vesuvio 3yr report - istituto nazionale di fisica...

A Project to provide enhanced neutron scattering capabilityat the highest energy transfers.

Financed with TMR-Access to Large Scale Facility (RTD)

VESUVIO3rd Annual Report

INFM

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VESUVIO, a novel instrument for spectroscopicstudies in condensed matter with eV neutrons at

ISIS Facility (UK)

The VESUVIO project is financed within TMR-Access to Large ScaleFacility (RTD)

http://www.roma2.infn.it/infm/vesuvio/

VESUVIO is a spectrometer for inelastic neutron scattering at high energy andmomentum transfers at the ISIS pulsed neutron source, designed and built by Italianand British scientists. The project has been financed within the Large Scale Facilityprogram of the European Union. The VESUVIO project aims to establish a routineexperimental and theoretical program in neutron scattering spectroscopy at eVenergies. The potential of neutron scattering at energy transfers in excess of 1 eV isso far largely unexplored. This instrumentation has been specifically designed for highmomentum, (20 Å-1

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be effectively reduced by cooling the filters. The three nuclear resonances ofuranium foil, centred at E1= 6.7 eV, 20.7 eV and 37 eV, strongly absorb neutrons innarrow energy ranges. Although the intrinsic width of the U resonances is small (i.e.the Full Width Half Maximum, FWHM=0.04 eV at 6.7 eV), at room temperature thesewidths are significantly Doppler-broadened by the lattice thermal motion (up toFWHM=0.11 eV). VESUVIO will improve the resolution of the analyser foils up toFWHM=0.066 eV by cooling the foils to 77 K, using a closed-cycle refrigerator. Thetank has been specifically developed to provide cold filter analysers for the entireangular scattering range. The developments proposed in the VESUVIO project willalso be directly applicable to the proposed European Spallation Source (ESS), whichwill provide a much more intense neutron flux in the eV region (see web pagehttp://www.fz-juelich.de/ess/CUR/ESS_currentRD.html).

The two participating laboratories:

1) ISIS Facility - Rutherford Appleton Laboratory (GB) and TheUniversity of Liverpool (GB) (400 KECU);

2) The INFM - Rome Tor Vergata (IT) (400 KECU).

ISIS team:J. Tomkinson (Project Coordinator), J. Mayers, N. J. Rhodes, E. M.Schooneveld, B. Holsman, H. Jones, Zoe Bowden.

The University of Liverpool team: W. G. Stirling, A. L. Fielding

INFM team:C. Andreani (Italian Co-ordinator, University of Rome Tor Vergata andINFM UdR Rome Tor Vergata), M. Nardone (University of Rome III andINFM UdR Rome III), D. Colognesi (CNR and INFM UdR Rome TorVergata), R. Senesi (INFM Udr Rome Tor Vergata), E. Degiorgi (INFMUdr Rome Tre).

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INDEX

• 1 - Vesuvio installation report pag. 5

• 2 - Project deliverables report:

2.1 Instrument Tank with cold filter analysers pag. 9

2.2 Detectors pag. 9

2.3 Training, testing and theoretical aspects pag. 14

2.4 Specific goals and tests in experimental physics pag. 23

• 3 – Scientific Highlights from ISIS Annual Reports pag. 41

ro senesi

ro senesi

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1. Installation report

The new capabilities offered by VESUVIO are provided through novel concepts for theexploitation of detectors and neutron absorption foils. These concepts are materiallyexpressed through specific mechanical designs for both components. Each componentwas installed according to the installation schedule given in the previous annual report.Here we report on how well that schedule was followed and the consequences. Most ofthe preparative work in the eVS blockhouse had already been completed during theprevious year.

- Foil Changer and Sample Tank, see Figure 1a, 1b and 1c.

Before installation, mechanical tests on the foil changer showed that its required pull-out torque was much higher than design estimates had implied. A more powerful devicereplaced the original motor and its base-plate on the support frame was reengineered.This work was done in parallel with some electrical installations and no delay wasincurred, indeed in general all the electrical and mechanical design was completed ontime.

FIG. 1a. A front view of the new VESUVIO sample tank with Dr. E. Degiorgi standing aside.The picture was taken at the RMP Costruzioni Meccaniche site in Rome on September 2000,few days before the delivery to the ISIS facility.

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Fig. 1b. Side view of the Sample –tank and cold rotating foil device assembly in the RMPsite before the delivery to ISIS.

Fig. 1c. The VESUVIO sample tank after the installation in the instrumental blockhouse withDr. T. Abdul Redah standing aside. The forward scattering side of the sample tank has beenrefurbished in September 2001 for optimization of forward scattering measurements. Ahelium cryostat (in orange) is sitting in the sample tank compartment for cold temperatureexperiments. Two 8-elements eVS detector modules (mounted on the blue stands on theright) are placed in forward scattering configuration.

