy, as mentioned earlier, should be distributed amongst various

materials according to their mass number and their macroscopic elastic

cross section, say, at 0.1 MeV. However, the 'Non-center-of-inass energy

in absorption reactions' (1.062 watts) is not transferred to materials

as kinetic energy but appears as radiation (e.g., gamma-ray) energy.

Table VIII gives energy absorbed by various materials in the central

dosimetry hole. Variation of energy absorbed by hydrogen (W/g) with

radius is also shown in Figure 8.

k—i

CO

era

n03l — i

83

Q .>-J

C"

f — f

- j -

ra. •

'?,—,

c'Jl

o

rrj«—•

'*/3

i - t

n

oo

=To

oc

X

. - *

r.7T

'—'

-r., .cX

5

o

!—_

OJ |—

i• * ^

33 " » > -

o

, ,r - i

3

QD i

E>

2mj

o_j >

œo33CD

moCD

I

ooom2

o

nm

i

"Tl|—cx

X

HnO

-ni

cX

~ C

O

o

O

NEUTRON FLUX (n/cm2 sec)

t>

t>

t>

oo

o

o

t>

oo

D>

ENERGY ABSORBED BY HYDROGEN (W/g)

CENTRAL HOLE (AIR)- ZIRCONIUMCOOLANT

FUEL+

C00LAN1

-^-COOLANT=—-PRESSURE TUBE (IROW

C O ,

--«-CALANORIA TUBE(ALUMINUM)

O IP10

a.

10'

MODERATOR REGION

(1= 24)

...A I..' J4 5 6NEUTRON ENERGY I M e V l

CENTRAL DOSIMETRV HOLE (1 = 1

i

i

10

FIGURE 9a: Fast Neutron Energy Histograms for WR-1 Fuel Site (stainless steel pressure tube,large calandria tube)

zoŒ

10"

CENTRAI D05IMETRY HOLE [! = I )

\

MOOERATOR REGION

il» 24)" \

I 1 i4 5 6

NEUTRON ENERSV I M i V )

l \10

FIGURE 9b: Fast Neutron tinergy Spectra for IVR-1 Fuel Site (stainless steel pressure tube,large calandria tube)

- 50 -

TABLE VII

VARIOUS ENERGY VALUES FOR WR-1 FUEL SITE

Total energy input 25.214t

Total f ina l energy 25.251§

Total energy transferxed 20.388*

Energy flowing out of c e l l 8.842

Energy flowing into ce l l 8.842 (since i=l)

Energy lost through 0.756*lower energy bound

Non-center-of-mass energy 1.062*in absorption react ions

Gamma-ray energy in 3.045*inelastic scattering

Energy transferred to 16.942materials outside pressure tube

Energy transferred to hydrogen 2.132in the entire cell

Energy transferred to carbon 0.503in the entire cell

t All energies given in watts

§ All asterisked quantities add to give 'Total final energy1

- SI -

TABLE VIII

ENERGY TRANSFERRED TO VARIOUS MATERIALS IN THE CENTRAL

DOSIMETRY HOLE OF WR-1 FUEL SITE

Material

Hydrogen

Deuterium

Carbon

Oxygen

Aluminum

Iron

Zirconium

Uranium-235

Uranium-238

watts/gram

2m

0.

0.

0.

0.

0.

0.

0.

0.

555

882

0395

0244

00826

00207

00126

00021b

000226

- 52 -

From energy absorbed by hydrogen and carbon, one can easily

calculate energy absorbed by cyclohe.xane (CfjHi2). For the central hole,

thi^ is calculated to be 401.7 mW/g (normalized to 1.0 kW/cm reactor

fission power). This value is in good agreement with 384.9 mW/g from

the measurements of M. Tomlinson et al. '3 The difference is less than

5%. Another quantity of interest is the energy absorbed by the organic

coolant*. N'EVEMOR yields a value of 3.184 W/cm per 1.0 kW/cm reactor

p ow e r.

It is also easy to calculate contributions of the adjacent

fuel elements to flux or to dose rates. We have assumed all along that

albedo is unity. This means that the outgoing neutron current is balanced

by the incoming current. Thu incoming neutron current is mads up of

two contributions. The first contribution is due to neutrons originating

in the adjacent fuel elements and entering the cell under consideration

(and not being reflected back). The second contribution is due to neutrons

leaving the cell and being reflected by D-,0 of the adjacent elements

to re-enter the parent cell. Thus, by varying the value of albedo and

the outer radius of the unit cell, the contributions due to neutrons

originating in all the neighbouring fuel elements can be estimated. In

the central dosimetry hole, this contribution to dose rate is only 4.4% in

the case of hydrogen and 4.2% in the case of zirconium. Also, the effective

Ni-flux at this location is increased bv 3o0% due to all the neighbours,

while the integrated flux (from 0.1 to 10 MeV) is increased by 5.5%.

5.2 NRU REACIOR

NEVEMOR lias run for the NRU reactor at Chalk River Nuclear

Laboratory for the case of the fast neutron facility in position G-20

to calculate close rate in cyclohexane. The calculated value is 43.25 mW/g,

while Boyd's luJ experimental value is 47.37 mlV/g (for effective Ni-flux =

1012n/cm2.sec). This is a fairly good agreement considering that the

uncertainty in the CosS activity (effective Ni-flux measurements ) is

* Coolant is assumed to be C H j . ^ with hydrogen content of 8,6 wt%and density = 0.81 g/cm3, (See Ref. 13).

- 53 -

estimated to be ± 5% ! . Also, the value used by Royd for the radiolytic

hydrogen yield from cyclohexane, G(ll2), is somewhat higher. A better

value of G(H2) seems to be 5.0 rather than 5.2 at doses of 5 x ]Q:: uV/n,

(see Figure 10, Reference 15).

5.3 NRX REACTOR

NEVEMOR was also run for the NRX reactor at Chalk River for

the case of an annular uranium rod in a lattice position to calculate

the energy absorbed by cyclohexane (C6H-l2) from the fast neutrons. The

computed value is 40.75 mW/g, which can be compared with Boyd's 15 value

of 46 mW/g (for effective Ni-Flux = 1012n/cm2.sec). Here, again, arguments

similar to the NRU case above can justify the discrepancy between the

calculated value and the experimental value.

- 54 -

6. REFERENCES

1. Driggers , F .E. , A Method of Calculating Neutron Absorptions andFlux Spectra at Epithermal Energiest AECL-1996, Atomic Energy ofCanada Limited, (1964)

2. Ha l sha l l , M.J., Modifications to the Computer Code Epithet,AECL-1996 (Supplement), Atomic Energy of Canada Limited, (1966)

3. Evans, R.D.j, The Atomic Nucleus, Appendix B, McGraw-Hill BookCompany, I n c . , New \ o r k . , (1955)

4. Moteff, J.t Neutron Flux and Spectrun Measurements with Radio-activanta , Nucleonics, 20, 12, p 56, (1962)

5. Askew, J .R . , Mesh Rcauirnnt-ntp for Neutron Transport Calculations,AF.HW-M 760, United Kingdom Atomic Energy Authori ty, (1967)

b. Yif tah , S. and Sieger , M., Unclear Cross Sections, IA-980, I s r ae lAtomic Energy Commission, (1964)

7. Schmidt, J . J . , Neutron Cross Section for Fast Reactor Materials,KFK 120 (EANDC-E-35 11), P a r t I I and P a r t I I I , G e s e l l s c h a r t f t l rKemforschung , Germany, (1962)

8, l l o w e r t o n , R . J . , , Sem-Enpiriaal Neutron Cross Sections, P a r t I I ,UCRL-5351, Lawrence Radiation Laboratory, Univ. of Ca l i fo rn i a ,(1958)

9O Sher, R., Signa Center - Neutron Civs s Section Evaluation Group,Neutron Cross Sections in Zirconiwn, BNL-666, Brookhaven NationalL a b . , N.Y. (1961)

10. S t . ehn , J . R . , G o l d b e r g , M.D. , Magurno , B.A. , W i e n e r - C h a s m a n , R,.,Neutron Cross Sections, Vol 1, S u p p l e m e n t 2 , 2nd E d . , BNL-325,Brookhaven N a t i o n a l L a b . , N.Y. (1964)

1 1 . Kon i jn , J . and Lauber , A . , Cross Section Measurements of the A'i5 8

(n,p) Co 5 8 and Si2'* (nta) % 2 6 Reactions in the Energy Range 2.2 to3.8 MeV, Nuclear Phys ics , £8 , 2, 191, (1963)

12. P a s s e l l , T.O., "The Use of Nickel-58 and Iron-54 as Integratorsof Fast-neutron Flux" Neutron Dosimetry, Proceedings of IAEASymposium at Harwell, Vol. 1, page 501, IAEA, (1963)

13. Tomlinson, M., et a l . , Radiation Energy Absorption in WE-1: Measurementsat Low Power, AECL-2763, Atomic Energy of Canada Limited, (1967)

- 55 -

14o B o y d , A . W . a n d C r o s s , C . , Neutron Flux and Uoainetrij Mean-.in ••(.•>:<.•in an NRU Fast Neutron Facility, U n p u b l i s h e d r e p o r t , CI 2 3 2 ,Atomic Energy of Canada Limited, (i9f>5)

15. Boyd, A.W., e t a l . , Methods of Dosinetry ami Flux Mr uturrr:, .. ' «•»..'Their Application in the NRX Reactor, AliCL-2203, Atomi.: linerjjy ofCanada Limited, (1965)

ACKNOWLEDGEMENT

It is a pleasure to acknowledge the deep interest of

M. Tomlinson in this work, who not only instigated this investigation

but also spent many hours in discussions with both the authors,

We also wish to thank W.G. Unruh for his help in general,

and in particular for making available the energy group cross sections,

- 57 -

APPHXIHX 1

AN a n LINK or- INPUT DATA AND AVAIIAHU. e n IONS

1 . I N P U T DATA

A . O P T I O N ( I ) ( 1 = 1 , 4 0 )12

B . HNHRGY DATA

R e q u i r e s O P T l O N ( l ) = : o r Î

( i ) T . ' T H ( I ) ( 1 = 1 , 2 0 )A4

l i i ) I : L ( 1 ) , V K ( l ' ) , KLM, K I N , IMA I , NMAl , V-.UKF 1 f)„ 5 F ! ' . 7 ! 3 ]7, 1 3 1 3 1 3

( i n ) H L ( K J ( K = 2 , k L M )

F 1 0 . S

( i v ) T h i s s e c t i o n i s r e p e a t e d NMAT t i n e s .

(SUBSTIMRI-MMI ,1.11.= 1 , U . M I ' R ' M ) , AMASS I MIM< • "

C.

A4

S 1 G A ( M P R (F 1 0 . S

S I G l i ' M P R iF 1 0 . . '

S I G I IMI'K!ï i o . r.

I.GAMAf.MPRF 10. "'

(v ) R e q u i r e d

SOURCllk;F 1 0 . S

vi ] Requi r ed

SIG1N( I )F 10. S

GFOMhTRY DATA

R e q u i r e s OPTION!1

( i ) TITG:1)A4

i i ) N,13

M)

Ml

M'

•; \ |

or.

un

i i

<J

- i

FS.

1

i f NSOR

1 f \ 1 N

( ) r 3

i : F' s . 4

! K = 1 , K 1 . M )

I K - 1 . K I . M ,

i K - 1 . K l . M i

! } . - } , > l . M '

' ' '

( K = = ! > N S . » K

' l r l l > ' "

1 M.iRV

1 1 4 . "

( 1 i 1 )

( i v )

JL(I?

=1,N

! 1 = 1 , N " )

ivi M K C i l , . n , lli-NSil,.J) (J=l ,.JL{ I') 1 (1 = 1,N")1 3 M l . il

ivi I Required uni y if OPTION(41 = 1.

M N •. M i - 1 , MY".\

n . A r r i V A ' i I O N F O I L I I A I A

R e q u i r e s O P T l O N i . i O i t u , a n d r e p e a t e d f o r t h e n u m b e r

o f d i f f e r e n t f o i l ::.at r r i a i - .

( i t I AI.P. 1) , 1 = 1 , ' J : , MP.i, CRUS- . , r lAII , A, AL

Al 111 I K ' T. 1 1 1 . " [;t.i. " l-"ii.™

( i i ) Requ i rev.1 on l> i f MP.I - d .

S K ; A l ; ' k i i K - l . K l . M l

OFl'IQXS

OI'T I ON ( 1

O P T I O N ( 2 )

OPTION (.3")

OPTI O N ( 4 )

O P T I O N ( 5 )

0: l.nd ot pros',ram

1: New i;eoi:it.'t r\ d a t a only

2: New energy d a t a on 1 >•

3: Al 1 new dat a

4: No geonu-'trv or energy d a t a , c a l c u l a t i o n sbypassed

U: T r a n s p o r t c o r r e c t i o n s not a p p l i e d

I : T r a n s p o r t c o r r e c t i o n s a p p l i e d

0: No d a t a output

1: Geometry da t a ou tpu t only

2: Lneryy d a t a output only

3 : Al1 d a t a output

0: Uniform f lux assumed

1: F lux shape fed in

0: No f l u x out [nit

1: No f l u x p e r u n i t l e t h a r g y or energyo u t p u t

- S 9 -

0PTI0N(6 t o 11)

OPTION(12)

OPTION ( H to IS)

OPTION(16)

OPTION(17)

OPTION(18 to 23)

OPTION(24 to 27)

OPTION(28)

2 : F l u \ p r r n i ; ! T ' - n e i v . • • • . . - i t p : ; t

3 : F l u x p e r n u i t l e t h a r v . y o u t p u t

4 : F l u x p e r u n i t let har , ;v ,iml u n i te n e r g y mit put

= I : R e g i o n - n u m b e r s fo r wh ich f l u x s p e c t r aa r e o u t p u t

= 0 ; I n t e g r a t e d f l ux v s . r a d i u s i s noto u t p u t

1: I n t e g r a t e d flu.x v s . r a d i u s '-- uni put

= MP : M a t e r i a l s t o w!n>\i f l u x : mwe i j;h t i'il and i s nut put

= 0 : K i n e t i c e n e r g y t r a n s i ' e r r e d not comparedt o e n e r g y l u s s e - ;

1: K i n e t i c enen. ;y t r a n s f e r r e d comparedt o e n e r g y ]o . ; s e s

= 0 : l ine r jjy b a l a n c e not done

1: I iner^y b a l a n c e done

= I : R e g i o n - n u m b e r s f o r w h i c h e n e r g y / ^ r a n .t r a n s f e r r e d and t o t a l e n e r g y t r a n s -f e r r e d f o r each m a t e r i a l a r : o u t p u t

= MP : M a t e r i a l s f o r winch t o t a l k i n e t i ce n e r g y t r a n s f e r r e d c a l c u l a t e d ando u t p u t

= I . \ „mm

Total iMierj'.y t r ans f e r r ed between

tliese l imi t s is ca ! m l at eilmax

= 0 : No fo i 1 t realed

= IO P T I O N ( 2 9 )

OPT I O N ( 3 D )

= Ni : N u m b e r o f r e g i o n s t h e f i r s tm a t e r i a 1 a p p e a r - - i n , ! \ ;

O P T 1 O N ( 3 1 t o ( .'SO+N i ) ) = I : R e g i o n - m i n i u - i - * ; i n w h i J i t l i ef o i 1 m a t i.'r i a 1 a p p e a r s

= 0 : No f u r t h e r f o i l s t r e a t e dOPTION(31+Nj'

= N . : N u m b e r o f re^ioir- ' h e -.i-i'oiul toilm a t e r i a 1 ajiptar-- i n , ( \ '"--'• >

O P T I O N f 3 2 + N , ) t o ( 3 1 + N j + N ; ) - I: I- ei; î o: -irimb. r- 1 1 • w : ;

OPTION(32+Nj+N;)

„„. etc.

OPT ION(40)

the1 s e c o n d f o i l m a t e r i a l a p p e a r s

= 0 , o r N , ('-' ',"-*•• y-

= 0: I - ' o i 1 n v . •• • '> t i i i - / - . i r - M i l . ' U !

I ; l u i 1 , r - •• • • • i l l •;; . m m i t ; . i t

- 60 -

APPENDIX

EXPLANATION OF NOTATIONS

1. NOTATIONS USF.D IN THE REPORT

Subscripts

J

k

Variables

A

c.

the subscripted quantity refers to region i.

the subscripted quantity refers to material j.

the subscripted quantity refers to group k.

atomic mass of a nucleus tin units of neutron mass),

the minimum fractional energy remaining with a

neutron after an elastic scattering reaction with

the j material.

the factor which normalizes the calculations to one

neutron in group 1 over the whole lattice cell,

number of collisions in zone (i,k) every second,

(sec"1).

lower energy bound of group k, (MeV).

average energy of neutrons in group k, (MeV).

an energy, (MeV);

Superscripts

p_rec£ding_ apostrophe ( !E): energy measured re la t ive

to the laboratory co-ordinate system,

absence_ of_th_is_ j>up_ers£rip£ (E) : energy measured

relative to the center-of-mass co-ordinate system,

£p2_l£win^ ap£stxrophe (E1): energy after a col l i s ion,

abs_enc£ of_this_ superscript (E) : energy before

the coll is ion,

bar_ oyer_E_(Ë) : average value of E,

y_ (E ) : energy associated with a gamma ray,

- (il -

Subscripts

j_(H.): kinetic energy associated witli a nucleus

of material j ,

n_(F. J : kinetic energy associated with a neutron,

c_(T:): energy associated with the motion of the

center-of-mass in the laboratory system.

H. , , , gamma-ray energy associated with an inelasticJ ,K , K

scattering of a group k neutron into group k' off

material j„

E. , ,, average kinetic energy transferred to a nucleus-1 • ' rh

of the j material due to group K neutron

inelastically scattering into group k' (as

measured in the laboratory co-ordinate system).

E. . , kinetic energy transferred to the j material in1 J J y K

region i from group k neutrons.F. . , gamma-ray energy associated with inelastic scattering

reactions of group k neutrons in region i with

material j which has group-to-group cross sections.

E energy lost to the system due to neutrons inelast-

ically scattering below the lower energy bound of

the system.

I:.' . eiiergv lost to the system due to group k neutrons1>J> ' til

elastically scattering off the j material inregion i below the lower energy bound of the system.

E', gross energy flux due to group k neutron currentK

at outer cell boundary;

x +: radially outward

x - : radially inward

F. input flux in group 1, region i.

4). average neutron flux m r.one (i.k), (cm 'sec ' ) .

tj,. average neutron flux in group k weighted to the

amount of material j in each region, (cm • sec ' ) .

I. . , number of group k' neutrons inelastically scatteringoff the i1"1 material into group k in region i per

orÏ , , second, (sec"1.).

- 62 -

,1. group k neutron current at the outer surface of1 j K

region i, (sec M .

+ superscript refers to the radially outward current,

- superscript refers to the radially inward current.

K number of energy groups considered.

K the last and the lowest group for which group-to-

group inelastic scattering cross sections are given,

first energy group consists of all neutron energies

above Ei. The number of absorptions in this group

would then be infinite unless some upper limit were

chosen. This upper limit for absorptions in group

one is ^E;, where „ is chosen to correspond to the

absorption cross section used.

N number of homogenised annular regions.

N. . atomic density of the j material in region i,2 u atoms/cm?).

N. . , number which is proportional to the number of1 » .1 > Kreactions or collisions per second o f a group k

th -1neutron with the j ' material in region i, (sec L).

x ~ I: inelastic scattering reaction which

leaves the neutron in group k.

x ; s: elastic scattering collision which leaves

the neutron in group k.

x = c: any reaction or collision.

q. • i,, i, number of group k' neutrons elastically scattering

off the j ' material into group k in region i per

second, (sec"1).

Q- , number of neutrons entering zone (i,k) due to

scattering collisions in higher groups in region

i, and due to sources in region i every second,

(sec"1).S. , number of source neutrons produced in zone (i,k)

* _

every second, (sec 1 ) .

S, number of source neutrons in group k produced every

second over the whole cell, (sec"1).

- 63 -

Ci. i t. microscopic cross section for a group k1 neutron

to inelastically scatter off material j into group

k, (barn) .x

o- k microscopic cross section tor a reaction x between

a group k neutron and material j , (barn).

x = E: elastic scattering

x H I : inelastic scattering

x - A: absorption of a neutron

x - t : any reaction

Y]- ,. macroscopic to ta l cross section in zone ( i . k ) ,

(cm"1).

8 neutron scat ter ing angle measured in the center-

of-mass co-ordinate system.

V. volume of region i , (cm3).X V

W.'[ the probability that a neutron which enters zone1 ,K

(i,k) by process x will undergo event y.

x = v: a scattering reaction in a higher group,

or a source, in region i.

x ; d: through the inner boundary of region i.

x = o: through the outer boundary of region i.

y ; v: a collision in zone (i,k).

y ; d: leaves through the inner boundary of

region i0

y = o: leaves through the outer boundary of

region i.2. VARIABLES USED IN THE PROGRAM

A* atomic mass of foil atoms.

ABSE neutron absorptions in group !„

This variable is also used as a dummy variable elsewhere in theprogram.

- 64 -

AL*

ALP

ALPHA [A)

AMASS(M)

AND RM

CMl\

COJ

CROSS

CS1(M)

D E N S ( I , J )

EBAR(K)

EEL

EEX

EGAMA(M.K)

EGAMT

EL(K)

ENIN

ETRAN(M.I)

ET RAT

F I N ( I )

I MAT

J J ( 2 , I )

J L ( I )

KIN

fractional isotopic abundance.

alphameric description of foil data.

maximum fraction of energy left to a neutron after

scattering e las t ica l ly from material Mo

atomic mass of material M.

normalization factor.

conversion factor from MeV to watt-sec.

neutron albedo of the material around the ce l l ,

mean neutron absorption cross section of foil

material.

average logarithmic decrement associated with

material M.

atomic density of the J material in region 1.

average energy of neutrons in group K.

energy flux through the lowest energy bound.

non-centre-of-mass energy in absorption reaction.

average gamma-ray energy due to ine las t ic scat tering

of group K neutron off material M.

tota l gamma-ray energy due to ine las t ic scat ter ing.

lower energy bound of group K.

source neutron energy entering the system.

neutron energy transferred as kinetic energy to

material M in region 1.

total kinetic energy transferred to a l l the materials

in the ce l l .

input group 1 neutron flux in region I.

material to which SIGIN is assigned.

neutron in-current at the I surface.

neutron out-current at the I surface.

number of materials in region I , (JL(I) .? 20).

If JL(I) > 100, then LIKE(I) = (JL(I)-IOO) is

the region which I duplicates.

lowest energy group for which group-to-group ine las t i c

scattering cross sections are assigned.

* This variable is also used as a dummy variable elsewhere in theprogram.

KLM number of energy g r o u p s ,

MPJ m a t e r i a l r e f e r e n c e number of f o i l m a t e r i a l ,

MRC[I,J) material identification number for the J material

in region I,

N number of regions.

NSOR number of energy groups i n t o which s o u r c e neu t rons

e n t e r .

OPTION(I) one of 40 o p t i o n s .

PHI( I ,K) a v e r a g e neu t ron flu.x in r.one ( I , K ) .

PIUH(K) f l u x pe r u n i t energy in zone ( I , K ) .

PHTK(I) i n t e g r a t e d f lux in r e g i o n 1,

PIIIL(K) f l u x p e r un i t l e t h a r g y in zone (_ 1,K).

PHIW(K] weigh ted average f lux with r e s p e c t t o a m a t e r i a l

component.

QF(I) number of neu t rons e n t e r i n g zone ( I ,K) due t o

s c a t t e r i n g c o l l i s i o n s In h i g h e r groups in region I ,

and due t o sou rce s in reg ion I .

R( I") o u t e r r a d i u s of r e g i o n !„

S ( I ) o u t e r s u r f a c e a rea of reg ion I .

SEL net energy f lux at t h e ou t e r boundary of the l a t t i c e

c e l l .

SELI g r o s s energv flux i n t o the c e l l at the o u t e r boundary

of t h e l a t t ice eel 1

SELO g r o s s energy f l u x out of the c e l l at the ou te r

boundary of t h e l a t t i c e c e l l .

SIGA(M,K) a b s o r p t i o n c r o s s s e c t i o n for m a t e r i a l M for neu t rons

in group K.

SIGAF(K) a b s o r p t i o n c ross s e c t i o n for f o i l m a t e r i a l for

n e u t r o n s in group K.

SIGAT(I) macroscopic a b s o r p t i o n and i n e l a s t i c s c a t t e r i n g

c r o s s s e c t i o n for n e u t r o n s in zone ( I , k ) ,

SIGE(M.K) e l a s t i c s c a t t e r i n g c r o s s s e c t i o n fo r m a t e r i a l M

f o r neu t rons in group K.

- 66 -

SIGET(l)

SIGI(M,K)

SI GIN IN'I

SIGSUM(K)

SIGTT(I,K)

ST(I.K)

SOURCE(K)

SPDL

SRAV

TAU

TCOL

TSCOL

TITE

TITG

WXY

macroscopic elastic scattering cross section for

neutrons in zone (I,K).

inelastic scattering cross section for material

M for neutron in group K. When the neutron undergoes

an inelastic scattering reactiont it loses any energy

EGAMA(M,K) to a gamma ray.

inelastic scattering cross section data in the

order o , J . c , . .2 > N x N 3 » 'J 3 » 'I

GKIN,KIN-^3,KIN' ak

KIN

E -macroscopic total cros.. section for neutrons in

zone (I,K).

number of source neutrons entering group K.

slowing down density at the lower bound o: group 1.

total number of source neutrons entering zone (I,K).

half-life of an activated foil atonu

proportional to total number of collisions in

zone (I,K1,

proportional to total number of collisions in zone

(IjK) causing secondary- neutrons.

alphameric description of energy data.

alphameric description of geometry data.

the probability that if a neutron undergoes a

process X it will undergo an event Y

X H 0: enter zone (I,K) from outer surface.

X = I: enter zone (I,K) from inner surface.

X î V: enter zone (I,K) due to a fission or

collision in region 1»

Y : 0: leave region I by outer surface.

Y = I: leave region I by inner surface.

Y = V: a collision in zone (I,K).

- 67 -

APPENDIX 3

NORMALIZATION FACTOR ANORM

If E. is the U-235 fission-energy per fission and v is

the average number of neutrons produced per fission, then EJv is the

fission energy per virgin fission-neutron. If S is the number of

virgin fission-neutrons per second per centimetre thickness of

lattice cell,) then SE_/v is the U-235 fission-power produced per

centimetre thickness of lattice cell. If one wishes to normalize

the results of the reactor calculations to x kilowatts of U-235 fission-

power per centiirietei thickness of lattice cell, one then multiplies

the results by the factor

ANORM = v-gv i i. , vrhere E~ is in kilojoules.

For NEVEMOR, S is calculated assuming a virgin fission-

neutron spectrum1-2 , F(E), defined by

F(E) = exp (-E/0.965) sinh /(2.29E) ,

which is normalized to one fission-neutron above 10 YieV per centimetre

thickness of the lattice cell»

- 68 -

APPENDIX 4

SIMPLIFIED FLOW CHART OF NEVEMOR

\ IF OPT'ONUI.Jotî

CALCULATIONS

OfRT«IN!Na TO

E4CM BEOION:

5 , v , 4 V B , » C E L

y<f J L ( 1 1

\

•h

\

> i o

/

' i E T u P R E 01

j \ TO SE

/ T O REÊI

/ JL III -

IOEN'

ON

1 0 0

L

0 ^/

X

0 H I

J

1tk

\ /\ IN?UT /

' \ OENS U, J ] /

\ MRC I I . J 1 /\ /

r' / I F O P T I O N I Î I M /

AET JP FICTITIOUS/ • . U T E O I A L S FOB /

/ T R A N S P O R T /

/coBnecTio«s /

I N I T I A U I I » U

P2RTINENT

BC'ORC 9TARTIN0

CALCULATIONS

0 0 •<

CALCUi ATE

Q U I N T I I I E ; RELS'ED

TT GROUP I

NEUTRONS S L O « .

1 0 DOWN DUE T 0

ELASTIC SCATTIRINQ

(SOOJIt, Jl I

CALLAVENS (N,rt ,«IN, "

WrttCHCUIATE3 NEUTRONS '

.OWING Ù 0 4 NNTO QROUP

CALCULATE

EN IN

ADO SOURCE NEJT

SONS TO OF ' p

'AtCULATE NEUTP.ONS

1LO«INI1 0 0 * N

INTO 3N0'jP I

CALCULATERENO i j9 ,

THE NORMALIZATION

TO ONE NEUTBON

ABOVE 10 "11

I CALL/LENOSI lN.COJ,

/HOPE, « I WK.CM\CALCULATt5 NEUTRON\ CURRENT^ AND

PROBABILITIES/VCâLÎULATE

AVERAGE NCUTRON

* LU'- , PMI ( I , P» I .

ANO J I L I , « t i O

NORMAL IJE

THE F L Ul

IN «IIOUP I

- 69 -

r~S57

Y

^OPTION (91 =0

ICALCuiATE THE 1iENERGY PER SECOND \

5 1 * TRANSFERRED TO ONII — ' SRAM OF E VE R V k

* MATERIAL FOB ATMOST 6 REGIONS

E.NIROY/5EC GMTRANSFERRED,

"" ETfWN I MP. 11FOR AI

M05T 6. REGIONS ;

. O P T I O N ( 1 2 ) • 0

AN (MP 1)

O J T P J T

\ THE ENEROY

^ JUST

CALCULATED

SUM OVER THCWHOLE CELL rHtENERGY TRANSFERWC

' TCI EACH OF AT MOST4 MATERIALS

! CALCULATE THE

INTEGRATES NCUTRO^

FLUX IN EACH |REGION I

\ FLUI

* fc 0

v S

l A i

EVRAN

1

E

O P 1

. C U L O '

( MPEEx

TflflT

r

ION lifi i

t

. 1 1

CALfULATE THEFLUX PER UNIT

V

--RTIOM 'EQUALS

0

! TOTAL FAST NEUTRONENERGY TRANSFERORTO MATERIAL* 'M THfAN^UluS DCFINET B'r H f S F O P T I O N * . I»;

T I 0 N I 5 ' • ? > * " LETHARGY FOR

AT MOST 6 REGIONS\ / PHIL ( K ) j

CALCULATE THEGROUP ! COTO ENIN. CEEL.SE_

CALCULAIT THE

FLUX PER UNIT

ENERGY FOR I T

MOST 8 REGIONS.PHIC ( K )

OUTPUT

PHIL 1«)

OUTPUT

CTRAT

SELO

\ SE L IS C L

\ e t L• 1

OPTlON(Sl i3

CALCULATE THl ,

i MATERIAL -WCIOHTEDl

! AVIRAOt FLUX, j

PWIWIK I .FOR ALL IMATERIAL? RC0UE3TH)

\ OUTPUT ,

\ PHIW ( K )

ERAP |K I

\ OPTlON(l7)rO > •

CALCULATEEGAMT,ENOUT

OUTPUT '

EN I N /

EN OUT il—

EOAMT iE e x

' THERE IS •

A TOIL TO BE

- TRE4TE0 .

INPUT

FOIL

•ATA

C A L C U I.ATEACTIVATION

IN EACH RCQICHSPECIFIED

OUT PUT

ACTIVATIONS

J

- 70 -

APPENDIX 5

LISTING OF NEVEMOR

cool

,002

Q003

0004

00050006000700060009001000110012

001300140015001600170018001900200021002200230024002500260027002800290030003100320033003400350036003700380039004000410042004300440045004600470048004900500051

COMMUN/ALL/OPT I UN(40 ) , V ( 30 » iQFI 30 I

COMMON/LFN/Rt 30 I , S ( 3 0 ) , T ( 30 ) f J J t 2 , 30 1 t WVV ( 30 ) , WOVI 30 1 ,WI VCÎ0I ,1S1GTTI 30,60)CCMMON/KAV/VM 60) .UV160) , LIKE( 30» . JLI30I ,MRCO0,20) ,TFNS< 30,?0l ,

1 S I G 1 N ( 1 8 0 0 ) , S I G Ê ( 2 C , 6 0 ) , E B A R < 6 0 ) , EGAMA<20,60 I,SDUJ(30,20 ! ,2PHI(30.c.0l,4LPMA!2C)tAMASS<2C)fSlGI(20i60).CSI(20)DIME Ni I UN tL(60),SÎGA<20,60l,SIGSUM(60),AVR(30),F IN<30)iSOURCE(60)

l,TITEI2OI,r!TG(20l,SIGAT(30>,SIGET<3O),PHlKMO),PHIt(6Ol,PHIrf(ft0),2tTPANl 20,30 ) .SFGAFI 601 , A LP ( 9 ) , SUBST ( 2C , 4 ), 5UB ( 4 ) , MPR < ?0 I , PH I L ( b"> IRfcAL*4 JJINTEGFR*2 OPTIONE X T E K M i L HL1PL

C M W = 1 . 6 0 2 1 * 1 1 0 . ) * * l - 1 3 )100 READ ( 1,11)(OPTION!I I ,1=1,401

IF(OPTTON(ll-i)101,102,133101 CALL EXIT103 IFIOPTIQNl11.E0.4I GO TO 557COMMENT, INPUT THfc ENERGY DATA

READ ( 1,18) (T1TEI I ) , 1=1,20)RtAD(l.l2IEHlltVK(l»,KLM,KIN,IMAT,NMAT,NS0PREAD (1 ,13)IbLIK),K = 2,KLM)DC 120 K=2,KLMVMK)=EL( H-l I/ELIK)UV(K!^ALOG(VK(KI)

120 EBAR(K ) = ( E U K.-1 )-f L (K) I /LJVtK.1UV( l)=ALDGl V M 1 ) )DU IZZ M=l,20AMASS(H)=1.E+1OALPHA!M)=1.CS I (M)='J.DO 145 1=1,4

145 SUBSTIM,I 1=0.DO 122 K=1,KLMSIGA(M,K)=O.SIGE(M,K)=-O.SIGI(M,K)=O.

122 EGAMA1M,K)=O.DO 121 M=1,NMATREAD 11,33) (SUBII) ,1=1,4),MPRIM1,AMDO 128 1=1,4

128 SUBST«MPR(M),1)=SUBÎI)READ (1,131 (SIGA(MPRIM),K),K=1,KLM)READ (1,131 (SIGEIMPR(M) ,KI,K*l,KLM »READ (1,13) (SIGI(MPR(M) ,K),K=1,KLMJREAD (1,13) (EGAMAIMPR(M),KI,K>1,KLM)AMASSIMPR(M))=AMALPHA(MPRIM))=(AM-1.»*(AM-1.)/((AM+1.)*(AM+1.|)AL = ALPHA(MPR(,M) )IF(AL.EQ.O.) GO TO 127IFJAL.NE.l ) CS. I (KPRIM) I = 1. +ALOG( AL )*AL / «1.- AL )GO TO 121

127 CSKMPP.IHI ) = 1.121 CONTINUE

IF(NSOR.EQ.O) GO TO 148DO 137 K=1,KLM

137 SOURCE(K)=0.«EAD (1,13) (SOURCE(K),K=1,NSOR)

00520G53

0055005600570056005900600061

0063006400650C66006?00600069007000710072007300740Ù750076007700780C790080008100620083008V0065008600870C88008900900091009200930094009500960097009800990100010101020103010401050106010701C8

1 irt

129

126

[F ( S(U)M-L ( 1 I . fcO.O. ) GC TO 149oc i iM K ». = i, r.suP

SouRLf. (K ) = bUUP-LHK > /SPUPCE ( 1 Ilit TI • 1 <• h

WP1TE ! 3 ,4II H LJP t I L . M 2 I • t b > 0 ) GO TO 123OC 12 1 K - ! ,KLMOC U'? M= l ? , ? jSU.f ( H , - I = J (,,fc ( f - Q . K II l ! « n . ; u . n i GU DC 126M * n 1 N- — ! s - t l / iK l / > . ' i , 1 i ' i i , i b l N ! I ) , 1 = 1 , t c l IOG ! <J "•• K- = ;> , K l rj

l'L 1 , . . f . ' , > M , VI ••

ïf ( (i ^e b A -11•*(• i r t (W f- 1 T t

WP i T t

W P I T t (

h f i I T t (

KHTM00 i 4 <•w f -1 T e t

WkîT l1« M T [ (WO J T L (W R I T t (WPITF (*k]TE IWR 1 ï tI F ( M P «

i MAT .

r ;. * N <I = q ) M

3 , 1 I

l J , 2 (

3 , i<+ )

3 . 3 5 )3 , 3 1

3 , 363 , 3 73 , 383 , 3 73 , 3 ^3 . 3 73 , 4 0( 3 , i f( M I . M

,K)-SIGSUM(KI)»AMASS( I«AT I/1AMASSI ÏMATI + 1. )

1 l.tO.C J.DP. « 3PT!ONI3),EO. J.) I GO TO 105

) 1 T ] T H 1 ) , 1 « 1 , 2 0 )

NMA7< SUBST(MPR'.H) , 1 ) , 1 = 1 , 4 )(K.SIGAIMPPIMI ,K|,K=l,Kt«l

<SUBST1MPR(M),I),I=1,4)(K.S1GE(HPK(M) ,K) ,K=1,KLM|

(SUBST(HPRtM),I1,1=1,4)(K., S1GI I M P R { H ) , K Î , K = 1 , K L M )

1 S U b S T ( M P R i M ) , 1 ) , 1 = 1 , 4 1) ( K , E G A * A I M P R ( H ) , K ) , K » 1 , K L M )fc. IMAT1G0 TO 1 4 4

KR I T! ! 3 ,H? I K.KK-KlK'i K-Z!-(K-3)*K/2KF=KX»KIN-KDD 144 fJM=KX,K> , 10K 1 = K < N *< - K. XK2=NH

105

U-( (NM + 1 0 1 . G T . K F ) K2MAX=KF

WRITE- ( 3 , 4 5 ) ( I » [ - K 1 . K 1 H A X IrtPl T M 3 . ?3 I ( S I G I N ( l ) , i = K 2 , ! < . 2 M A X )CONTÎNUFIf- ( N S O P . E U . O ) l i d TO 1 0 5W R I T t ( 3 , 7 1Wf- ITF ( 3 , 2 2 ) IK. , SOURCE (K ) , K = 1 , N S O R II F ( O P T I U N C 1 ) . E 0 . 2 ) GO TO 1 0 6

COMMENT. I N P U T THE GEOMETRY DATA

-72-

01090110OUI01120113QU4011501160117011801190120012101220123012*01250126012?01280129QUOOUI01320133013*0135013601370138013901*001*101*201*3014*014501*601*701*801*90150015101520153015*015501560157015801590160016101620163016*0165

102

139

131

132

133

130

IS*135136

1*6

HEAD (1,181 (TITG(I»,I = 1,20)READ (1,151 N,C0J,EN0RMANOPM=ENORM*8.*23E*1OIF(COJ.LT..001I COJ=l.READ (l,10( (JL(IIt1=1,NIRCAD Jl.lt.) (R(l),l = l,N)V(1) = 3.1*159*{RU)»R<1M

S(1)=6.28318*RU»VCEL=3.1*159*R(N)*RIN>DC 130 1=1,NIF I I.EQ.L » GO TC 13<5V(II = 3.14159*(R( 1 I * R ( I » R ( I 1 I * R ( I 1 MAVRII 1=2.09439*1 M l ) *fi ( I ) *R( II -R « 1-1 )*RI1-1 I *R( 1-1 M /V « I IS(I>=6.28318*R(I IIFIJLi I I.GT.IOO) GO TO 133MAX=JL(I)READ (1.17) (MRC ( I , J I ,DbNS( 1 , J > ,.l»l ,WAXIIF(OPTILJN(2I.EQ.O) GO TO 132NU«=0DO 131 J=1,MAXIF t IMRCII ,JI.LT.8).0R.(MftC(I,Jl.GT.in I GO TO 131NUH=NUM*1J1=JL(i)+NUMMP=MRC1I,JIMRC1I,J1)=MP*1O9DENS(I,JIl=DENS(I,JI*(-2./(3.*AMASS(MP|lICONTINUEJL1I)=JL(II*NUMLIKEUI--0GO TO 130MP=JL(I)-IOOJLUMJUMP)LIKE(I)=HP

TO 13*l,Nt

1*1

DO 130 J=1,MAXMRC(I,JI=MRC(MP,J)DENSIÏ,J)=DENS(MP,J)CONTINUEIF(OPTION(*).EQ.O)GOREAD ( 1, 16)(F IMj I ) ,GO TO 13600 135 1*1,NFIN(I 1 = 1.IF((0PTI0N(3).EQ.0l.0R.<0PTI0N(3I.EQ.2»l GO TO 106WRITE(3,1)WRITE(3,*3)DO 1*6 M=1,NMATMRITE(3t** l (SUBST»MPR(M|,I I,I«1,*»,MPR(Ml,AMASSIMPR(M I )

1ALPHA(MPR(H!I,CSI(MPR(H)IWRITE (3 ,1 )WRITE(3 , *6 ) (T ITG( I I , I =1 ,2O IWRITE (3,5100 1*0 1 = 1 , NI F I L I K E m . E Q . O ) GO TC 1*1MRITE(3,6) I , F I N ( I ) , R ( I » , L I K E ( I IGO TO 1*0WRITE(3,2OI I , F IN( I ) , R( I I ,MRC < I » 11 t O E N S d t l l

01660167C1-S30169017001710172017301740175

01760177017801790180018101820163018*018501860167

0188016901900191019201930194019501960197019B0W90200020102020203020402050206020702080209021002110212021302140215021602170218021902200221

I.Ea.1IG0 TO 140MAX»JL(I IIFIOPTIONC2I.EQ.0I GO TO 142DO 143 J«2»MAXI f M M R C U , J I . G T . 1 1 6 J . A N D . (MRCI I , J ) . L T . 1 2 1 > ) GO TO 143WRITE < 3 t 2 l ) J , M R C ( I . J ) , 0 E N S I ! , J )

143 CONTINUEGO TO 1 4 0

142 WRITE (3,211 iJ,MRC(I,Jl,DENS(I,J),J=2,M4XI140 CONTINUECOMMENT. INITIALIZE SOME VARIABLES1G6 ABSE=Q.

SPOl«O.EMN-0.ETRAT»O.£EX=O.fcfL=0.SLL*O.SElI*O.SELO=O.EGAMT»O.Tf=O.S R A V S ' l .