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Serious delays were incurred during the installation of the electrical trunking, whichsupports all of the detector cables. The cause of the delay centred on the productivity ofthe single worker performing the job, concerns over the delay and attempts to bye-passthe bottleneck were outweighed by the real possibility of precipitating industrial action.When this element of the work was complete the other manpower resources, whichwould have been available according to the original schedule, had moved on to otherjobs. The total delay was about two months.

After the sample tank and foil changer were installed and working a secondary problemarose with the foil changer limit switches, which control the final positions of thechanger. New mechanical parts were designed, made and fitted to overcome theproblem. Also during this period the unsatisfactory shadowing of the original detectorbank was discovered. The problem arose from a combination of an over ambitiousdesign of the sample tank and a poor choice of construction materials. The tank designwas simplified, it was remade in a better material and reinstalled. This introduced afurther two months delay. The mechanical support for the backscattering detector sectorwas installed last.

Detector Installation, see Figure 2a and 2b:

Fig. 2a. Schematics of the backscattering detector bank, as installed in the instrumental blockhouse(incident neutrons from the left).

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FIG. 2b. The VESUVIO detector sector (where the constraints imposed by the mechanical supportsstill have to be introduced), showing the arrangement of the 44 lithium-glass scintillator blocks inrelation to one another. The layout of the photomultiplier tubes behind the scintillators is also shown.It is to be noticed that each scintillator block has a dedicated shielding from magnetic interferences,light-pipe scintillator–to-photomultiplier assembly, and photomultiplier tube.

The design layout shown in the previous report proved to be readily amenable to theconstruction of suitable light-guides. These are shown in detail in Figure 2b, where thedeceptive simplicity of the directly coupled photomultiplier tubes is apparent. Thedetector bank was tested in the laboratory to ensure that all elements were workingbefore its installation in the mechanical support on the beam line itself. Extensive datawas taken from the standard lead sample, to show that the detectors were performingreproducibility and that the data was understandable. This also served to demonstratethat the predicted improvements of the new instrument over the original design had beenachieved. Initial measurements with more demanding systems appeared to show someanomalies that were gradually resolved. However, a concern regarding the temperaturesensitivity of the detector at high count rates remains. This is proving somewhat elusivebut points to local air conditioning as a possible way forward. During the early tests thestray magnetic field from the neighbouring spectrometer caused considerable disruptionto the work. This was countered by protecting each photomultiplier with a mu-metalshield, however, this increased the overall size of the detector and a new light tightcowling was required, this has now been fitted. This stage of experimental verificationwas completed more or less on schedule.

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2. Deliverables report

2.1 Instrument Tank with cold filter analysers

The new tank, constructed by RMP - Costruzioni Meccaniche [Acilia (Roma), Italy](with M. Praitano as responsible for the engineering), is capable of operating witheither a cold or a room-temperature filter analyser, covering the entire back-scatteringangular range. The present detector modules will cover the remaining intermediateangular range.

The sample compartment-filter exchanger unit (see Fig. 1a, 1b and 1c) is a singlestainless steel vacuum vessel made up of two mechanically independent parts: thesample chamber which sits on four adjustable feet, and the filter chamber which is ableto rotate about the incoming neutron beam axis. The sample chamber is equipped with aDN400 flange on the top to allow the insertion of ISIS standard sample cryostats (asshown in Fig. 1b). The entrance and exit ports can both be vacuum-tight coupled to thefilter chamber which can thus be used to cover the back-scattering geometry out to some±30° aperture. A special kinematic vacuum seal allows the rotation of the entire filterchamber, supported by a large diameter ball-bearing, also under vacuum. The filterchamber contains a removable aluminium filter holding wheel, which is cooled using aclosed-cycle refrigerator. The filter wheel is divided into six equal sectors thusallowing both single-difference and double-difference measurements to be performed.A motor driven rotation of the entire filter chamber covers ±60° about the beam axis.

2.2 Detectors

The detector bank is designed as a Debye-Scherrer half-cone centred around theincoming beam, and consists of specifically built scintillators (see Fig. 2 a and 2 b)covering the angular range 135-175 degrees.For the proper set-up of the new detector bank, several tests for the effects of thesingle-detector dead-time on the scattering spectra were performed along the followingprocedure:

2.2.1 Effect of detector dead time

The 6Li-glass detector electronics have a fixed dead time that is effectively set by thewidth of the digital pulse that is triggered whenever an amplified analogue pulse risesabove the discriminator level. The discriminator level should be optimised to allowneutron pulses to trigger the system but ‘reject’ noise and other secondary lowamplitude pulses. Figure 1 shows schematically the analogue signal from thephotomultiplier tubes and the resulting digital output from the discriminator electronics.