COMMENT. CALCULATE THE SECONDARY NEUTRONS AND MACROSCOPIC CROSSDO 160 K - l . K L MDO 150 1 * 1 , NSIGAT1 I 1 = 0 .S 1 G E T I 1 1 * 0 .S I G T T J I , K I » O .TCOL=O.TSCQL=O.M A X * J l J I >DO 151 J«1,MAXMP=MRCtI tJ»If-i i (HRCJ I r J i . L T , 3 0 0 ) . Q P . Î K . E Q . I I I . O P . < K. GT.K IN) ) GO TO 153MP*HP-300

153

TCOL=TCOL*DENS<I (J)*ISIGAfMP ,KI*SIGE<MPiKi»SiGIIMP tKM*UV(K )IFMMftCI I, J».LT.100».0R. (MRCII , J ) .GT. 200 » ) G O T O 154TSCOL=TSCOt*DENS(ItJ)*S1GEIMP,Kl*UV!K)GO TO 155

15*. IF(VMK)*AL.LT.l.) GO TO 156TSCOL-TSCOL + DENSU.JI^SIGECMP.KI^UVItO-AL^ALOGIAD/ALl-l. IGO TO 1 5 5

156 TSCOL=TSCOL*OENS(I,J»*SIGEIHP,K)*(UVIK)»1./VK(K>-1.I/AL1155 SI GAT( II = SIGAT( I}*DENS(I.JI»(SIGAiMP,K)»S1GHMP.K) )

SI GET I i» = SIGET(1J*DENS(I,J)»(SIGE(MP ,K) I151 CONTINUÉ

IFISI&ATIII.LT.I.0000001 11 S I GATtIt=.0000001SI&TTtI,K)=SIGAT(I»*51GET t I I

TCOL*DENS(I «JI»UV«K>*SIGSU"(K)TSCOL = TSCOL*DENS(1»J)*UVIK)»SI GIN( KX )SIGATI1) = SIGiT(II+DEN II,J )*SIGSUM(K)IF1MP.GT.200) GO TO l.-lIMMP.UT.10QIMP=MP~100

-74-

022202230224022502260?.270228

02290230023102320233023*»023502360237023802390240024102420243

024402450246024702480249025002510252025302540255

0256025702580259026002610262026302640265

0266026702680269027002710272

02730274

IF(SIGTT< I ,K).LT.U0OOOOl> » SIGTTII ,K I =. 000001IFUC0L.E0.0.1 GO TO 157T( I ) = TSCOL/TCOLGO TO 1 5 0

1 5 7 T ( I » = O .1 5 0 CONTINUE

I F I K . G T . 1 1 GO TO 161COMMENT. 00 THE GROUP ONE CALCULATIONS

00 170 1=1 ,NTF=TF*FIN( I » * V U )Q F U ) = 0 .MAX=JL(I)DO 171 J=1,MAXMP=MRC<I,J»!F (MP.GT,300» MP=MP-300IF (MP.GT . IOO) GO TO 171SOOJ( I , J > = C S I ( M P » * D E N S I I , J ) * S I G E I M P , 1 ) * F 1 N < J ) * V I I iSPDL=SPOL+SOOJ( I , J>AL=ALPHA(MP»I F U V K ( 2 > * A L ) . L T . 1 . ) GO TO 172QF<I) = QF( I ) *S0OJ( I t J )GO TO 1 7 1

1 7 2 0 F i n = O H I > + < ( < V K ( 2 ) - 1 - W V K 1 2 J ~ A L « U V « 2 » » / « 1 . - A L » I * S I G E < H P ,l D E N S H t J ) * F I N ( I ) * V ( I t

171 CONTINUE170 ABSE=ABSE*UV(1)*FIN(I1*VII>*SIGAT(!»

RENO=l./(SPDL*ABSe)ABSE=ABSE*RENOSPDL=SPDL*RENODO 173 1*1, N0F(I»=QF(I)*RENOMAX=JLtItDO 173 J=1,MAXSD0J1I,J»=SOOJ(I,J)*RENi

173 CONTINUEGO TO 160

COMMENT. CALCULATE THE FLUX I N ALL THE OTHER GROUPS161 I F I K . G T . 2 » CALL R A V E N S ( N , K ( K I N , E H K » )

00 163 1 = 1 ,NSRAV=SOURCE» K » * F I N ( I ) * V ( I » / T FSRAVS=SRAVS*SRAVQ F ( I ) = Q F ( I ) * S R A V

163 ENIN=ENIN+SRAV*EBAR(K)' CALL LENORE(N,COJ,HOPE,K)

PHI(l,KI=(QF<l)*WVV(l»*JJ(l,l)*WOV«ilI/(SIGTT(1,K |*V(1 I IDO 164 1=2,N

164 PHKI ,K) = (QF( I »«WVV(I I*JJ( 1,I)«WOV( I )+JJ(2, 1-1 ) *WI V ( I ) I / (1SIGTTI I,KI*V«I) »SEL0=SEL0+JJ(2,NI*EBAR(K)SELI=SELI*JJ(1,N)*EBAR<K)

160 CONTINUEDO 165 1=1,N

165 PHI(I,1|=FINU)*J»ENO5 5 7 I F < 0 P T I C t N < 5 ( . E Q . O t G O T O 5 1 0

I F (OPT ION(121 .EQ.O) GO TO 500COMMENT. CALCULATE AND OUTPUT INTEGRATED FLUX

DO 508 I = l , N508 P H I K 1 I ) = O .

) *

027502760277027802790280026102820263028*0285

0286028702B802890290029102920293029*0295029602970298

02990300030103020303030*03050306030703080309031003110312031 1031*031503160317031803190320032103220323032*

032503?60327O32R0329

WRITE ( 3 , 1 1WRITE<3,50) ENORHWRITE ( 3 , 8 1DO 502 1=1,NDO 501 K=2,KLM

501 P H I M I ) = P H 1 M I » * P H I ( I , K >P H I M I > = P H I M I )*ANORM

502 M R I T E ( 3 , 2 * ) P H I K ( I I . A V R d )500 I F ( O P T 1 O N < 5 ) - 2 I 5 0 4 , 5 5 1 , 5 5 *55* DO 553 LM=1,6

I F < O P T I O N ( L M « - 5 » . E Q . O ) GO TO 551COMMENT. OUTPUT FLUX SPECTRA

WRITEO.l)WR1TE(3 , *7 )OPTION(LM*5»00 553 K=2,KLMPHtL(KI=PHlIOPTION(LM»5I,K|/UV(K»«ANOR«

553 WRITE(3,2*)PHIL(K) .EBARU»IF(OPTION(5I.EQ.3I GO TO 504

551 DO 503 LM=1,6IF(0PTIdN<LH*5I.EQ.O» GO TO 504WRITE(3,IIWRITE!3,9(OPTION(LM*5)DO 503 K=2,KLMPHIEIK)=PHIf 0PTION<LM+5>iK)/(EL<K)*(VK(M-l.H*AN0RM

503 WRITE(3,2*)PHIE(K»,E8AR(K)COMMENT. CALCULATE AND OUTPUT WEIGHTED FLUX50* DO 507 NN=1,3

IF(OPTI0N(NN*12».EQ.0> GO TO 510DENO=0.DO 509 K=1,KLM

509 PHIW(KI"0.WRITE(3.II00 50b I-l.NMAX = JL(I I00 505 J=l,MAXMP=MRClI,JIIF(MP.GT.300 IHP=MP-300IF«MP.GT*2OO)MP=MP-2OOIF <MP.GT.100)MP=MP-100IF(0PTIDN(NN*12).NE.MPI GO TO 505MX = MPDfcNO=DENO*DENS(I,J)*V(I>DO 556 K=2,K.LM

556 PHlfe(K)-PHIW(K)*PHI(IfK)*V(I)*DENS(I,JIGO TO 506

505 CONTINUE506 CONTINUE

Wfi I T E ( 3 , * B I ( SUBST(MX,L) , L = 1 , * IDO 507 K=2,KLMPHIW(K) = PHIW( K)*AN0R>1/<DEr4a*EL(K,l

507 WRITE13 .2 * ) PH IW(M,EBAR(K)510 IF (OPTia 'Jd I . E Q . * I GO TO 5 1 *COMMENT. PERFORM THE ENERGY CALCULATIONS

DO 550 M = l , 2 0DO 550 K=1,N

550 ETRANt M,K.(=O.WR ITEJ 3,1»WPITE(1 ,5O) ENORM

-. o-

03300331033203330334033503360337033803390340034103420343034403450346034 703480349035003510352035303540355

035603570356035903600361036203630364036503660367036603690370037103720373

0374037503760377

03760379

0380038103820383

516515513

552

555

512511

DO 511 1 = 1 t NMAX=JL(1)DO 512 J=lfMAXHP=MRC(I iJ)I H M P . I T . 3 O O ) GO TO 513MP=MP-300A=AMASS(MP)AL'ALPHAIMP»A L l = < A - l . ) / ( A * ( A » l . I >DO 515 K=2,K.INK X = K I N * ( K - 2 ) - K * ( K - 3 ) / 2FACTOR=O.KF=»KX*M N-KDO 516 KS»KX,K,FFACTOR»FACTOR*EBAR(KS-KX*K)/A*SIGIN(KS)ETRAN(MP,1) =ETRAN(MP,I)*PHKI,K)•(FACTOR*EBAR«K)*AL1»SIGSUMIKI >IF1MP.GT.200)MP=HP-200IF<MP.GT.100IMP«MP-100!F(OPTION(2 ».EQ.OI GO TO 552IF1MP.GE.17) GO TO 511A-AMASSIMP)AN«l,m.»A)ALl»l.-ALPhA(MPI00 555 K=2,KLMEEX«EEX*PHI(I,KI*EQAR(K)«StGA(MP,K»*AN*A*V(I)*DENS(1,J)ETRAN(MP,I )=ETRAN<MP,I)*PHI(ItKI*EBAR<K»*(SIGEIMP,K»*AL1*. 5*1SIG4(MP,KI*AN+SIGI(HP,K)*AL1*(.5-EGAMA(MP,K)*AN/(FBAR(K)*AL1)))ETRANIHP.t)=V(J)»DENS«I,J(*ETRAN(MP,I IETRAT*ETRAT»ETRAN(HP,I)CONTINUEIF(0PTION(161.EQ.0) GO TO 514Ei=Elil)EKL-ELIKLMI00 517 1=1fNMÛX=JL(I)DO 518 J«l,MAX

IF<MP 3GT.30O) MP=MP-300IF(MP.GT.2OO) GO TO 518I F I K P . G T . I O O ) GO TO 519

5 2 1

520519

AL = ALPHA(MP »AL1=1.-AL.ENIN=ENIN*.5»DENS(I,Ji*PHI(I,l)»V(I)*SIGE<MPf1(*AL1*E1IF(<E1*AU.LT.EKU EEL-EEL* . 5*DENSI 11J »*PHI (I ,1>*V( M*SIGE( MP , 1 )*

1EKL*(EKL/É1*-AL*AL*E1/EKL-2,*AL»/AL1DO 520 K=2,KLMIF((EL(KJ«AL).GE.EKL) GC TO 520IF((El(K-l)*AL).LT.EKU GO TO 521EEL-EEL-,5*0ENS(ItJI«PH1(I,K»*VtI»*SIGE<MP.K)/IUV(K»*AL1t*EKL*iEKL1/EL(K)*AL*AL*EL«K»/EKL-2.*AL)GO TO 520EEL-EEL*.5*0ENSUiJI»PHIU fKt*V(II*SIGE«MP,K»/<UV«R»*AL1l*«EKL*EKL

1*(1 . /EL(K) -1 . /EL(K-1H-AL*AL*«EL1K-1 I -EL(K) »)CONTINUEIF(MP.GT.IOO)MP»MP-1OOIF(OPTION(2J.EQ.O) GO TO 529I F ( M P . G E . i 7 ) GO TO 5 1 7

038403850386038703880369039003910392039303940395039603970398039904000401040204030404C40504060407040304090410041104X204130414

04150416041704180419042004210422042304240425042604270428

04290430043104320433043404350<*36043704380439

529 A=AMASS(MP>

518517

AN=A/<(A+L. ) * (A*1 . )>00 518 K=2,KLMFRAC=AM*EBARU)-AN*EGAMAJMP,K)lF<FRAC.LT.EKMEEL=EEL + DENS<I tJ I*PHI( I tK)*VU)*SIGMMP,K)*FRACCONTINUECONTINUEETRAT=ETRAT*ANORM*CMWEEL=EEL*ANORM*CMWSELO=5EI.0*AN0RH«CMWSEU=SEU*ANORM*CMWSEL=SELO-SELIWRITE(3,25» ETRAT,SELO,SELI,SEL,EELIF(OPTION(17>.EQ.O) GO TO 514DO 522 I = l f NMAX=JL< I IDO 523 J=1,MAXHP=MRC(I,JlIF<MP.LT.30O) GO TO 526MP=MP-300A=AMASS1MP)A M = l A * A + 1 . ) / ( A * ( A + l . I t

DO 525 K=2,KINKX=KIN*(K-2) -K»(K-3>/2

FACTOR=O.DO 524 KS=KX,KF

524 FACTOR=FACTOP*EBAR(KS-KX*K)*SIGIN<KSI52 5 EGAMT = EGAHT*DENS«I«J»*PHI< I ,K»*V»I)*(AM*EBAR(KI*SIGSUM(KI-AN*

1FACT0R)526 IF(MP.GT,200) GO TO 523

IF(MP.GT.IOO) MP=MP-1OOIF(OPTI0N(2),E0.0) GO TO 528IF(MP.GE.17I GO TO 522

528 DO 527 K=2tKLM52 7 EGAMT=EGAMT+DENSU,J)*PHI( I , KI«V U )*S IGI ( MP,KI*EGAMA ( MP,K )523 CONTINUE522 CONTINUE

ENIN=ENIN*ANORM*CMWEEX=EEX*ANORM*CMWEGAMT=EGAMT*ANORM*CMWENOUT=EGAMT+EEL*SEL*ETRAT*EEXHRITE(3,26I ENINfENOUT,EGAMT,EEX

514 WRITF(3,1)COMMENT. OUTPUT WATTS/GRAM AND WATTS TRANSFERRED TO MATERIALS IN CERTAIN REGIONS

DO 537 I N = l i 6I = 0 P T I 0 N ( 1 7 + I N )I F ( I . E Q . O ) GO TO 5 3 1MAX=JL(I)WR1 TE I 3 ,49 i IDO 530 J=1,MAXMP=MRC( I i J )IF( MP.GT.3O0)HP=MP-3OOIF(MP.GT.Z00)HP=MP-2 00IF(MP.GT.100)MP=*P-100IF(0PTI0NI2 l .EQ.OI GO TO 536

--'8-

04400441

0443

044504460447044a0449Û45Q04510452045304540455

04560457045804590460046104620463046404650466

04670468046904700471C4720473047404750476047704780479046004810462048304840485048604670468046904900491049204930494

IF(MP.GE.l7) GO TO 537536 ET=ETRAN(MP,I)*.6023/(DENSU,J»•V(I»*AHASS(MP>(•ANOR**CMW

ET1=ETPAN(MP,I)*AN0PM*CMW530 WRITEI3.27) ( S'ja ST ( MP , L ) ,L = 1,4 » , ET , ET l537 CCNTINUECOMMENT. OUTPUT TOTAL ENERGY TRANSFERRED TO CERTAIN MATERIALS531 DO 532 MAT=1,4

IF(OPTION(MAT*23».EO.OI GO TO 533ET*O,MP=OPTION(MAT+23JDO 534 I= L , N

534 ET=ET+FTRAN<MP, I )

5 32 WRITFI3,2B)fcr»(SUBST(MP,L),L=1,4»533 IFI(OPTrJN(28).E0.0).0R.(OPTIONS29».E0.0)) GO TO 540

I 1=OPTIOM(28)

CJMMENT. OUTCUT ENERGY TRANSFERRED BETWEEN REGIONS II AND IFFET = O.DO 535 ! = 1 I , IFF

535

DO 535 J=MP=MRC<I,JIIF(MP.GT.300) MP=MP-300IF(MP.GT.2OO) HP=MP~200IF(MP.GT.IOO) MP=MP-100fT = ET*eTRAN(MP , I I

WRITE! 3,2e?) I I , IFF,ETCOMMENT. CALCULATE: AND OUPTUT540

11=1,5

((3O*NO».EQ.4O)) GO TO 100

NICKEL ACTIVATIONS.N0=000 541NI=DPT I'JNI -)0IF((NI.EJ.O)HP I TF ( "i , 1 IWRITfc(3,50) ENORMRt AD( 1 ri1)) t ALP ( J) . J= 1,91 . M P J U C K O S S . T A U . A . A LHRI TF( 3,<.M ( ALP( Jl , J=l,9)IFJMPJ.F-J.O! GO TO 542DO 545 K-l , KLM

545 SIGAF(K)-jSGA(MPJ,KIGO TO 5^3

542 READ(1,13!(SIGAF(K),K=1,KLH)5 4 3 - IF(OPTION(<*O) .NE.O) W P I T E O . 3 0 1 ( K , S I GAF ( K I , K=l , KLM)

DO 544 L 1 = 1 , N II=OPTION(30+NO+LI)A B S F = S I G A F ( 1 ) * P H I ( I , 1 | * U V ( 1 )DO 546 K = 2 , K L *

546 ABSF=ABSF*S IGAF(K) *PHI ( I ,K )ABSF=ABSF*ANORMABSFT=ABSF*AL/(A«TAU)»,0250468PHIEF=ABSF/CROSSW R I T E ( 3 , 3 1 I A B S F T , I

5 4 4 W R I T E ( 3 , 3 2 ) P H I E F5 4 1 NO-NO*1*NI1 FORMAT(8H1NEVEHQR)2 FORMAT(28H-ENF.RGY DEPENDENT INPUT DATA//13 F0RMATU2H0CRGSS SECTION DATA AS A FUNCTION OF GROUP I

04950496

049704980499

0500

0501050205030504050505060507050805090510051105120513051405150516

45

67

e9

10111213141516171819202122232425

0517

0:521

0522

26

051605190520

272829

30

31

052i05240525

00260527052S0529

0530

0531

05320533

323334

35363738

39

40

4142

FORMAT) 15H-SOURCEUJ IS 0»FORMAT<30H-GE0METRY DEPENDENT INPUT DATA////3X,•1•,6X,•FIN(I I' ,6X,l'R (I)' ,5X,'J',iX,'M«C(I , J) • ,4X, 'HU,J>«/T<,9,'(10**24ATOMS/CC)t ,F0RMAT(//2X,I2,3X,F9.4,2X,F9.4,<,X,'THE SAME AS REGION «tt2)FORMAT(16H-S0URCE SPECTRUM»FORMAT)//' INTEGRATED FLUX IN/CM*»2-SEC) AS A FUNCTION OF RADIUS1/l/« FLUX',12X,'VOLUME WEIGHTED1/T18, ' AVERAGE RADIUS»/T23*•(CM) • / (FORMATJ//' FLUX (N/CM**2-SEC) PFR UNÎT ENERGY AS A FUNCTION OF ENE1KGY IN REGION',2X,12///' FLUX',6X,•AT»,6X,•ENERGY EBAfi IN WFV'/IF0RMAT(26I3 iF0RMATU0I2)F0RMAT<F10.5,F9.T,5I3)FORMAT(8F10.5IFORMAT»1QF8.4)FORMAT!I3.F8.6.E14.7!FORMAT (1 1F7.<»)FQkMAT)S< I 3,f- 11.9) )FORMAT(20A4IFORMAT(9A4,I2,F1O.5,F14.71F9.5,F9.7»F 0 R M A T ( / / 2 X , l 2 , J X , f S . 4 , 2 X , F 9 . 4 , 4 X , ' l ' . 5 X , I 3 , 5 X , F 1 1 . 9 )F O R M A T ( T 3 U I 2 , T 3 8 , 1 3 , T 4 6 , F 1 1 . 9 IF Q R M A T ( 4 ) I 3 , ' , ' , 3 X , F 1 0 . 5 , 4 X I )F O R M A T ( • • • » 2 X , F 9 . 5 t 9 ( 3 X , F 9 . 5 ) lF O R M A T ( i H t . 7 , f a x , F 8 . 5 IF O R M A T ) / / ' T O T A L K I N E T I C E N E R G Y T R A N S F E R E D = ' . E 1 4 . 7 , ' W A T T S ' , / / '

1 E N E R G Y L E A V I N G r f L L T H R O U G H C E L L B O U N D A R I E S = ' , E I 4 . 7 , « W A T T S ' / / '2 E N F . R & Y E N T E R I N G C E L L T H R O U G H C E L L B O U N D A R I E S = ' . E 1 4 . 7 , ' W A T T S ' / / 1

3 T O T A L E N F R G Y L O S T T H R O U G H C E L L B O U N D A R I E S = ' , E 1 4 . 7 , ' W A T T S 1 , / / '4 T C J Î A L E N F R G Y L U S T T H R O U G H L O W E R E N E R G Y B O U N D = 1 , F 1 4 . " ' , ' W A T T S ' )

F Û K M A U / / ' T O T A L F N E H G Y I N P U T = ' , 6 1 4 . 7 , • W A T T S ' , / / 1 T O T A L F I N A L E1 N E R G Y - ' , t l 4 . 7 , ' W A T T S * , / / 1 O F W H I C H ' , F 1 4 . 7 , ' W A T T S C O M E F R O M GA2 M M A F-AY E N E R G I E S I N I N E L A S T I C 1 / / ' S C A T T E R I N G C O L L I S I O N S , A N D ' ,3 E 1 4 . 7 , ' 1 W A T T S C O M E F R P M N O N - C E N T E R - Q F - M A S S 1 / / • E N E R G Y I N A B S O P P T I O4 N R E A C T H J N J ' I

F O R M A T ) ! * » 4 A 4 , < , X , E 1 4 . 7 , 9 X , E 1 < « . 7 IF O R M A T I ltr\<*. 7 . ' W A T T S n F . R F T R A N S F E R R E D T O ' , < » A < » IF O R M A T ( / / ' T H h T O T A L K I N E T I C E N E R G Y T R A N S F f R R P O B F T W F f N R E G I O N S ' ,

I I ? , 1 A U D ' , U ' , ' I S ' , L 1 4 . 7 , « W A T T S ' )F O R M A T ) / / ' r M r ' . t , n S S S F C T i O N O Û T A I S A S F O L L O W S ' / / 7 ( I 3 , ' , ' . F 1 0 . 5 ,

1 2 X 1 1F O f M A T ! . ' / • l ' < . ' . ' ! M S I N T E G R A T I O N S P E R S E C O N D P F R M G . P E R M I N U T E O F

H k « A U ! A M U N ! ' . M l O I O N ' , ! 2 IF ( j k M A T ( / ' i t f K . l l v f F L U X = ' . F 1 4 . 7 , ' N / C M * » 2 - S F C IF O R M A T 1 * 4 4 , I 2 , F f l . 4 >F O R M A T ) ' L n w t R E N E R G Y B O U N D ( E L ( K ) ) A N D A V E R A & F N E U T R O N E N E R G Y ( E B

l A P . ( K ) ) A ! ) A F U N C T I O N 0 ? G R 0 U P ' / / 4 ( ' K ' , 4 X , ' E L ( K ) ' , 6 X , ' E f i A P ( K ) * ) / 42 ( 7 X , ' ( M f V I ' , if,,' I M h V ) ' , I X ) )

F C ' R K A T C t ( I 1 . 2 X , F H . ' . , 2 x , F d . 4 , 2 X l )F O R M A T ) • » l H O A B S u R P T I L i N C R O S S S E C T I O N S F O R u 4 1 4 / / 1 0 M K ' , 9 X ! )F U R M A T ) 1 0 1 1 H . F 9 . 5 ) )F O R M A T ( 3 9 H C E L A S T K S C A T T E R I N G C R O S S S E C T I 0 N 5 F O R , 4 A 4 / / 1 O ( I K « , 9 X

1 ) )F O R M A T C - l H ^ l N t L A b T I C S C A T T E R I N G C R O S S S E C T I O N S F D R , < 1 A 4 / / 1 P ( 1 K ' ,

1 9 X ) I

F O R M A T ( b O H O A V F K A G E G A M M A E N E R G Y I N I N E L A S T I C C O L L I S I O N W I T H , 4 A < t / /

1 1 0 ) ' K * , 9 X ) IF O R M A T ( 3 3 H O I N E L A S T I C S C A T T E R I N G K A T P I x F O B , A A A )F O R M A T 1 l l H C F ^ O M G P O U P , I 3 , L 1 H T O G R O U P K / / 1 0 ) ' K e , 9 X I )

-30-

Ob J5

O-i i 70533

0*i 39

43 F 0 R M A T U 5 H C M A T E P IALS IN THE P E A C T O R / / ' M A T E R I A L « , 5 X , « R E F . N 0 . ' , 4 X1 , ' M A S S ' , 5 X . ' A L P H A ' , 6 X , • C S I « / T 1 7 , • I M P R ) « T 2 7 , • ( A M U ) ' / / I

4* FCRMAT ft A*. , 1 X , I 3 , 3 X » F 9 . 4 , 2 X , F 8 . 5 . 2 X , F 8 . 5 >4 5 FORHATl 1 Û U 3 , 9 X i I4 6 FORMAT!/. ' . X . 2 0 A 4 )47 FCRMATU/' FLUX <N/CM**2-S EC ) PER UNIT LETHARGY AS A FUNCTION OF E

1NERGY IN REGION',2X,t2///« FLUX',6X ,• AT • ,6X ,'ENERGY E8&R IN M E V / >48 F0RMAf(//« AVf-'AGE FLUX ! N/CM**2-SEC > PER UNIT ENERGY, WEIGHTED BY

1 •,4A4///' FLUX' ,6X,«AT1,6X,«ENERGY EBAR IN M E V / I49 FÙRMAT1////1 KINETIC ENERGY TRANSFERRED IN REGION •, 12//• MATERIAL

I'ilOX,21'ENERGY TRANSFERRED'tSXl/TZSi'lWATTS/GRAMt'fTABt'fWATSl'/l51 FORMAT(E14.7)50 FORMAT!//' THE FOLLOWING DATA IS NORMALIZED TO ',E14.7,' K W A T T S V

1 OF U235 FISSION ENERGY PRODUCED PER CM THICKNESS OF LATTICE CELL'21END

\

000100020003

00040005000600070008000900100011001200130014001500160017001800190020002100220023002^002500 26

002 7002 8

00290030003100320033003*0035003600370038003900400041004200430044004500460047004800490050C051005200530054

220

221

219

210218

SUBROUTINt KAVtNi»<N,K,KIN,EN»COMMON/ALL/OPT ION(40 I , V H 0 I ,QF ( 30 )C0MMÛN/RâV/VK(60l,UV(60 > tL IKE(30 I,JL(30>,MPC(30,20 I , n N S ( VIS I GIN!1300 I,S IGEI 20,60) , E.9ARI60),EGAHA(20,60 I,SDOJ< 30,20),ZPH1(30,601,ALPHAJ20),AMASS(2OI,S!GI(2O,fcOI,CS!(20;DIMENSION RK. ( 60 ( , ARK I 60 I , Q< 30, 60 IINTEGER*? OPTIONRKUi=VMK)APK(1I=UV(KIKM = K.-200 220 KP=1,KMKMI=K-KPRK (KP+1 I=RK.( KP(*VK (KM1 »ARKIKP+1I = ARK(KPI*UV(KM1)DO 203 1=1,N0F(U=0.DO 221 KP»1,K.M

0(1,KP)=O.MAX=JL<1IDO 201 J=1,HAXMP=MfiC(I,J)If (MP.rjT.3OOI MP = MP-300

TO 201TO 210

212

214

21 o

215

GOGO

I ) 1

If(MP.Gr.2OO)I M M P . G T . 1 0 0 iAL=ALPHA(MP)IF ( ( RK(K-1 I*AL I .GT.RKU ) ) GO TO 21BIF< (RK.(K-1 >*AL).LT, 1. ) GO TO 2190F(II=OF!I)KRK(l) PK(K-1)-AL*( l.*ARK( 1I-ARK1K-1 I-6L0G (

1SDGJ< I,J)/(CSHMP)»(1.-AL)IGO TO 216QF(M.«OF(I)t((RK(l )-l. )/«K(K-l »-AL*ABK(l) )«SDOJ(I ,J> /(CS1(«P )•(!.

1AL! 1GO TO 218HP=MP-10QIMLIKEI I ).NE.O) GO TO 213AL=ALPHA(MP)A=AMASS(MP)AM=(A*A*1.)/((A*l.)*lA+l.)iAN»A/JA*l.>DO 202 KP=l,KMKM1=K-KPIF ( (MP.C( I , J I ,GT» 100) .AND. iMPC( I , JI.L1.200) I GO TO 211IF((MRCII,J).LT.3OO).OR.(K.GT.KIN)) GO TO 212

0 ( I , K P I = U ( I , K P ) + D E N S ( I , J ) * S I G I N ( K X )I F ( ( R K ( K P ) * A L I . G T . R K l 1 ) ) GO TO 211P R = S I G E | M P , K M 1 ) * D £ N S ( I , J ) / ( U V ( K M l ) * ( l . - A L I II F ( ( R K ( K P f l ) * A L ) . G E . l . ) GO TO 2 1 40 ( I , K P > = 0 ( I , K P ) + I R K ( l ) - l . ) * ( K - / R K ( K P ) - l . / R

GO TO 2 1 1I F ( ( R K ( K P ) * A l l . L T . l ) GO T O 2 1 5I F ( ( R K l 1 I ) , G T . ( R K ( K P + 1 ) * A L ) ) GO T O 2 1 6O < I , K P ) « 0 ( I f K P ) + P R * ( R K ( l ) / R K ( K P ) - A L « ( I . • ARK ( 1 ) - A L O G < A D - A R K ( K P 1 1 )GU T O 2 1 10( I ,KP)=O( I , K P ) + P R * ( R K m » U . / R M K P ) - l . / R M K P + l l ) - A L * U V I K M l » lGO TO 2 1 1I K « R K ( K P + U * A L ) . L T . R K « 1 > ) GO TO 2 1 7Q ( I , K P ) = Q ( I , K P ) + P R * ( ( R K ( l l - l . ) / R K l K P ) - A L * A R K ( l ) )

- 82 -

00550056

00570058005900600061006200630064006500660067006800690070

217

211

202201

213204223

203

GO TO 2 1 10( I ,KP)=Q( I , K P | * P R * < ( R M 1 I * I 1 . / R M K P ) - 1 . / R K ( K I > * L > ) >- l . /RK U P

l l . - A R M K P * l >-ALOG(AL ) MVKN=<AM«EBAR<KM1 )-AN*EGAMAIMP,KM1»1/ENÏ F ( V K N . G E . R M l ) IG0 TO 202I F i V K N . G E . l . ) Q ( I t KP» = Q I I , K P | * S I G I I M P , K H l » * O E N S I I t J ICONTINUECONTINUEGO TO 223DO 204 KP=1,KMQ ( I , K P ) = Q ( L 1 K E ( I I ,KP)DO 203 KP=l ,KMKM1=K-KPO." in = QFJ I ) * 0 ( I , K P ) * P H N I , K M 1 ) * V ( I ICONTINUERETURNEND

-83-

000100020003

0004000500060007000800090010001100120013001*.0015001600170018001900200021002200230024002500260027002800290030003100320033003*00350036003700380039004000410042004300440045004600470046004900500051005200530054005500560057

310

3! I

320

SUBROUTINE L E N O R E < N , C C J , H O P E « K ICOMMON/ALL/OPT I ON U O ) , V( 3 0 > , OF < 3 0 )C O M M O N / L E N / R 1 3 0 » , S ( 3 O | , T i 3 O > , J J ( 2 , 3 O ) , H V V ( 3 0 ) , W O V i 3 0 ) , w I V < 3 0 ) i

1 S T 1 3 0 . 6 0 )0 1 MENS ION A ( 3 0 ) , B ( 3 0 ) , C ( 3 0 ) , D ( 3 0 )R E A L » * J JC < N * 1 t = » C O JD ( N « - l > = 0 .DO 3 0 0 I ! = 1 , N1 = N - I 1 + 1

I F ( I . E O . l ) GO TO 3 0 1TH = R ( I l - R ( I - l )X = S T ( I , K ) * T HY « R ( S - U / R I I IAVL = 4 . « S T ( 1 , K ) * V ( I I / S f I II F ( S T ( I t K ) . L T . 1 . ) GO TO 3 1 1I F < ( S T ( I , K I « R ( J ) ) . L T . 4 . ) GO TD 3 1 1G = 2 . * S T I I , K ) * S O R T ( 2 . * R ( 1 ) * T H )1NTEGER*2 OPTIONP - 4 . * G » 2 1 .

P = ( 1 . * 3 O . 7 5 / I P * P ) ) / S Q R T 1 P )

PC0=3.*(l.-4.2554*EXPl-C)*OI/(1IF1X.LT.4.I GO TO 310POI=.OO552?*EXP(1.14*I4.-X))»SQRTIY)PIO=PQI/VPOV=1.-POI-POOPIV=l.-P10PVI=Y»PIV/AVLPVO*POV/AVLPVV=1.-PVI-PVOGO TO 320CALL HOPE(X.Y.PVI,PVB)PIV=AVL*PVI/YP I O = 1 , - P I VPC) I =Y*P 10

PVO=POV/AVLPVV»I.-PVI-PVOGC TO 320C A L L H O P E ( X , Y . P V 1 , P V O )PVVM.-PVI-PVOPCV=PVO*AVLPIV=PV1*AVL/YPI 0=1.-PI VPOI=Y»PIOPOO=1.-POI-POVZ=l./(l.-T(I)*PVV»ZL = l.-Ml.-.75*Tm

WVV( I ) = P V V ZDA=10.*(.15-P10)DB=10.*(PI0-.05)IF(DB.GT.O.I GO TO 321H O V d ) = tl.-2.*P0I )*ZLWCI=P01•!.5»P0V*T(I)*POI«ZL

-84-

005800590060006100620063006*006500660067006800690070007100720073007^ÛC75007600770C780079008000810Q820083008*0035008600870088008900900091009200930094009500960097009800990100OlOi01020103010*010501060107oioa01090110OUI01120113Oil*0115

>*ZLWlVlI > = (l.-?.*PIO»*ZL

321

322

301

312

313

323

32*

Ml 1=.25*PIV*T(I)«ZLGC TO 302IFIDA.GT.O.) GO TO 322MOVU >=POV*ZW01=P0I+P0V*PVI*TU )*ZWOO=P00*P0V*PVO*T(I)*lMlV(I)=PIV*ZWIO=PIO*P!V*PVn*T(I)*ZMII=PIV*PVI»TlI)*ZGD TO 302MOVU)=DB*POV*Z*DA*(1.-2.«POII*ZMOI=POI+POV*T(I)*(DB»PVI*Z»DA*1.5*P0I*ZLMO0=POO»POV*T(I)»(DB*PVO*Z*DA«.25*ZLIWIVII)=DB*PIV*Z+DA*(l.-2.*PI0)*ZL

HII=PIV»T(II*(DB*PV1«Z*,Z5*DA*ZL)GC TO 302X= .T»1 ,K)*R( 1 )V = 0.

IF(X.GT,4. ) GO TO 312CALL riOPE(X,Y,PVI,PVOIPVV=1.-PVOPOV=AVL«PVOPCO=1.-POVGD TO 313P00=.125/1STlitK)*ST(1,K»*RI1)*R(1J)PCV=l.-POOPVO=POV/AVLPVV=1.-PVOPV1=O.PIV=O.PIU=O.POI=0.Z=l./(1.-T(l)*PVV)ZL=l./(l.-T(l)*PVV)wvr=pvi«zHVO=PVO*ZWVV<1)=PVV*ZMOI=O.WIV(1!=O,WIO=>O.WII*O.DA = 10.*U2-PVOIDB»10.*(PVO-.1IIFIDA.GT.O. ) GO TO 323WDV«H=POV*Z

GO TO 302IFtDB.GT.O.» GO TO 32*WQVIII»POV*ZL

GO TO 302MOV(II=>POV«<OB*Z*DA*ZL)

-85-

01160117011801190120012101220123

01250126012701280129

302 DEN=L./(l.-M00*C(I*llIIF(I.EQ.l) GO TO 300A(I)=WI0*06NB< I»=WOO»DCm>WII»MQI*C(I*ll*A(ItD(1)=WOI*(C(

300 CONTINUEJJ(Z,1)=(WOO*D(2JJ(1,1)=C(2I*JJ(2,1)*D(2)DO 303 1=2,NJJ(2i I)=A< I J*JJ(2,I-IKBUI

303 J J d . I 1 = C*RETURNEND

II*DEN

-86-

0001000200030004000500060007

oooe00090010ooii001200130014001500160017001800190020002100220023002400250026002700280029003000310032

400

401

402

404405

SUBROUTINE HOPE!XCY,P,Q)IFU.EQ.O. 1 GO TÔ 400ÏF1X.LT.1.» GO TO 401E=EXP(-X>

G=4.*X*13.GZ=(.5-E*SQRT(2.54647/G)»<Gl = l.5-E*(i.*3.08/<F*FM/F>/XH=1./»X*X)SZ=((<(-.12032*H*.26569)«H-.GO TO 402GZ=.63662

. 75/(G*GM

-.19625I«H*1 2*X)

GO TO 402A=ALOG(XIXX=X*XGZ=.6 3662-.5*X*.106l*XX*(1.94926-A)•.00265*XX*XX*t1,89926-A>Gl = l.«-.5*X*U-.9228)-.1660*XX*.0177«X*XXSZ=1.-1.3333 33*X-XX*« i.0 3243»XX*.49872I*A-,05505*XX-,68542»IH (Y.EQ.O. ).0R. (Y.EQ.l.M GO TO 404ALAM=i(SUKT(l.-Y*Y|»ARSlN(YI/Y-1.5708*YI/(1.-Y 1-2. )*.87597GO TO 405ALAM=YANU*l.8*.3/<(1.01-Yl*(l.*4.*XI)ALPH«Y-JY-ALAMI*EXP(-ANU*X»P=((l.-ALPH)*GZ*ALPH*Gl)*Y/(1.*Y)YBAR=1.-YAL=Y»YBAR*t6.*X-3.)/(2.*X*l.)O=((Y8AR-ALJ*SZ*Y*G1)/(l.-AL)-°RETURNEND

APPENDIX

SAMPLE OUTPUT FROM NEVEMOR

NEVEMGR

51 GROUP ENERGY DATA FDR NINE MATERIALS INCLUDING INELASTIC MATIX FOR U23P

ENERGY CEPENDENT INPUT DATA

LCWER

K

159

13172125293337414549

ENERGY

ELCKI( PEVI

10.00006.9C004.8C0 03.3C002.3COÛ1.60001. 10000.76000.525C0.36000.25)00.17500.1200

BOUND (ELiK

E9ÛRJK)(MEV)

7.24445.02173.44782.39861.67391.14930.79450.54960.37970.26230.1B240.1261

) ) AND

K

26

10141821263034384246 .50

AVERAGE

ELIKI(MEV)9. 10006.30004.35003.00002.10001.45001.00000.69000.48000.33000.23000.16000.1100

N E U T R O N

F B A R (I M E V

9.54306.59554.57133.14762.19851.52381.04920.72440.5C220.344B0.23990.16740.1149

ENERGY

K| K1

37

1115192327313 D

39434751

(FBAR (K) |

EL(KI( HE V I8.30005.75004.00002.75001.90001.32500.91000.63000.43500.30000.21000.14500.1000

AS A FUNC

EB4R(K(MEV)

8.69396.02084.17^62.873?1.99831.39660.95430,65950.45713.31480.2',9R0.15240.1049

TION

1 K

48

12162024283236404448

OF GROUP

FL(K)MEV)7.60005,25003.60002.50001.75001.2000o. moo0.57500,40000.27500. 19000.13?5

753•j

11P000,00

FBAR(K)(MFV)

, 9 4 4 9. 4 9 b ?. 7 9 6 5. 6 2 3 0« B 2 4 0. 2 6 1 5. B6 94o6021.417^*. ? 8 7 ?.1998. Î 3 fl 7

CROSS SECTION OATA AS A FUNCTION OF GROUP

ABSOKPTIGN CROSS SECTIONS FOR ALUMINUM

K1

1121314 151

0 . 00 . 00 . 00 . 00 . 00 . 0

K2

1222324 2

0 . 00 . 00 . 00 . 00 . 0

K3

13233343

0 . 00 . 00 . 00 . 00 . 0

K4

14243 44 4

0 .0 .0 .0 .0 .

0 '0000

K

515253545

0 . 00 . 00 . 00 . 00 . 0

K6

1626364 6

0 .0 .0 .0 .0 .

0000

K7

17273 74 7

0 . 00 . 00 . 00 . 00 . 0

K8

1828384 8

o.c0 . 00 . 00 . 00 . 0

K9

1 92 93<54 9

0 . 00 . 00 . 00 . 0C.O

K10203 0^ 050

0 . 00 . 00 . 00 , 00 . 0

ELASTIC SCATTERING CROSS SECTIONS FOR ALUMINUM

K1

112 13 14 151

O.231CO1.004501.827002.533002.205003.55200

K2

12223242

0.251601.092001.385002.227252.98650

K3

1323334 3

0.262501.210001.947003.100003.31200

K4

142 43 44 4

0.313201.416001.902752.623504.65000

K

515253 545

0.361001.616502.025003.300003.27250

K6

162 63 64 6

0.409501.666002.115003.825006.11000

K7

172 73 74 7

0 .1 .2 .3 .9 .

4600068150016006700045000

K8

1828384 8

0 .U2.?,5o

56700710C0346002620070000

K

i -

2 93 94 9

0.68200I.7«i?753.074003.71700?.09000

K1020304 050

0.860?51.7B1252.409004O 0 94T02.433^0

1KELASTIC SCATTERING CROSS SECTIONS FOR ALUMINUM

CO1

1112131415 1

1.000000.690000.130000 . 00 . 00 . 0

212Zl3242

AVERAGE GAMMA

K1

1121314 151

7.000001.950001.100000 . 00 . 00 . 0

K2

1222324 2

0.990000.650000.100000 . 00 . 0

ENERGY IS

6.400001.600001.100000 . 00 . 0

31323334 3

0 .0 .0 .0 .0 .

97000590000500000

414243 44 4

0.940000.530300.ClOOO0 . 0O.C

INELASTIC COLLISION WITH

ft3

1323334 3

5.1 .1 .0 .0 .

65000300001000000

K4

14243 44 4

5.150001.150001.100000 . 00 . 0

•s1525354 5

K5

15253545

0.920000.470000 . 00 . 00 . 0

ALUMINUM

4.600001.100000 . 00 . 00 . 0

616263 64 6

K6

16263 64 6

0.880000.400000 . 00 . 00 . 0

4.100001.100000 . 00 . 00 . 0

71727374 7

K7

1727374 7

0 .0 .0 .0 .0 .

3.1 .0 .0 .0 .

8500033010000

6000010000000

8

18283 84 8

K8

192B1 94 8

0,810000,280900 . 0o.r0 . 0

3,150001.100000 . 00 . 00 . 0

919? 9394 9

KQ

1 92 9" \94 9

0,78000C.22COO0 . 0C.O0 . 0

2.75000U100000 . 0C . O0 . 0

1020i n4 05 0

K1020304 P

5 Û

0,73000C.1RCOO0 . 00 , 00 , 0

2,300001, 1 00rn0 , 0runO.P

AflSGRPTICN CROSS SECTIONS FOR CAR3ON

K1

u2131M51

O.13O0O0.00.00.00.00.0

K212223242

0.jdOOD0.00.00.00.0

ELASTIC SCATTERING CPOSS

K1

1121314151

0.4000C1.842751.846322.935943.827824,37663

K212223242

0.431602.244001.961403.033243.38846

K3

13233343

0.035000.00.00,00.0

K4

14243444

SECTIONS FOH

K313233343

0.436242.314752.0O4603.131263.93960

K4

14.243444

0.0

cec.o0.00.0

CARBON

0.760001.605402,206263,264004,00656

K5

15251545

K5

15253545

0.00.00.00.00.0

0.811802.458702.3150C3.316444.(16805

K6

16263t4'>

K616263646

C O0.0C O0.00.0

0.510Û01.691202.407603.393904.12141

K7

17273747

K7

17273747

C O0.00.00,00.0

Q,9lS801.57542?,549253,477544.17763

K8

18283848

K6le2flîa48

0,

n.0,n-,0,

î,1,

z,3,4.

Crc00

023C06)5??6^765578642'-576

K9

!929•»9

4 9

K.9

19293949

0.C.r.0.0.

0.1.2.3.4»

000

0

8 340 071020746456557629P40

K1020304050

K1"?.r>3o4050

0.fi.

0,

r-,0,

1,1,2.3,4,

nnn

00

1470074^ÇPliOl'?T*bC S

3 3 ? 6 C

INELASTIC SCATTERING CROSS SECTIONS FUP CARBON

K1

1121314151

0.26C000.00.00.00.00.0

K2

12223242

AVer "(JE GAMPA E

K1

1121314151

• 55000u.O0.00.00.00.0

K2

12223242

0.120000.00.00.00.0

NERGï IÎM

4.430000.00.00.00.3

K3

13233343

0.300000.00.00.00.0

K4

14243444

0.43500C Oco0.00.0

INELASTIC COLLISION KITH

K3

13233343

4.430000.00.00.00,0

K'414243444

4.43000O.C0.00.0O.C

K5

15253545

C

K5

15253545

0.0.0.0.0.

245000000

ARBON

4.0.0.0.0.

430000000

K6

16263646

K6

16263646

C.270000.00.00.00.0

4.430000.00.00.00.0

K7

1727M47

K7

17273747

0.Z30000.00,00,00,0

4.430000,00.00,00,0

KP

18?8IP48

KA

182818

0.100000.00.0O.P0,0

4-430000,00.00.00.0

K9

1929

3949

K"5

n293949

0.0,0.0.n.

4.Co

04000000n

4 ~<.r o 00

0.0p ,

a.n0

K10? 0• o

4050

K1C20304PR P

C0,0,0,

c

0,

c0.0.0.

000o0

000

n0

ABSORPTION

K1

1121314151

0.0.0.0.0.0.

000000

CROSS SECTIONS FOR DEUTERIUM

K212223242

0.0.0.0.0.

ELASTIC SCATTERING

K1

11213141SI

0.1.2.3.3.3.

600006600069000110002900C39000

K212223242

1.1.2.3.i.

0

a000

CROSS

1000096000750001400030000

K3

13233343

0.00.00.00.00.0

K4

14243444

SECTIONS FOR

K3

13233343

1.180002.080002.830003.160003.30000

K4

14243444

0.0.0.0.0.

00000

K5

15253545

DEUTERJUM

1.2.2.31.3.

2500015000850001800030000

K5

15253545

0.0.0.0.0.

1.2.2.3.3.

00000

3200025000900002000032000

K6

16263646

K6

16263646

0.00.00.00.00.0

1.420002.350002.930003. 200.503.31000

K7

1727}747

K717273747

0.00.0O.C0.00.0

1.500002.430002.980003.220003.35000

K

aîfl28

48

K8

182B3941

0.00.00.00,00.0

1.600002,510003,0?0P03,240003. if-rnc

Ko

19293949

K9

19293949

0.00.00.00.00.0

1.690002.SP0O03.950003.2TC003. ?=?noo

K10203040•>0

K10203040SO

0.00,00.00,00.0

1.7 80C0?,6ïoon3.0P0003., 2 W i O3,3300"

^ELASTIC SCATTERING CROSS SECTIONS FOR DEUTERIUM

K1

1121314151

0.00.00.00.00.00.0

AVERAGE

K1

1121314151

0.00.00.0o.ô0.00.0

K2

12223242

GAMMA

K212223?42

0.00.00.00.00.0

ENERGY

0.00.00.00.00.0

K3

13233343

0.00.00.00.00.0

IN INELASTIC

K313233343

0.00.00.00.00.0

K4

14243444

0.00.00.00.00.0

COLLISION

K4

14243444

0.00.0O.C0.00.0

K5

15253545

HITH

K5

15253545

0.00.00.00.00.0

DEUTERIUM

0.00.00.00.00.0

K6

16263646

K6

16263646

0.00.00.00.0O.û

0.00.00.00.00.0

K717273747

K7

17273747

0.00.00.00.00.0

0.00.0O.O0.00.0

KBIS•>H

3&46

Kfl

182838'.H

0.00.00,00.00.0

0.00,0

o.n0,00.0

KQ

19?9394<?

K9

19293949

O.C0.00.00.00.0

0.00.00.00.00.0

K10?0304050

K10?0304050

0.00,00.00,0

o.n

0.00.00.00.00,0

IO

ABSORPTION 1

K1

1121314151

0.00.00.00.00.00.0

:ROSS SECTIONS I

K212223242

0.00.00.00.00.0

K3

u233343

-0« HYDROGEN

0.00.00.00.00.0

K414243444

ELASTIC SCATTERING CROSS SECTIONS FOR

K1

1121314151

0.470001.310003.150005.250008.5000012.500G0

KZ122231'42

0.980001.920003.J50005.500008.9OCOO

K313233343

ifccLHSTIC SCATTERING CROSS

K11121314151

0.00.00.00.00.00.0

K212223242

0.00.00.00.00.0

AVERAGE GAMMA ENERGY IN

K11121314151

0.00.0G.O0.00.00.0

K212223242

0.00.00.00.00.0

K3

13233343

1.055002.O5OOO3.500005.800009.20000

SECTIONS

0.00.00.00.00.0

K414243444

FOR

K4142434

1

C O0.0

o.c0.00.0

HYDROGEN

1.14C002.130003.750006.100009.70000

K515253545

K5

15253545

HYDROGEN

0.00,00.00.00.0

INELASTIC COLLISION HlTf

K.3

13233343

0.00.00.00.00.0

• K

14243444

0.00.00.00.00.0

K5

15253545

0.00.00.00.00.0

1.220002.320003.900006.40000

10.00000-

0.00.00.00,,00.0

1 HYDROGFN

K5

15253545

0.00.00.00.00.0

K616263646

K6162b3646

K6

162636"b

K616263646

0.0.0.0.0.

1.2.4.6.

10.

0.0.0.0.0.

0.0.0.0.0.

.0,0,0,0,0

3100045000loono7000040000

00000

00000

K717273747

K7

17273747

K7

17273747

K7

17273747

00,00,0,

1,2,4,7,

10,

0.0.0,0.0.

0.0.0.

a.0.

.0

.0

.0

.0

.0

.40000

.58000,30000.00000. BOOOO

.0,0.0.0,0

00000

K8

18253R49

K8

m21384fl

KB

19293H43

K

1826384*

0,0,0,0,0,

I»2.4,7.

1 1.

0.0.0.0»0»

0.0.0.0.0.

.0

.0

.0

.0

.0

.52OPO,70000,^500040000,30000

00

c00

00n0n

K9

19213949

Kc>

192e)3949

K9

19293949

K9

19293949

0

00,0.

1,2,4,

7.1 1.

0.0.0.0.0.

0.0.0.0.0.

.0

.0

.0

.0

.0

.6J000

.88000

.75000

.BOOOO,60 000

,0,0,0,00

00000

K1020304050

K102010'.050

KIC20304050

K1020304050

00000

135fl,

12,

0,0«0«0.0,

0.0.0,

n.c,

.0

.0

.0

.0

.0

,7?ono•nsnoo. oono»toono.noon

>o

• n,0,0

000n0

I—1

I

ABSORPTION CROSS SECTIONS FOR IRON

K1

112131415.1

0.0.0.0.0.0.

000000

K2

12223242

0.0.0.0.0.

001000000

K3

13233343

00000

.0

.0

.0

.0

.0

K4

142434

44

0.0.0.0.0.

00 ,000

K515253545

0.0.0.0.0.

00000

K6

16263646

0,00.00.00.00.0

K7

17273747

0.0.0.0.0.

00000

Kfi

IH

384H

0.0.0»0.0.

0

00p

KQ

1929394<3

P.0.0.0.0.

000

o0

K10?0104050

0.0 .

0.0.0.

00000

ELASTIC SCATTERING CROSS SECTIONS FOR IROK

K1

112131

51

K

0.26520 20.88000 121.650C0 221.89000 321.98875 <>23.31200

K0.31320 30.93240 131.71000 231.92000 33?.T75OC 43

K0.35720 4i.Il 390 141.69600 242.16000 342.60400 44

C. 40200 51.I96JQ 151.86430 252.531-30 354.488J0 45

K0.44520 6l.?4 740 S 61.41C0O 262.97500 361.410CC 4*>

K0.51293 71.42730 171.6500G 273.65400 372. 7<-050 47

K0.57750 P1.44300 131.39500 ?fl

3.32SC0

KO..6*IPO «1.5400 0 19l.o 7^P0 ? 91 . P t 5 ? 5 ""3

0.70500 101.7? ?n

1 •» î. •=• )

INELASTIC SCATTERING CROSS SECTIONS FOR IRON

11121314151

1.400001.450000.580CO0.00.00.0

212223242

1.400001.400000.510000.00.0

313233343

1.390001.100000.4 70000.00.0

414243444

1.380001.020000.400000.0

o.c

515253545

1.3 7OOC0.810000,46000O.CC.O

6

162!:364 6

l.360000.900000.3S000O.ÛC.O

7172 73747

1.36000,7.890000.21COO0.00.0

31928

1.350000.P500ÛO.O^OPO0.00.0

q

19293949

I.34000P.6 7P00o.Or.or.o

10?Q(04T

50

11, 3P0<" 0O.ftlOCC0.00.00.0

AVERAGE GAKPA FNERGY IN INELASTIC COLLISION WITH

K1

1121314151

8.600012.35C0O0.845000.00.00.0

K212223242

8.000001.950000.845000.00.0

K313233343

7.450001.55CC00.845000.00.0

K414243444

6.750001.300000.84500O.CC.O

15253545

6. 10000l.OPOOO0.S45000.00.0

K6

16263646

5.450000.96O00C.845000.00.0

K7

17273747

4.8000C0.855900. 845000.00.0

Kfl

l*2fl3P

4.150P0

o.a'^o0.84SCO0.00.0

K,

919293944

?.0.0.0.0.

6"C(84e'0

00

10 ?Cir

•iO

2- «350"n

0.00.00.0

coo

oo

* o« 4

oco^

«c o-

ocor a i

oo

ooooo

ooi ra-—

o

o

o00

oo

oM

O

o

a—'

oo

a:

oo

- i

o

o

•cI -

1

o

oc

om

C

o

rg

O

o

0PA J

O

o

I M

O

o

rg

o

oo

o

o

o

am

co

m

O

o

oo

O

o

o

oirv

oc

oo

CO«^

oo

oo

i l• »

o

, - t

a:

o

•J

r.0

L.D-

C '

V rr

o.0

°

co0-

^)

c

^ -C

o

I fir

c

-

Q

Oi rrr,

tr

~

g

- >

^ j

O

-

CE—*

i!o

oCLi n•Dco

O

-0

0D

C71

r.

oc

^

„I M

C-Jcer*c

C

>t

%

" •

rM

u-r-

cr

" • »

o

cf ~

•c

C)

C ltu

i ^

* - •

0'

• *

O

?

r

c-r~Ou ^

-

•L.

h -

cc

oI Aac

r-

J

CL

Oi n

c-

r"

U"•OOcr

o

c c r o c c. c c c. c

C O O O C C C O C- Ô

c c. C c c

ff ? tr,_ rg r

c o c» c- o LJ o o o c

c o r- r o o c- r' o c.

C O C O O O O C1 O O

o o o e o o r o o o

— r\i n-. j

COO

c c o c o

o c o c- c-

c oo oo c

- - O O O O u. — Ci Ci O O• • e * * '_^ f • • • •

O O O O O u C ^ * " O O Ci O C" > C• O •"> C îJ

O 0 0 0 0 0 2 - 0 C C>TJ N O O n r i t r: •— OO 2 T 0 " t ? " 0 O > û O ' — ' J I O

fM O O ^ O O in p« Oii O J _•< (ij û U CJ O J2 i - ^ o O O t j

O O O O O « O ~* f f"1 O CJ O »_- C' — ii O U O O

a. —*#•*•*< se W - : «f •,' u i t - i -r >t -J i -j ^ -J- * *J -T •»•

i-4rsir^->r a: -vr^ ^ j u. — r r ,j _j H N I ^ jO ^u. " j iT> O J^ O L/I O - <•''

O « t o ^ ^ 0 i— *i o O O ^•— » * • É • J * * « « •H Of^"Mnj-5- ai O O O O O

i/i ^ r*i n i n ^ " ^ t/i ^ m pi n-, m m

oo a o -r CJo 'J* O O — Of -G vi- J-- > f -if « r *•* n o o r - N

* • — , . » • t -I»%! ^ a. O O O O C • ^ »?

O O < Q O O 4 Ç . I O . / Ï O X C-*r o o u r " • •© ^ o o -saLJ O O t/> o •» r- i» r*-, cJ *_J O O O»4 O V ( O i B ï l N ^ O « O O* - mooooo o ^ > ^ <r N ^ - î — •* o o »"3 o o -*J ra. • • • • • » « » • • • • * ^ . • * • • t j> ,QC OOOOOO h- O'-*|MfKJ-t'*1 < O O Û O O O -f -OO s/1 - * *I/) <f IU u»

> -

°aa

di-

UJ

00

0

IM•

O

rooo

«M

O

O

•O

m

LO00

o

o

o

a

m

O

o

o

ô

£!

oo

o

o

3

o

o

ABSORPTICN CROSS SECTIONS FOR URANIUM 233

1u21314151

211112,

•590C0.23000.37000•3500C.65000.26000

212223242

211I1

.61000

.2 5000

.37000

.39000

.70000

313233343

211,1.1,

.60000

.2 7000

.37000

.40000

.76000

414243444

ELASTIC SCATTERING CROSS SECTIONS FOR

K1

1121314151

0.1.1,2.5,8,

.62055,05558.75338.85750,71285,24320

K212223242

0,1,1,3,5,

INELASTIC SCATTER

K1

11ai314151

0.2.1.1.0.0.

,21000,05000, 60COO,06000700CO32C00

K

z12223242

0.2,1.1.0.

•61035.16145.77080.11125,94960

K313233343

ING CROSS

.24000,05000,50000,32000,66000

AVERAGE GAMNA ENERGY IN

K1

1121314151

9.3.1.0.0.0.

600012500013C0025COO0fc500038C0

K212223242

8.3.1.0.0.

510011000001000210000620C

K313233343

0,1.1.3.6.

,61440,34100,80500,33630,30360

SECTIONS

0.2.1.1.0.

3000004000,4500000000620C0

K414243444

FOP

K414243444

21111,

.40000

.31000

.36000

.41,000

.84000

URAMU* ;

0,1.1,3.6.

.64320

.55008,85652.59840,59650

515253545

?35

X5

15253545

2.1.1.I.1.

0.I.1.3.6.

URANIUM 235

0.2.1.C.0.

,50030,00000,37030,«59030,56000

INELA5TIC COLLISION HITI-

K313233343

7.2.0.0.0.

6000080000910001700005800

K414243444

7.2.0.0.0.

0000050000

eiooo14010C560O

K515253545

0.1.1.0.0.

,11000,33000,350004300087000

6867672327936558394091120

800009700033O0C9700056000

' UKANIUH ?

Kc

15253545

b.2.0.0.0.

3500C2500071000115000K 1 nO

616263646

Kt16263646

K61626?6ut

35

K

6

16263646

11111

01247

111rc

5,2,0,0,0,

.88000

.35000

.32000

.46000

.91000

.72038

.80525

.03970

.10755

.13090

rl2000.9 5000.30000.94000.5^000

. 75000

.00000

.61000

.09800

.05000

717273747

K717273747

K

717273747

„717273747

11112

01247

I1100

51000

.34000

.39000

.32000

.49000

.02000

.78925

.79340

.18400

.46400

.38720

.70000

.90000

.25000

.90000,47:?00

.20000

.80000

.51500

.06700

.04800

81628384S

K818283848

K8IB2838

Ks18283849

l.lflOOO1.3HOC01.330001.520002.07000

0.854361.801442.3*1104.781707.63875

1.950001,870001.200000.B60T00.4400C

4.7P0001.6?0000.4-^00O.OROOO0.04400

919293949

K9

192939«.9

K

919293949

K919293949

1.170001.360001.340001.540002.12000

0.921571.738002.516005.101H07.84090

2.030001.800001.150000.820000.40COO

4.250001.440000.365000.077000.04100

1020304050

K1020304050

K1020304050

K10?.r\304050

1.190001.350001.330001.S90C02.18000

0.961751.742122.654295.390958.03640

2.050001.70000I.I 30^00.760000.36000

3.900001.270000.300000.071000.04000

ABSORPriCN CROSS SECTIONS FOR URANIU» 238

1112131415 1

2.500000.580000.480000.160000.1*0000.28000

212123242

2.460000.580000.3 80000.150000.17000

313233343

2.340000.530000.24G000. 160000. 15000

4

1424344 4

2.100D00.560000.170000.17000O.lQQOa

1525354 5

1.630000.590000.210000.15000

o. nooo

162 6364 6

0 .9Q0000 ,610000.250000.140000.?noO0

71727374 7

0.630000.610000.220000,130003.21000

1»233°.4 R

0.590CO0.610000.230000.140000.?3r>00

91 929394 9

0.570000.620000.200000.140000.25000

10?0304050

0.5 80C00,590^00.17000C.140000,?60oo

t U S T I C S C A T T E R I N G C « , J S S S t C T I J N S F f i f i 2 3 R

KI

1121314 15 1

Q .

I .1 .i .£>,

1 0 .

54175103 788222355&CC7 '-J1 5 G

30400

Ki

12^i

0. 11 . 21 . •'

3 , i7. :

5 9 6 5C : 6 CC 1 2 63 1 7 5

' c< r c

K

i

1 j2 3334 3

C . 1 9 3 2 S1 . ' 0 4 8 -2 . J 1 i 7 c

4 * i 1 i 41' . - . Ï Î * 4 C

K4

i >•2 43 4

' , 4

c .1 .

4 ,

7 .

t ' I S£. '. ; i

! 04 1V Ï 4 ?

P 4 9 3

. " . 2 '• -1

i .c! i

7 c. *, i

1 72 7

12

. 82 2 35

. 60 44 2

Q

1 «•» P

- 7

- cK

10?C

6 . 4 5 3 4 0

I C • S « . F T T H ' N s f t P .; s I

K

i1121S L

4 i

5 1

0 .j .

0 .

~" J a

SJ.

5000(j00CC100 L u3r c c r cooec c

12 0 . '. •: •. . i

• • - •

0 C 0 i." C U 2

. - C l• 'Ct 1

K K

. :o os 14^ J 2 r • j 4

1 ~ . 0 i > 4I^CCi - ~ -

^ * c ,I,1 ^

' " • -

r, ; .'

K

C K ^C T 0 1 c

.- ^ . i c

, - " . • • • • *

- c . o : o :

' • , • " r •

r . - •' 7 '

71 727

0.00000

1 . 0 0 0 n '^,PC n i n••« 4 32 I

0 .0 TC0.0 00r. ion" . • < " " •

• " . 4 • • •*

-1

0n

?t ,

4

• ;

1

ï C?ci n

4 f

0 ,o.0 ,

0 ,0 ,

0<"*0

oonnon00°4 7C

Avf^âGt i . a f - i , f I N ; •-.11 , : i L L t ; i i

1t"

3<4

l11l11

4 .

1 .0 .0 .0 .

01 !>4S5& 6 1 6 2

65t 7626 1 2C1 C 4 4 R

c

*' £

32••2

J . '?

5, '1 , s

J ?tb•" G 4 6 11 7 3 4 29 9 e " - *

IBP11- 4

"i

3

J

a.i ..>.' a

»>5 7 2 2

"- 13 2 7

1 B 0 7 1•S4 7 3 0

2 1 3°2

4

1 42 4:>4

4 4

7 .3 ,

1 .- B

0 .

9 1 1 1 5134 it.2S615500041 9 g 39

c

2 e-^ c

4 e

* k n K. KT . 2 1 i r t 0 6 6.5t.7*>4 7 5 . 9 ^ 5 4 2 ? S . 4 7 ' C 3 9 c . C i r 4 5 10 4 . 5 5 2 C 3.•" . a 6 1 <"• f 1 * ? , M l ' k 17 ? . 3 P " 5 1 19 ? , l o c ? l 19 1 . ^ 1 9 0 0 PO 1 , •< 1 f> 7 91.1444J i t U 0 4 4 7 8 27 3.9=,027 ?« 0 , .•"• " 7 ? ? <3 0 . 7 9 1 ) 4 3P p . 7 2 1 - > a

16 0 . 4 15S0 37 0 . 3 7 B 0 5 1» 0 . 1 < - 3 3 3 3o " . M T - ' i 40 0 .2R6 ' l-7 0.15173 4f> n,13PO7 49 n.l?«i61 0 0.114-4

INELASTIC SCATTERING MATRIX FOR URANIUM 238

FROM GROUP

K212223242

0.00.001210.013840.014360.00501

FPCH GROUP

2

K313233343

3

TO GROUP

0.00.001200.014300.013250.00472

TO GROUP i

K

K414243444

K

0.00.002040.016810.012090.00443

K5

15253545

0.000030.002630.015250.012240.00313

K616263646

0.000050.00347C.017090.009620.00296

K7

17273747

0.0Û0060.004670.017270.010920.00280

K8

18283P4P

0.000070.006420.016860.008020.00220

«C919293949

0.0PC080,008170.015910o007880.-0207

Kin20304C•50

r0000

.00040

.00727

.01700

.00646

.00157

K11•? J

314151

C.0.0.0.0»

000700102 %01541006'îbnoi'.9

3 0.0 4 0.0 5 0.00001 6 0.00002 7 0.00003 B C.00003 9 0.0C003 10 0.00045 II P.00035 12 0.001*013 0.00150 14 0.00257 15 0.00333 16 0.00441 17 0.00604 1H 0.00836 l<? 0.01067 20 0.0OQ53 21 0.01379 22 0.01903233343

0.019B70.019130.00691

FRGM GROUP

K4

14243444

0.0C.003780.036910.028070.01051

FRCM GRCUP

K515253545

0.00.006560.052810.049440.01342

FROM GROUP

K6

16263646

0.00.011710.090970.063980.02137

243444

0.023510.017470.0C648

4 TO GROUP 1

K515253545

0.00.004920.333720.028500.00744

253545

K

K6

16263646

5 TO GROUP K

K616263646

0.00.008900.060170,039260.01279

K717273747

6 TO GROUP K

K7

17273747

0.00.018390.095810.073390.02039

K818283848

0.021430.017710.00458

0.00.006530.038070.022470.00706

0.00.013130.062510.044890.01217

0.00.026760.096260.054330.01612

263646

K7

17273747

K818283848

K919293949

0.024120.013950.00434

0.00.009050.038S80.025560.00668

0.00.018700.062210.033160.00959

0.00.035140.092790.053720.C1519

273747

K818283848

Ko

19293949

K1020304050

0.024530.O15S-50.00411

0.00.0*2600.038230.019830.00523

0.00.024270.059560.032730.00900

O.0OC730.031850. 100780.04430n.01148

28384H

K91<?293949

K!020304050

K1121314151

0.0.0.

0.0.0.0.0.

0.0.0.

c.0.

0.0.0.0.0.

024050116700322

001615036280185400489

0007002185064350269500678

0014404817092670438801089

291949

K1020304050

K1121314151

K1222324252

0.022770.011470.00302

0.000610.014440.038920.015220.00366

0.001300.032620.05891O.02"*50.00642

0.0025'.0.068370.088640.03480

304050

K1121314151

K122232425?

K1323334353

0.024^9O.CO9<,10,00226

0.00121O.O21?30,035420.015020.00344

0.002480.045930.055820.02110

0.00260C.072400.053650.0?~P6

314151

K12223242S2

K132333435^

K1424

344454

0.022160.0092B0.00213

C. 002170.029610.03314O.Oll87

0.002490.04B450.052260.01999

0.005730,086430.077790.03132

3?4252

K13?3334353

K1424344454

K.1525354555

0,0.

0,0.0.0.

0206"0P731

OC218OMCfl0306901119

0-004770.p.0.

0.0.0.0.

05769048?701867

00841079240801502235

^ • - t r in

<\j r- C f-

o «-< c o0 » o r

o o o o

CD r O CDO rr o <MO O ^ - o

• • • *o o c **.•

«M -^ r\j *rx a - rcr a; c Œ

, - | «~ Q-. (\J

9 * 0 0

C O O C

r- r- r- r- r-- - (V ^ J IT

— C 43 O"-i ,-J rr ru

o «-• o o

r* C -C- *£>•— u a rC7 f> 4j **-it*' rv P- r\.

c .- c cV t 0 f

c c c cIL ce (s a a)

a IT r\, _0 * - 4" ?Πc r . f

0r-j j

* • (

C

o

a-

r go-

oo

or

P .

—

c

s.a

r

rZc

cri T

Occ.

c

Cr(*

0-ac

o

l-J

•£p.,gfi s

c

c.

(7

o-

I f

c

c - c c3 f * •

c c c c

r — u- A.

o — c rC C f « C

•H rg n *j

O CT- - I -^ f - oo r-ir* -H 43 a-o o a mC —i C C

« « » *•o o o o

r-4 f\l (*• ^ I

m o ••< C1

0* i-H 43 CD*-* \f\ ff\ ,-4o a1 o • *o o — o

• • * •o o o cr

: m m ro m et•-< c\j r*i •# tn

r- O O Ocr ^- -< o-4 o a **o c r o - *o o —' o

• • • •0 0 0 0

Ci

c-o

* If

o

o

IL J

CTO

O

•

a

oo°"IT

O(T

O

•

-0

CO

o

c

o

in

0-

o

o

pn

o.—1

ft

o

in ir

•J-

ot

rvj

•O

43 Œ tr OCo ^ o- —•c. M- o —^* — a: roC »-i o C

o c o c

o a- — mo o *-* o

p- tn 4;O PU ^

O O O >f0 - ^ — 0

• » * •0000

ï a. a u: x i

4 43 C*. n,a N iC rN C I ry

>« f\l m tf IT

m *r» m r.io p- œ 4;CL C7- r*- rr\

o < o o

c- r» c r

iT• tn 43C- CT -*

: o a c a cr-

ry r 0" cra J f > *j<*" f1 IT P-r\j r. j fO —' C Ce « • »

C C C O

or a a* tr cc

o «- — oo o c* c.

u- -*• cr ITt f 45 F- rf"C. O CT rrc — o o

* • • •O O O O

a

oa:

a

r -

0-

a

uatUL

of - <

> - i

ooo

i ni nooo

°

oo

f -o.0IT '

O

o

r g

•D•Ûro

°orgr gruo

oo

,1 "mopn

o oo o

CO

i n

oIMo oo o

roPO

Cl

enCM

°PO

i n•ar g

1 - 4

o

5r-IM-Ci—4

- ^

o

COIM

oa*•-*

o

p .

I Ti f '

O

o

*-«P T

i ni n

°?rvj

r-

«O

o

«

oCD<OO

o

CO

p -I MI Mt rO

o

i nO•3-•—i

oo

i n

CDp -

4-* - 4

o

°om, 4

UNO"^4

oo

i n•oo

oo

-»~Da<0CMO

O

r»

K:

aoa :

a

00

a3< j

a.

X

uau»

CO

o

ooo

o*0oo•J

o

•F-4

o

oooo

࣠O

oo

o

_^ro

oro

o

rg

_

•n

o

-M

i n

>oroO

O

orgIM

oOO

O

C^

IM

c*IM

oo o

•X. CD CD,_!

m—4

o

ro

c

o

ro

COpg

- •

o

PO

I D

r»

1 -4

o

r g

o**IM

O

00IM

^r-» -O

o

i nr~0-i n

O

IMr goo

o

oi »

«cI Mr*o

O

m

i ni nmr-oo

CO

00

i n_<oo

mmi—4

•a*•*o

o

i n

00fM- 4

r gO

o

V

«7-

IMIMO

O

CO

a.a

at -

o

a.

oot

o

us

Opr-.

ooo

o

oroOoo

to

p - l

ooo

o

adooono

si O

oo

X cr

r-•cccc

o

IN*M, - t

^0

O

C j

!M

rg•Ci noo

r g

roP_4

•o

oo

o

crIM&moo

cr

r*1 rg

>r r-—4 - *

-> o

O Ci

m ÎCO CA* ^ f*~

tr a1

•-• ^-• o

. to o

IM rg

in sf

m org rsiru JO- • O

o o

ro J-

o oIM -4rg mPO -C-• O

o o

o oPO 4>

m -tm roO •£IM r-— oO O

CF O*1

!n

m

_r".

—<oo

i n

• - 4

oo

Q

_

mr gr goo

gf

a.13Or f

a

o

oa.ouIXu.

-4 m

rg ^O CO —

• •o c

mm

roo oo o

* !H So43COP-

o oo o

•j-.

mm

o oo o

- * rg

r*Q

enO O

O O

tt O O

—' -J--» cr4—4 S /

— C• 9

0 0

m -4

r» 43in p*P- 0

*-« 0

0 0

r*1 •!"

ra f nm4 Orj mr\j in•-4 O

0 0

m «*•

•«T i n43 in<£* 4

—« r ;

0 0

m «*

o*< aom 43n*i 4?*4 O

0 0

0 0

m

! P

m

43

p»

0

0

i n

p-

.—1

O

O

0i n

a

O

0

0

—

IDOa

x( j

a

CO*n

c0

0

"»i. in

rvjf^r - «

O0

•0

0

0

0

^ IM

0

roceO*CD

C

mrg

<Jr g

CU

O

mi n000

O

0

IM

r*0

0

r g

mm0i n0

O

—t

r g

a. ^

O r-

^- D

C C

Sîm rNJC* " "

•-< in

• •0 0

•& '•t

CC 43GD i nO »4Î

rg in~- 0

O O

m .*

43 CD4 43rg m—* 0

O Ô

rr\ f

LÎ m0 043 *"•tM P*- É 0

O O

pn j -

i n

«f

m

> * •

r*as

°O»-<

pj o m ccr if. ce CL-•o o g; o1

gr rg r- *-*O -4 O O

e 9 e %O O O O

ci in mW-* *0 Oo r- cig} rg -ao ~> o

• • oo o o

r- c p-in ^- mp- r- • *•O CM J 3O — O

• I •o o o

rg C C•a o —in ci •£

c — or» e »

O O C

a. .* Cgr * —o ci mo — o

• p »O O C

CM or

o c J-4 O O

* - • • - « • • - » -

ct>t—1

CD

O

o

V CCM

CDP-

crINIO

CC

1*1

O

oC l

oC I,—i

pg

t i

. » •

-O•4-P-

O

O

oJ-

oC l

crCC

o

oPJ

co

om

•0cOOr*.o

: M cw pg egrvj !*> «f in

O tf> C f*l/\ ff1 4 (01*1 *D CO O•$" C\J P- *NO <-* O O

• • • •O O O O

(\J i . **• m

o c o c

m i»- f\i sff i IT O>\lT» J CD Nr\j r^ r- (SJO •-* O O

« 9 * mO C? O C

M r*" st tTi

_ i <*•* m

^> tsi «oO -< C

o o o

rg f\i fsi (M

Cr -O *T CM^ rg in xC- <£> <M (Mff. i \ (£ rO ^ O Ot e a *

O C O O

•4- rsj CD

F-* P- P-

O - « O

c o cC l

Pg

ir.ci n

o

Cl P"Ci J?

cr r-r-i ITr- IT-rvi c-> O

C l

m

ir.CM

1-4

a-J3O

•O

pg

•7-

r-mmo

mC l

CMp-

O

C i

CCI

p -r g— ^

m•4-

rv.CïcrJ3O

O

^.

• *

P ^

CD

Op~

c

mI T

i r

PJ

i / i

PJ.$•aso

•

o* m

p j

o•o**crc

••0

en•o

fc-

mm

C i

•atn•-

O• *

o<0

oo

J-l

gr

ITp -I T

\rO

•ai n

i n

m

o o o

cr

CD

O2

oe

opg

<r

12

H

cr

o

089C

•g-

cr

02

9«

g•r P- o p-o o ci o~rg Pg (J1 <\jD «••« O O• • n t

O O O O

£ 7 Ntfl•H| 1T' 00 PJ

pg ci cc (MO - i O O

« t »O O O O

<\j pg rg rg*vj ^ ^ m

m *J O P-J•o m o ost ci « mci rg co ryO —' O O

a • • •O O O O

m Ci ci Ci

.c in oci o cia g; PJ•T pg p-o — o

• • •o o o

rg

r-

p -

o

c

COrcipg*-4

-r g"st in

•oo•£tn

o

a3QetO

Oh-

2Ja.3OceoXuaiIL

M. CO CO• ^ pg

P- Cl

O O-4 -O—4 •—t

O —• •

o o* p- p-

-4 pg

cr p-O mci PJo oo -4

o o

x * «»•• r g

O OO r-

O coO O

• aO O

x m m<-* CM

gj sfcr mO CM

o cro oo o

«c <* *-4 PJ

tnen«p *

o oa a

O O

* CI m• * CM

CMOr-

© o9 #

o oa i NJ CM

~« CM

00 fQci gr

O f-rg p-C0 P-—t ci"H O

O O

p- r-ci gj

rg —'rg o-< crO ci— O

O O

•O -CCl gr

p.j mes pggr org gr-* oo o

in mCi gr

00 Or- gjr» Ifl-4 m1-4 O

O Ô

gr *ci gr

cr CM-H COCl P*rj m-4 O

o o

Cl Clm gr

eo ci- * O•O O

• •

o oCM IMc i gj-

*

0 .3O

gO*~

c i

0 .3OOC

19

KU

u.

ac t r cr cr crP4 N Kl 4

o r- ci cro ^ g Œ0D O CM —•^4 pg CT C i

o •-< o oo o o o

ac CD CO OO CDi-c M ct ^

eo CD J J r-m gj CM »-4cr ci PJ oo -w j -o — -• oo o o o

w p- r- i>- r--« PJ ci gr

r- o «-4 crr- cr m cio co gr -<o cr o gro o — oa a a a

O O O O

y Jl Jl t/l ^

-i CM c i gr

OOONin co r*- J3O -4 P- CMo co PJ gro o -t o

a o o o

ae in m m m-4 CM Cl J T

gr o CD c iCM - * * r>-o co o coo co rj mo o -J o• • • •

o o o o

* gr gr * • *i-4 PJ Cl g>

£$o,CM m or- CM gj

o O M o• • • •

o o o o

x m m m m-< CM en <«•

Q .

3Oceoa•-g>

a.3OacO

X

uacu.

at oCM

cocrrgCMO

o

at cr

p -j -

in

O

o

•X 03

p -

crp .

ooo

oo

ai «

C3

O

C O Offi ^ in

p-* «^ r j

o- r- Mt*. (y- rn- O O

• • •t o o

o» cr crPJ Cl J .

J3 in mHr4Ulco gj -T-> cr ci-H O O

o o o

CO 0 0 COpg ci *t

p- m in-4 m ciO g] ClMM J;M -4 O

O O O

K p- r»PJ Cl *

g» r- co— gr •»•gr p* grcr o •*•O -4 O

oôo* gj J3rj ci gr

« >4 >Wcr o g}J3 -4 mf1* ci gro — o* é 9OOO

in m mCM ci gr

- r > * •-•»•o cr uCM CM PJeo CM «

O o — O• • •

OO OO

* g* * * gr

N en *

a

oceoa*-m

a.

aceoX

aesu.

rg ci

co ** * —4CD O•M Cl

o —o o

K: o o

M0 ^

O m

o -•ô ô

je tr o- 4 CM

O P-

PJ C l- 4 - *CJ <-4

O O

X co co- J CM

m g}gj f-

o aO -4

o o

«t r- r-- ^ CM

crJ3f^co

o oo o

* g} g j•-4 CM

cror»

O O

o oM; inm

- * C M

sj* m

gT f\CP sfJ- -O00 CM

o oo c

o ogr m

- H PU

m oo mo m-4 O

O Ô

C l .»•

OD mcr PJa) r-O ClO O

ô ô

co colT| gf

co crm <t(r oN -t-J O

# •O O

p- r-Cl gr

CD <O•*• -tcr p.o <r~i oa a

O O

•o <oCl gr

m jfco *CM 00m gr— o

• aO O

m mm gr

a£Q.3OacO

O

•o

a.3aacO

Xua.14V

ac rgpg

a1

— 4

OC l

eo

a^ i-4rg

00

Om^4O

o

* oPJ

c.

mv-4

Oe

O

a£ cr

C l

moO

o

ac co•-<CM

mooo

ae r»

Oa

o

•t J3—l

r j CM pgci sf in

g; ci pgcr - i c-o cr r-rg cp rg—4 O O

c ô c* - 4 ^ 4 ^ 4

ci vr in

co o CMcop- g;•C P - 0Drg co CM-< O o

O o ô

O O Oci gr m

r~ o tra> in cr— m r-—i o ci—1 ~4 O

a • aO O O

c^ cr crCM Ci J T

P- CM CD<r m gscr -4 cro o m-1 -H O

a a aOOO

oo co coPJ ci gr

CM C0 grr- CM cicr CM crcr ci gro — oa a a

o o or- r«- r»pj m gr

cr P- oo•O CM -4,4 -4 Oco • - ! mO -4 O

• • aOOO

<o « «i C M < n <»•

0 .

oceoo

f—

0 .

oacoX3d

u.

^ rO ffi mINJ f*> »t

,}• i r r-m -J" f>- - C <if1» ^ if>o ^- o

o c o

a pg pg pjPJ Cl ^

— cr O•JCJ - ^ C l

cr in o4- ci p-O -4 O

O O O

V -« -4 -CM c i gr

gr ci pg•»i œ -4-4 Cl O— * r-O >-4 O

O O O

* o o oPJ Cl gr

•o r- op- pg cr—i ce m•4 PJ COO ~4 O

a a aOOO

ac: cr cr cr•-4 pj rn

CM ci gro m g]P* C"" ClO CM Oo «g o

* a aOOO

JE co eo co-* I>J m

CQ CO CMO •"• **gr cr **

O --4 *-•• • •

min

m

CDf i

f\J

o

o

^in

0»t )rgPgU

O

ominp -

oC l

O

o

cr•4-

CMv-4CIClo

aO

CD

mCM

groa

o o o oK r- r- r

»-# rg pnr»gr

-'•ri-

r-or"~-O r> A,

o o o- O O

x r-r\j

O-mrtpo•-*

mO

r~tn

mCOO

of

o

r- r-

oCO

tr

or

-t - i o• o •

O O C

CC-ru

n"if \ j

c*

rr\

m,_,cc>oo

cr o:-t utr<G

o

: r- r- r-

— o o

CO

or^cr

«o

ccr\ j

CO

CO

!Zc

O

o

oo*

o

ccm

r j

CO

o«

o

r-r^m

C

o

tt" COJ If

IM

o

t

o

o

^1

en

e

oa

O

OJ-

i ra>r-r v i

C

ir~

c.a

C

c cIT ^cr

CD

r-C

•

o•Cf>,_(

a

c0

O

„

c

o**•o

o

cT_i r

I T

U'

c

c

r

x rv.

03

r».

c.

*

r\im

ir

^.oo

* a a c cr

•* tn —*

- O O• • *

O O O

— O C* m *

O O C

in cr CDJ3 O m

-i O -J—' . - O

^- 01 <VJr\j co r\jx O O

«^ O •-«m <"_ l/•O U' —— o o

• f to c o

<r oc co x

cr cr -ùr ^ * j - w*m CD ir»cr ~i - «

— o o« e p

O O O

fNJ C "-<a j 1 —CM O O

t • •

o a c

c e o•^ -* IT

1*1 C fjcr iri o.- o o• • »

o o o

o » ir

•o

oo

•om

i n

o

o

o

oo

« H O O• • •

o o o

ID h- m

—i — O* t •

o c o

-C ^ ""ri m i

o tr- r-tn»— oO T i ro en —«—< O O»«*

o o o

^ if. r*\-*> fv. —*- - O O

• • •

M O O• • •

c o o

f v J O O• • •

o c o

as

i/> ir in i

o-O**-

oO ' - ' O O

• * t> *

O O O O

ID -

• • • •

oooa© O O O«\i fl ^ .ï\

3OOfO

aaO

SCU

CD a.3O * O J O

O*-«OO a*• • • • O

aoooo

o*-<OO• • • •

OOOO

3

cc

0 0 0 0

QO —» O O• • • •

0 0 0 0

O O O O

00 -Û -4" rsicrooo

o*^oo• • • •

OOOO

c? a* 0" a-

a

O

a.O

a.

0 0 0

r * oto O O CD H O

• • • •0 0 0 0

OQf

fv

O O r O

o--*oo• • • t

O O O O

^ 0 0 0 0

a.Q

0 0 0

a j r r j.-« c- ote m r«

0 0 0

O N CD

O O O O

O

O

0

rg rr nj- » O O• • •

o o c

*t -T *r

• • •0 0 0

•0 « r~

O ^ HU

O O C

a.oor

n n ^• • •

o o o

It •* * •*

00 ^ r\i

cr r- -«

o — oft • ft

o o a

-100-

• * er•-t p~— co a

rr, rn r*'m .1 ir

13651

04556

re i"O O

e •O O

10396

04493

I\J S iTCC fn r*~ #H C Of*"1

^ O rO f*l 0* ™ ^ ^ V* •***co rv CO—- O^O * O / O

oc oo oo oo oo#0 f > 6 »• • B AS

oo oo oo oo oo

^t tJ"1* W^ kC **0 *<0 D ^ l * i * " *vi> QÛ 09 00 i^ O* Q* I

>û IT l*-iyp »$• If* r-CT" IT C*-4 CC •—f CD fNJ C M <£ <£ CT1 * ^pg ^r p*-r*" •>o o f^ ^ fNj ••*O* c* —i .-- c * - ' OO *0 Ooo ~*o oo ••* o oo

• • • • • • • • • t • •oo oo oo oo oo oo

ctf*\.—»

^3

•o

o

*

oo•

o

r(X)OfN

«o

r \ jU"o«

ro sT ^

CD 1*

-. oO tf-< a

w *

o o

m -*• tA

as r»

CD cr

^ o• o

o o

* -0 0 -Ûm ^ u*\

(r r-pn ,—.on "m *-*.— o

t •

o o

Vi r*" v^ro ••—> Oco in^ g^O C4 o

o o

OBCO

CO«t

o1—4

CO• *

p .

P J

oo

00i n

o o

[ *f *t <f 1^ i T i / \ I T ^ '<D ^ <C frt! !"*• •*** f***

0 .

o

ac

O

N GROUP .

FRCI

0.18989

0.05303

0.00619

* o o om -or in

,19099

,06092

,00904

a o o

x: cr (T cr

,21963

,05796

,01048

o o o

i t 00 CD 00CM CO 4"

o -e ao

oo CM in• * P - - 4

o o o

lit p- p- p-IM rO *

.27858

,06349

.01835

o a o

4<4)««I M r o *

0.05081

0.08813

0.02162

ÏÉ m m mIMPI +

ro gr pgCD ^ cr«mnin fj» roo o o

• a ,O O O

I t * • * *

D,

O

3O

CM

A GRCUP ;

urxu.

0.13965

0.06291

0.00538

rn •*• \f\

,16900

,05938

,00593

• • •o o o

* o o om >»• m

,17536

,06660

,00819

• w m

o o o

* cr cr crpg p^ - ^

,20621

,06152

,00905

v • •

o o oXt 00 00 00

IV 1*1 *

,24416

,07413

,01361

o a o

* p- p- p-rg ro *

0.28362

0.06230

0.01607

K « J3 <0CM rO *t

0.01785

0.C8416

0.02254

x: ir. i/i miv ro *

ro GROUP *

-0

4 GRCUP ;

FRCf

Û.12602

0.0512?

x: CM rw

,14586

,06135

o o

,14213

,05337

o o

X. O Oro *

15043

,06611

o o

pg m

,18209

,06182

• •o o

* 00 COCM CO

0.21781

0.07576

«; p» r-PJ pi

0.25811

0.06444

x: « gjpg co

rjm

,00491

O

-

MCJmooo

oin

,00697

O

cr

,00746

O

CO• * •

0.01155

0.01615

•o• * •

0 GROUP N

P»

r-

4 GROUP ;

4*L

oatu.

0.15535

0.03701

3& e*i m f*if« *^ <f\

,18659

o o

M; rg rg f\(m -gf i/\

f i CO r\jr m f\jf\j u*> ^r>i ir» Oru O O

O O O

t*\ %t m

12225

,05572

,00449

o o o

*: o o am •• in

,12939

,06732

,00599

o o o

x: o> o- »IM CO *

0.15661

0.06782

0.0C641

xt x ca coCM »O «4

gf cr coC*l »H Cp- - 4 sr0- Cf O

** o oo o o

Jt p- p- p-i\im«f

0 GROUP *

r~

00

a.gocO

Xucr.u.

<r iMin CM-< o

» «o o

rn **• in

ro *«

-i rCT r\J

.- oo o

x: 1*1 fo PIm ^ m

,23409

,032

51

o o

J£ IM IM PJro »* in

28346

04408

00311

o o o

ro 4- in

,09019

,04792

o o o

x: o a oro >* m

0.09546

0.06257

0.00442

CM CO s f

0.11555

0.06809

0.00473

a; oo uo coCM 1*1 •*•

0 GROUP K

I—

1 GROUP i

•B.

uu.

0.15341

0.00844

^ \f\ fcTt it'

,17440

,01416

o o

x: •» «c J*ro ^ incr cr(O -TCO p-

CM O

O Ô

^ Ifl r" rir o »v «TN

,27015

,02081

m m

o o

Xi IM IM INm * in

,33047

,03225

,00199

• • •O O O

X! ** »-4| r-4r o >••» m

0.05775

0.03917

0.02212

* o o oro •*• m

0,06113

0.05615

0.00283

i f cr tr crCM ro *

0 GROUP K

r"

O

1 GROUP 2

4K.

UCf.IL

ro ^m Oo corx Or- O

• t,

O O

SC -G -U -Oro <r tn

,16406

,00391

o o

x: in in mm <*• m

,18875

,00656

* *o o

x; -T •* •»ro -a in

2386B

,00810

o o

X! ro ro roro <t m

29775

,00964

o o

* CM r\J CMro •*• m

0.36688

0.02071

0.00092

ro *t m

0.02675

0.03033

0.00098

X O O Oro •» m

-101-

^ «• IT ^ C ^ J,** C O Q- -O «4 ru™ ^ OT (C h- .• *O O C O O O O

* « r o r f B

o o o o o o o

: Q G C. i»! ^^ t—» s£ f\j CM ^rr i r r . s; <* .tf^ u"* < *fr in • * ir* ^ ir <^ir

o o 0s f\j ry*<î O" *J Q- \f\•* -« O fSl *f*fr r- • - , - ( ©o o o o —• c •-* -« o <r

• • • • * • • i « Voo oo co o o c c-

cr o cr *: C c *: —< *-• *; r>j r\i :* r** r^ ^ ^ ^. a: ;/•« mm ,» tr •* in »* in ,yir ,j in ^ m , , ^

O r- m <j cr m ^••* rf"1 •* ^ j ri h- (y.

rw »H r n j cr OJ

inr i

ovCOCT*

i n•J*

f^i

r-ooo

ini n

D

O

Ï

04

9

IT-ir

co

jt g.

o

coc -. o « o ."-<c - _ o _p » • • « • «t • « , roc oc oo oc o o o o

'CDcrco n: o e tfco ^-^^-< ^rgr*. s^r^m ^gtgf- * i n i r•^gf 'n I^J? j*m g/ir gpm i j i r g^in g/m

- S S * S g? S S Sœc 1 o o r*- o cr irv —O O rj ,4j ^ ^. pry ^ ^«-* O ^ O «-«O ^-*C p-< O —• —< —«

• • • * « < • # " # • # » .

oo oo oo oo oo o o o

; r- t~- t~~ a: I L n, j t o t r st o t ai^^^-i M i oij a c r i f x *t *tfl iT IA r^»t r''. sj- ^-i/> *t \f\ -t it\ ^ m j-ii^

- " ' r ' O O n g ^ (^ ^ ^ m

C T ' N ^ « r ^ O - <f cr O .$• ^)f * > O O O r o u ^ O" iO o f>. pr—• ^ c c c r ^ - cr r- r- m j .•-< O r-JO - * O ^-*O i-«O - - O —i r-i

• • • • « • « * • * • • » • •oo ce co oo oc oc o o

: o « O ^ gtff-r- ' HÎODCD s ^ a c ^ O O ^ ; « - - iC(Nr«g *r"»ri

o Œ ^ t r <jh- ^, oc r». u*»»j f-C ^ O tC Of*- -4" 41 CO ^ « û (TO O r ^ O Q- -f —* OD CT1 O - * »T^ O «-I C i f > O ^- - - N- i f » O in*-• O »™«O M O i"jO r\iO —« O - ^ o •—'

oo oo oo oc oo oo oo o

*: -a o i SN *: cp co a f o c r ^ o o ^ ^ ^ ^ r-g (M

O co ^ o ^ ty* ^* CÛ ^ «T ^ r^•/) «T* f** ' ^ "O «O «^ O O «^ O ^JO»-» ^J-T O-O O O fvi h -fi-T^)»-i 0" —4 OO (%J PJ lT»O PJ i-ir-*O OO f<vO fsJO (MO —• O i-«O

oo oc oo oo oo oo oo oo

a d ^ - ^ - j stif\ifi K; -3 o3 s^r-^- ^ ao oo ^17-0* ^ o o ^^-*?^0 « IA 1 -^ ffl .j" f*t yf f*y if r ^ ifs »r »r*

O O Zf1 *t QD gf r-4«O O"^" CT Œ) »O 0s r*lt " O CC-sgt" »-4 CÛ IA D f^tO O f*» f\J OCCN^-t <o rsj cr>^> NO ^ h- ^ u"\m P-ogt O O CT sJ «l pij . 0 ^ ."^O ** O3t-4 f\j rtjINJO « - O — O OO <*>O IMO -^O -HO• • • • • • • • • • ft* • • • •

00 00 00 00 00 00 00 00

^ r*i m n X. ~t *t •* IA \T\ ^ <o o acr*-r^ ^ootn î^O1^ ^ 0 0ro ^ i ro *J ^^ f ^ *f ^^ r ^ ^^ 4~ i»o

^ ^: *: ^ «: *: ^ ^Cp-h* (g o co N aof*^ (j* tst r*-rn • ^"^ rg^>

et i-*rv ÛL K > o a t r \ - O û . r- * CL. o tf^ a- h - ^ j c i , 0 ^ 0 . J 1 ^3 ffc»-t 3 O O D ^ *O3 r*t m 3 f V 1 ^ ^ - O a D ^ O ï ^ - 3 u->OO » ^ O o u n r ^ o « û » ^ O e r r n o ^ f M O O O O c o ^ ^ o i r * ^et rt o a? M O n c *•* o ar r > O n t * o o n C r ^ o c t - ^ o ce - • oO • • O 9 * 0 • • O • • O • • O A I Ô • • LS • •

00 00 00 oa 00 00 00 00o a o o a a o ah- H> H *— M. »-. h- *—

^ (NI t\l r j s £ W ( ^ ^ * t - f i^U^iH ^ O " 0 MÏ^f^ ^ cO cO £ & 0"r^ ^ ^ ifl r^i ro ^ r*"( vf »^ r iA t*\ -f J3 fo * f** "n j CD f*^»^^ f*i rO ^1 wi f*i fi '•

cr ^ N- <ij Of*" r*f*- •j'Cr aocr r*« - ^^">Ja O N <L h - r ^ - a c o i ^ a . c e m c u «4 - - Q, m <o a. c r o o . «•-«3 rarsi 3 s f c o ^ m ( ^ 3 « > r f > 3 o o e r o u o ^ - 3 m o ^ ^-rO C ? 1 ^ O H M O 0 > O L J O "û O > f f * " l O O f ^ o i n ^ C J ^^^a^et m o o a m a c e p g o o e ^ O a c o O n £ o o at « M O Q C —OO • • • O • • O • • O • « O » • O • • O • • ij) • «

0 0 0 00 00 oa 00 00 00 00X X X f X X Z Xo a a o a o o oac x-*-*-* ot v: N N a. ii<i«i ce x-i--*- a ^u\m a * -o <o QL ^ p- r- QC M: auu, f l >/ tA y. 'H u. r ^ - X i i » f O - ^ i t ci *f" IL, r n ^ f u . ^ « t u . **\ *j

-102-

X

3D3o

•m

3Oae

JJOetl i t

aooo

x oo ot.» m

m

mr»

O

X f- f»«t m

ôX -0 -O

.» iro>PJmMp <

•O

X tn ir><» m

m .mm•

o

X •* ** m03

•ûtnm*

Ô

X m m* mN

00m -P 4

O

X CM ex•*• mCM O•4 OO (M0» CMO OO Ô

X • * • *« m** m

0< mo o• to o

X O O<* m

•4 a»p* (M- 4 «O*4 O

O O

xo» o»

xa.§aeo

o

o•r

a.3aae«0

o

u.

CM

00

o•

o

X 9 0>^ &momO

O

X co a)* m

mm

O

X f- 1* m

p 4

m

ôX * «

•r m<M0P

om

Ô

x m m* m• *

•o

•o

X * • *

»a i

om

o

x m m* mCMp 4

CMm

o

X N CMs» m

O Q>•4 m

m Mes o• •o o

X "4 "4«fin• ^ CMoo m•«r *

m *O O

o ox oo

«r m

xa.8So

a.3Oaeo

RC

M

u.

mCD*fC

r

O

X O Cm «o

tn00

oo

x v crt# m

« 4

•1-« 4

• 4

O

X 00 OD^ IT

«t

Ô

x f- r~-*• m

mas

- 4

o

X 4] «0.» m

ro

ôx m m

«t tn

<ntn•ù—<

o

X • * • *«r m

mI MP 4

•ft-t

O

*f m(M03

(2.•4

1O

X «x CM

•t m00 10

CM U>CM (M

o o• •

o o

X ****•* i n

xa.oaeu

a

CM

3Oato

ROM

t ^

mcea-rvO

eO

X »-in

ocf»"

co

X Om•bmm00

oô

x a•*ro•am, •4P 4

O

X CO

o(M00

p 4

C

x r»«t

oo00mP 4

O

X «

osIM

•O

x m

m

o

x •*

«I-

ÔX "1

00MODp 4

P 4

O

X CM• »

X

a.Oaeo

o

try

a.3aœo

uaeu.

X (Mt r

r«-a<cif

oo

X —mCM

mtr

oo

X Ot r

»

mO

Ô

x a

•oo• M

m

O

X 00

oor-

o

X r>-«t

OD

«0

a

x «•*f .fw«0IMP 4

O

X tr

o>«M

m

t

o

X «•*

p *

lf\m

4O

X Cl• *

X

û.

o

3a

«r(X3Oae19

Uet

x cim

X (Mi n

#»*• 0

mr**oo

X ««in<•*•a00a>O

X Om• •o0 s

CM

X »"*mm

O

x ou•*i »<D

m**

ô

•t0>mtnCM

O

a «•rr*

m•o

O

X m

• •

o4fft

O

X *

X

a3

ace«9

o

m•r

&3aaeoaxu.

X «tn

X dm

X CM

mOOmOota

X xmomF*-

o•

X Omof -

ooo

X V«t

ot -f -<p

oô

X <S

oOOmO

ôX f-

«roCM• 4vOO

o

X O

o«0moo

x m*

xa.oae

o

4»>

Ou3oaeoaaea.

x mm

X *m

x mm

X CMmommr-o

ôX ->

mooo

o

X OmO

CM

Ô

X »

o<«>mo*oo

X 00

oo> • <

o

x r-

o

moo

• > -i•r

-103-

OIP

O

* •» * ITIT

oOS

oo

: oIT.

oIS

00

o

4n

O

oo

3oofooPh.

• * •

0.

osXoat

OOO<ooo

x at&

oasIM

oQ

X P"

a.3Ot±

o

a.3aaoXaat

om•ooo

oa-i / \

oo

K OD

a3OorO

o

a.3a6Xoacu.

o*01 0• f

oo

« oIT

ointni ^

O

O

*

a.3c

Q

Oi n

a3aaoaata.

o

oo

M - •mOirCE

o•o

a om

Q .

3OaruQ

mA.

Oac

oaa.

m

o•o

ABSORPTION

K1

1121314151

00,00,00,

.0

.0

.0

.0

.0

.0

CROSS

K212223242

00Q00

SECTIONS

.0

.0

.0

.0

.0

K313233343

FOR

00,0,0,0,

ZIRCONIUM

.0

.0

.0

.0

.0

K414243444

ELASTIC SCATTERING CROSS SECTIONS FOR i

K1112131415X

0,1.2,5.6.7.

.38400,06800,78400.71975,96325,46550

' K212223242

0,1,3,5,7.

.42075

.18575

.01275,98500,78800

K313233343

INELASTIC SCATTERING CROSS

K1U21314151

1.1.a.0.0.0.

73000590C049000000

K212223242

1.1.0.0.0.

,7300054000,4200000

AVERAGE GAMHA ENERGY IN

K1U21314151

8.3.0.0.0.0.

649990000098C00000

K212223242

7.2.0.0.0.

85000700009700000

K3

13233343

0.1.3.6.7.

.49400,27400,19125,13350,47600

SECTIONS

1.1.0.0.0.

7200049000340000.0

K414243444

FOR

K414243444

INELASTIC COLLIS

K313233343

7.2.0.0.0.

00000400009600000

K.4

14243444

000,0,0,

.0

.0

.0

.0

.0

K515253545

EIRCONIUM

0,1.3,6.7,

,55900,42800,45100,42 400,16000

K515253545

ZIRCONIUM

1.1.0.0.0.

71000,43000,2700000

ION WITH

6.2.0.0.0.

40000C500095CJ00

c

K515253545

L

K515253545

0,0,0,0,0,

0,1.3,6.6,

1.1.0.0.0.

.0

.0

.0

.0

.0

.63 750,57500,65800,64400,75000

70000,34000,220000,0

IPCONIUM

5.1.0.0.0.

70000650009400000

K616263646

K.6

16263646

K616263646

K6162'-.3646

0.00.00.00.00.0

0.681501.755003.905256.858757.09800

1.69000l.??0000.150000.00.0

5.100001.30000C.930000.00.0

K717273747

K.7

1 7273747

K7

17273747

K717273747

0.00.00.00.00.0

0.715001.925004.347006.966008.4160Q

i.69C001.020000.06COO0.00.0

4.650001.150000.930000.00,0

K

s18283848

K813283848

K818283848

K.818293a48

0.0.0.0.0.

0.2.4.6.7.

1.0.0.0,0.

4.1.0.0.0.

000

c0

7010018400699008062586250

68C0O80000000

20000

orooo000

K9

19293949

K9

19293949

K9

19293949

K919293949

0.00.00.00.0

n.o

0.877502.422505.063256. 720007.386'JO

1.65000fi.660000.00.00.0

3.800001.020000.00.00.0

K1020304050

K1020304050

K1020304050

K1020304050

0.00.00.00.00.0

•

0*954 502.616255.453006.754507.05000

1.620000.560000.00,00.0

3.400001.000000.00.00.0

1

1ï

SCURCEIt5,9,

13,17,21,25,29,33,37,41 ,45,49,

SPECTRUM1.000004.8644415.7241429.8245136.7803339.3127131.6483323.6267116. 6172012.401926.972093.679372.64709

2,6,10,14,18,22,26,30,34,38,42.46,50,

1.063226.7597021.4433435.8758740.8655541.8116632.4532023.6826614.766009.074995.414293.560162.03625

3,7,

lit15,19,23,27,31,35,39,43,*7 ,51,

1.834019.4393321.7974535.2019845. 1665036.6891629.777852J.2566414.526698.847965.253353. 430941.95912

4,8,

12,16,20,24,28,32,36,40,44,48,

2.8555812.5097431.8654340.6275836.7880438.2656426.8105218.45610li.090617.175535.C75972.75243

oVJ1

MATERIALS IN THE REACTOR

MATERIAL

ALUMINUMCARBONOEUTERIUMHYDROGENI PONGXYGENURANIUM 235URANIUM 238Z 1RC0NIUM

REF. NO.(MPRi

1210g91311Z614

MASS<AMU>

26.733911.90801.99560.998555.336115.8526

232.9021235.882190.3862

ALPHA

0.860V70.714120.110460.000000.930260.7767?0.982970.983190*95671

CSI

0.072980.158920.726430.999990.035710.121020.008560.008450.02197

TRANSPORT CORRECTION APPLIED TO WRl GEOMETRY

GECHETRY DEPENDENT INPUT DATA

FIM1 1

0 . 0

o.c

0 . 0

0 .0

0 .0

0.3660

0.6390

R( I)

0.1500

0.4000

0.6338

0.7611

0.8836

1.2646

1.6456

J

234567B9

THE

THE

1

12

123u56

123456

119

108

213

306

SAKE AS

SAME AS

910

9101411

23C6

910

i l3

ÎOfc

i\ N( l , . ' lU0**24AT0HS/CCI

10.0000527000.0000000010.OC00000010.0000000010.0000000010.OOOOOOQOl0.0000000010.000000001O.OOuOOOOOl

REGION 1

REGION 1

0.043030024

0.0316991810.Q409Z1271

0.0099288600.0128lfcfl5B0.0CB350OOO0.0225200060.0002600000.0109H999B

0.0028879790.0037?81360.0040099960.037630022C.0004400000.018369973

OO5I

-107-

U~> - O 0s (J1 O 31

O IT iT ^ O' ^

J? f" fi pf> O "OO O O n"* O —*o o o o o o

o o o o o o

^ N J ifCE (J- 0 —•

"^ %r o o o i"w r- O f~ O CTO- .C O O" C 1 T- < o o CT- o : r

CO

^ M O -- OOo o o o o o

o o o c o ooo

o o o*H i - 1 Û N û Ûa o o a o o

o o ^ o o o

r j C O cr a o

^ T O O O O

rg r<i m r- O tfO O O m O —o o o o o ou o o o o o

•y & o o o —•y"> * r o o c • o—< Xi o O C OCJ C f"\j (T ^-t r\j

C O O r*i C —'O O O O O O

O O O û O O

4 CT1

•T C

£ a

i-i O

c»oa*T

o

O

o oo oo o) _

•C Oj—« O

o o

(7

1tnoo

o 4- — «y of— -« — O

-oo

o

15

16

17

18

19

20

21

22

23

24

25

26

0,

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

.c

,0

,0

0

,0

c

0

c

0

0

0

0

4.1603

4.2644

4.8500

5.5000

6.0376

6.1900

7.0000

8. 0000

9.0000

IC.0000

11.0000

12.3 359

THE

1

12

THE

THE

1

123

THE

THE

THE

THE

THE

SAME AS

13

1011

SAKE AS

SANE AS

12

Bil9

SAME A5

SAME AS

SAME AS

SAME AS

SAME AS

REGION 5

0-086269975

0.000026000O.OCOO52OOO

RÉGION 17

REGION 17

0.060500026

0.0663999920.0332999830.000070000

REGION 21

REGION 21

REGION 21

REGION 21

REGION 21

O00

THE FOLLOWING DATA IS NORMALIZED TO O.IOOOOGOE 01 KWttTTSOF U235 F I S S I O N ENERGY PRODUCED PER CM THICKNESS OF LATT ICt CfLL

INTEGRATED FLUX ( N / C M » * 2 - S E C I AS A FUNCTION OF RADIUS

FLUX

0.1246307E 140.1246308E 140.1246308E 140.1245873E 140.1236958E 140.1265656E 140.1273732E 140.1233661E 140.11ST872E 140.1144204E 140.1125383E 140.UO8879E 140.1033788E 140.8983080F. 130.7861962E 13O.77560B8E 130.6913822E 130.6476210E 130.6201104E 13C.6222144E 130.5329843E 13O.43818I4E 130.3659159E 130.3162385E 130.2B454t3E 13O.2649338E 13

VOLUME WEIGHTEDAVERAGE RADIUS

(CM)

0.100000.293940.525710.69939O.823B71=085361.463411.842682.222552.412592.612732.993143.373683.754324.C51924.21259'..5o3465 . 1 8 1 8 05.772976 . 1 1 4 1 16.603287.51UO8.509799.5087610.5079211.DB067

oCDI

-llO-

ooc

a

o3

4

LUZLU

Z

1 52 2& z

LU

3LU

I(M UJ UJ tu IU UJ UJ UJ UJ \U UJ U IU LU MJ IU IM Mi U Ul UJ LU iU UJ LU UJ IU UJ UJ ' ' UJ UJ UJ IU UJ liJ UJ UJ

v m 4 ) O Q o ^ 4 r M f t # r « > i r * ? 0 > r \ r « D O O O ' ' > r o b ( r 3 > < \ j e * i f < > > r r '

o3 3 • "

U, O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

FLU* CM/CH*»2-SEC> PER UNIT ENERGY AS A FUNCTION OF ENERGY IN REGION

FLUX ENERGY ESAR IN MEV

C.10J4821É0.1769291E0.2979540EC.5095376E0.8488754E0.1274036EO.188O7OOE0.2607234E0.3575237EO.*587O73E0.5686042E0.7216339E0.101?829E0.1251119E0.14357C6E0.1618992E0.1753372E0.1905554E0.21275T3E0.23527l9BE0.2768914E0.S049904E0.3319219E0.3750687E0.3905515E0.432468BE0.5420863E0.594S460E0.5937227E0.649882CE0.6604735E0.6931127E0.6828309E0.5778707E0.5176332EC.8123063E0.9456791E0.9742685E0.1O1273OE0.1027562E0.1071947E0.1114445E0.1161501E0.1212065E0.1240763E0»12829gCE0.13663PIE0.1433152E0.1^9C939E0.155C793E

1111111111121212121212121313131313l-i13131313131313131313131313131313131313131414141414I t1414141 *1 *I *

9.542978.693927.944897.244386.595486.020845.496235.021654.571324.172573.796513.447833.147632.873192.623032.398632.198491.998341.823991.673891.523771.386561.261431.149281.U49210.954300.869390.794490.724440.659550.602080.5496 20,502160.457130.417260.379650.344780.314760.287320.262300.2 39360.2198 50.199830.IB2400.167390.152380.13B660.126150.114930.10492

FLUX IN/CM»*2-i£.r I PER UNIT ENERGY AS A FUNCTION (IF EN^HG* RtGION 13

FLUX AT

O.3957235Ç 100.1526650E I I0.2577801E 110.4395161E I I0.7312546E 11C.1CÎ7207E 120.16156I8E 120.221890TE 12Q.3040762E 12C.3901834E 1Z0.4800334E 120.6O34550E 120.8437453E 120.1052939E 130.1202659E 130.1361392E 130.14716316 130.1602047E 130.1786440E 130.1962862E 130.2298330E 13C.2500216E 130.266'»7fclE 130.2945151E 130.3071475E 130.3381<.68E 130.4286405E 130.4716776E 13O.*7^.53È5E 130.5141799E 130.522B744E 13

0.5449476E 13G.4530466E 130.4087727E 130c6<.535«lE 13Û.753757SE 130.775992'iE 130.8098102E 130.8317954E 130.8682<^8<iE 130.9077968E 13C.<5'i9610aE 13O.1O11558E 1 *0.1031533E 140.1076697E 140 t11663C6E 14C . 1 2 J 7 9 0 3 F 140.1290658E 14

ENERGY EBAR IN HEV

9.54297B. 693927.944897.244386.595486.020845.496235.021654.571324.172573.796513.447833.147632.873192.623032.39P632.198491.998341.8 23991.673891.523771.386561.2 614 31.149281.049210.954300.869390.794490.724440.659550.6020S0.549620.502160.457130.417260.379650.344780.314760.287320.262300.239B60.219650.199830.182400.16739O.lb23a0.1336b0.126150.11493rv. l n4<>?

tv.i

HLUX (N/CM»*2-SECI PER UNIT ENERGY Ai A FUNCTION V.f ENfRGV IN REGION 24

FLUX

0.2055851E0.3542197E0.6037971E0.1030565EO.1757100E0.2551260E0.3723633E0.4711875E0.6367606E0.7767477E0.6357957EC.9753959E0.167598CE0.2375443E0.2632347EC.3033067EC.31224C4E0.330572eE0.370378fct0.3974193E0.5024224E0.S540178E0.56i4356EC.6304597E0.625B799E0.7125663EC.1085453E0.1273497E0.1359867E0.1479390E0.1580709E0.174307BEO.18C39*3E0.1434901EC.124O158E0.2275090E0.2880671E0.3lb4 74lEO.3457664E0.3 76002 9EL.409 Id2 8E0.44693'JIEC•492 30 f 4EC.544O2C 3EC.5876 04 4E0.64173É6E0.712087OEC . 7B54 398fcC« 6o01943E0.9381JSOE

A T

1010101 1111111U1111111112121212121212121212121212121313131313U13131313131313131 Î1 3131 31 313l i1 11 31 i

ENERGY EBAR I N MEV

9.542978.693927.944897.2443 36.595486.020845.496235.021b54.571324.172573.796513.447833.147632.B73192.6230^2.398632.198491.998341.B23991.673891.523771.386561.261431.149231.049210.954300.869390.794490.72444O.t59550.602080.549620.502160.45713Û.417260.3T9650.344780.314760.28732C.2623D0.239860.219850.199830.18240C.167390 . 1 5 2 3 80.I3B660.126150.114930.10492

-114-

ooata

CD

O

O

Oetazai

OCUJ

uz

Oce

• z• UJ

1JJ UJ I U MJ I U l i J UJ M l I I I i l l l u t i l m I I I I I I l i t t i i i l l m i l l I I I I I I i n n l H i m l l i t , f 111 i . l H I i | f t i l i l t I t l H I ^f n i i l f i l l I I I m 111 111 I I I H I t i l I I I I I I I I I

UJ 3 QD^4rMirtiO<riiHi

4 u. O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O Cl O O O O O O O O O O O O

AVERAGE FlUX IN/CH*»2-SEC) PER UNIT ENERGY, WEIGHTED BV CARBON

FLUX AT ENERGV EBAR IN MEV

0.8228467E0.1406507E0.2364926E0.4042881E0.6745962E0.1009119E0.148807060.205489<>E0.2811614E0.3593288E0.4427138E0.5593988E0.7876793E0.9762594E0.1124849E0.1272994E0.13781U4E0.1500122E0.1677494E0.1B49553E0.2168790E0.2367956E0.Ï548167E0.283b2<>3E0.2963771E0.3268065EO.*U9*15E0.45«53l*FO.«5a*262EC.V983706E0.5082090E0.S336936E0.5327764EQ.*5*012*E0.*0<52265E0.6326-VL1E0.7378231E0.76253C3E0.7998031E0.8212216E0.8598381E0.9012KJE0.9't<ilb&<sE0,1006137EO.IO2T937E0. 10f«,l6 3EO.ll'>'.Të?E0.1Z-.575eEO.lZ'ÎOTl^E0. U^OIO'-E

10111111111212121212121212121313131313131313131J13

9.5^297B.693927.944897.24433b.59548S.020845.496235.02165i.S7132i, 1725 7i. 79651J.44783Î.147632.673192.62303Î.398632.19849L.99B341.823991.673891.52377•3E656

L.,26148L.149281. 04921

13 0.9H3013 0.8693*13 *(13 (

3.794493.72444

13 0.6595513 0.60208l i (13 [13 (

).549623.502163.45713

13 C.1T2613 0.3796513 0.3M.JB13 t3.3147613 0.2873211 0.26230l i 0.23986H C.2198513 0.199831". C/ . 1824.-014 C.167391<. 0.152381 4 C1 " . C

^.13966\ 12615

1*. 0.114931 4 Ci. 10492

THE FOLLGWING DATA IS NORMALIZED TO O.1O00000E 01 KWATÎSOF U235 FISSION ENERGY PRODUCED PER CM THICKNESS OF LATTICE CELL

TOTAL KINETIC ENERGY TRANSFERED = 0.2038846E 02 WATTS

ENERGY LEAVING CELL THROUGH CELL BOUNDARIES = 0.BB417B9E Oi WATTS

ENERGY ENTERING CELL THROUGH CELL BOUNDARIES = 0,884178^ 01 WATTS

TOTAL ENERGY LOST THROUGH CELL BOUNDAklES = 0.0 WATTS

TOTAL ENERGY LOST THROUGH LOWER ENERGY BOUND = 0.7559372E 00 WATTS

TOTAL ENERGY INPUT » 0.2521394E 02 WATTS £

TOTAL FINAL ENERGY = 0.2525114E 02 WATTS

OF WHICH 0.3044981E 01 WATTS COME FROM GAMMA RAY ENERGIES IN INELASTIC

SCATTERING COLLISIONS, AND 0.1061797E 01 WATTS COME FROM NUN-CENTER-OF-M&SS

ENERGY IN ABSORPTION REACTIONS

KINETIC EKERGY TRANSFERRED IN REGION 1

MATERIAL

OXYGENHVOROGENCARBONDEUTERIUMALUMINUMZIRCONIUMURANIUM 235IRONURANIUM 238

ENERGY TRANSFERREDIMATTS/GRAM)

0.2443530E-010.2554TUE Cl0.3954T54E-010.8B24A70E 000. 8256<H9E-020 . 125Ù762E-020.2157812E-030.2073074E-020. 225<H05E-03

ENERGY TRANSFERREDIHATS)

C.2395783E-O50.2993701E-090.5526B37E-100.2066715E-090.2590600F-I00.1333156E-100.5898010E-HC. 13'.62<59E-10O.6253886F.-11

KINETIC ENFRGY TRANSFERRED IN REGION 6

MATERIAL

HYDROGENCARBONZIRCONIUMOXYGENURANIUP 23SURANIUM 238

ENERGY TRANSFERRED(WATTS/GRAM)

0.2600850E 010.4030866E-010. 1280183E-02

O.22OO38OE-O3

ENERGY TRANSFERRED(MATS)

C.1100775E 000.262A364F-01

0.37882B9E-010.5668268E-0*0.25*8683F-02

HINETIC ENERGY TRANSFERRED IN REGION 13

MATERIAl

HYDROGENCARBGNZIRCCNIUMCXYGENURANIUM 23 5

238

ENERGY TRANSFERRED(WATTS/GRAM)

0.2136198E 010.3322593E-010.1052377E-02O.2035O21E-010. IB1959"'E-O30. 1901B92E-03

ENERGY TPANSFfcRRfD(WATS1

O.13«32T1F 00O.3215O5OE-O10.4739699E-02o.isî ' .giaE ooO.23273T«.F-O3O.IO3<>7BOE-O1

KINETIC ENERGY TRANSFERRED IN REGION 24

MATERIAL ENERGY TRANSFERRED ENERGY TRANSFERREDtWATTS/GKAM) (WATS)

DEUTERIUM 0.1754680E 00 0.2304249E 01OXYGEN 0.49414936-02 0.258519LE 00HYDROGEN 0.5527105E 00 0.3828544E-02

0.2131985E Cl WATTS WERE TRANSFERRED TO HYDROGEN

0.5025066E 00 WATTS WERE TRANSFERRED TO CARBON

0.1G92623E-C2 WATTS WERE TRANSFERRED TO URANIUM 235

0.4835545E-01 WATTS WERE TRANSFERRED TO URANIUM 236

THE TOTAL KINETIC ENERGY TRANSFERRED BETWEEN REGIONS 17 AND 26 IS 0.1694189E 02 WATTS

ooi

THE FOLLOWING OATA IS NORMALIZED TO O.IOOOOOOE 01 KHATTSOF U235 FISSION ENERGY PRODUCED PER CM THICKNESS OF LATTICE CELL

NICKEL FOIL TES? CASE

THE CROSS SECTION DATA IS AS FOLLOWS

L*8*IS,22?29,36,43,50,

0.660000.590000.200000.013500.00.00.00.0

2,9,16,23,30,37,44,51,

0.665000.560000.1*8000.008700.00.00.00.0

3,10,17.2*,31»38,45,

0.670000.510000.103000.006100.00.00.0

11,IB,25,32,39,46,

0.675000.435000.071000.003600.00.00.0

5,12,19,26,33,40,47,

0.65000O.35OOO0.046000.001500.00.00.0

6,13,20,27,34,41,48,

0.62500O.290000.029000.001000.00.00.0

7,14,21,28,35,42,49,

0.610000.247000.020000.00.00.00.0

0.3865601E 02 DISINTEGRATIONS PER SECOND PER MG. PER MINUTE OF IRRADIATION IN REGION 1

EFFECTIVE FLUX = 0.9097799E 13 N/CM«*2-SEC

0.3964046E 02 OIS INTEGRAT IONS PER SECOND PER MG» PER MINUTE OF IRRADIATION IN REGION 6

EFFECTIVE FLUX = 0.9329492E 13 N/CM**2-SEC

O.3355O7OE 02 DISINTEGRATIONS PER StCOND PER MG. PER MINUTE OF IRRADIATION IN REGION 13

EFFECTIVE FLUX = 0.7P96253E 13 N/CM«»2-SEC

0.5690973? 01 DISINTEGRATIONS PER SECOND PER MG. PER MINUTE OF IRRADIATION IN REGION 26

EFFECTIVE FLUX = 0.13393B6E 13 N/CM**2-SEC

THE FOLLOWING OATA IS NORMALIZED TO O.1000000E 01 KWATTSOF U235 FISSION ENERGY' PRODUCEO PER CM THICKNESS OF LATTICE CELL

IRON FOIL TEST CASE-FE54IN,P)HN54

THE CROSS SECTION DATA IS AS FOLLOWS

1,8,

15,22,29,36,«3,50,

0.640000.536000.131000.013000.00.00.00.0

2,9,16,23,30,37,44,51,

0.655000.488000.09Z000.008800.00.00.00.0

3,10,17,24,31,38,45,

0.657000.406000.073500.005400.00.00.0

4,11,18,25,32,39,46,

0.645000.334000.062400.003200.00.00.0

5,12,19,26,33,40,47,

0.626000.285000.048700.00150G.O0.00.0

6,13.?0,?7,34,

41 ,48,

0.598000.22*000.033000.00.00.00.0

7,14,?1 ,28,35,42,49,

C.580000.174000.021000.00.00.00.0

0.6*17570E 00 DISINTEGRATIONS PER SECOND PER MG. PER MINUTE OF IRRADIATION IN REGION 1

EFFECTIVE FLUX = 0.1111776E 14 N/CM**2-SEC

0.6581255E 00 DISINTEGRATIONS PER SECOND PER MG. PER MINUTE OF IRRADIAI ION IN REGION 6

EFFECTIVE FLUX = O.114O133E 14 N/CM*«2-SEC

O.55755OOE 00 DISINTEGRATIONS PER SECOND PER MG. PER MINUTE OF IRRADIATION IN REGION 13

EFFECTIVE FLUX = 0.9658961E 13 N/CM**2-SEC

0.9508288E-01 DISINTEGRATIONS PER SECOND PER MG. PER MINUTE OF IRRADIATION IN REGION 26

EFFECTIVE FLUX « 0.1647211E 13 N/CM**2-SEC

O

Additional copies of'this documentmay be obtained from

Scientific Document Distribution OfficeAtomjc Energy of Canada Limited

CrTalk River, Ontario, Canada

Price . $2 .50 per copy

'622-70