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Figure 1 Schematic example of the analogue input (top) and digital output

(bottom) from the eVS discriminator cards.

The digital pulses are then passed on to a time-of-flight scaler that time stamps them asthey arrive and bins them appropriately building up a time-of-flight spectrum. The time-of-flight scaler also will have a dead time after a digital pulse arrives that issignificantly longer than the detector dead time.

Figure 1 shows a possible sources of problems that could arise if the digital pulsewidth is set to be too short. Currently, the width of the pulse is set to be 0.05 µs on theeVS discriminator cards, during which time the discriminator system can be considered‘dead’ (i.e. will not trigger if another pulse arrives). However, the analogue pulsesproduced by the photomultiplier tubes have been observed to extend out beyond 0.5 µsso that if a secondary ‘noisy’ pulse signal arrives before the primary pulse has fullydecayed to the zero level then the secondary pulse could potentially still trigger thesystem as it is rises above the discriminator level. The question to be answered is whatproportion of the measured time-of-flight spectra is due to the secondary pulses, howdo they affect the data and if necessary how can the problem be removed? Theapproach taken in the series of tests reported here was to investigate the measuredsignal as a function of the digital pulse width (thereby artificially increasing the deadtime of the detector system) and also as a function of the sample thickness (effectivelyas a function of count rate).

1. Estimating the total dead time of the system

Discriminatorlevel

0 0.050.5

time (µs)

Primarypulse Secondary

pulse

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To a good approximation the count loss due to dead time can be estimated using theexpression [1]

(1)

where Ctrue is the true count rate, Cmeas is the measured count rate and τ is the systemdead time. The count losses will therefore be count rate dependent, an effect that can beused to estimate the system dead time τ. The method involves a fitting procedure on twodatasets and is outlined below

1 Two time-of-flight datasets with two different thickness of sample are required,e.g. 1mm and 3mm Pb sample

2 The two datasets are then corrected for dead time using the expression inequation 1, initially an estimate for τ is used.

3 The datasets are then normalised using the incident beam monitor.4 If the two corrected and normalised datasets are C1true and C

2true, both with n

datapoints then the expression to be minimised with τ as a fit parameter is

(2)

Measurements were made using 3 lead samples with thickness 1, 2 and 3 mm. The 1mm Pb dataset was fitted with both the 2 and 3 mm Pb datasets to obtain an estimate ofthe dead time of the system. The fitted τ values are listed in table 1 for 8 spectrameasured in a single eVS detector module. The 2 mm and 3mm datasets gave consistentτ values. The digital pulse width for these measurements was set at the standard 0.05 µsindicating that possibly the time-of-flight scaler is the major source of dead time in thesystem.

1 G.F. Knoll Radiation Detection and Measurement (Wiley, 1989)

τmeasmeas

true C

CC

−=

1

∑ +−

=n truetrue

truetrue

CC

CCF

12

12

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Spectra Fitted ττ (µµs) 2 mm Pb Fitted ττ (µµs) 3 mm Pb1 1.26 (0.26) 1.26 (0.13)2 1.02 (0.20) 1.01 (0.08)3 1.03 (0.24) 1.05 (0.09)4 1.12 (0.23) 1.12 (0.10)5 0.98 (0.20) 0.99 (0.09)6 0.94 (0.21) 1.01 (0.09)7 1.10 (0.20) 1.13 (0.09)8 1.00 (0.21) 1.02 (0.10)Mean (s. dev) 1.06 (0.10) 1.07 (0.09)

Table 1 Fitted dead times derived by comparing 3 different thickness samples of Pb.The digital pulse width for these measurements was 0.05 µs.

The same procedure was repeated four times with the digital pulse width extended outto 0.375, 1, 2 and 4 µs. Three measurements at each pulse width were made using 1, 2and 3 mm samples of Pb. The fitted dead times τ are listed in table 2. The fitted deadtimes are consistently longer than the fixed digital pulse width on the discriminator.

Digital pulse widthsSpectra 0.375 µµs 1 µµs 2 µµs 4 µµs

1 1.39 (0.17) 1.83 (0.20) 2.68 (0.26) 4.54 (0.54)2 1.12 (0.11) 1.65 (0.17) 2.48 (0.25) 3.88 (0.48)3 1.18 (0.12) 1.65 (0.16) 2.48 (0.24) 4.92 (0.58)4 1.23 (0.13) 1.68 (0.18) 2.44 (0.23) 4.87 (0.57)5 1.09 (0.11) 1.57 (0.16) 2.41 (0.22) 3.99 (0.43)6 1.14 (0.11) 1.57 (0.17) 2.34 (0.20) 4.63 (0.48)7 1.25 (0.15) 1.67 (0.19) 2.45 (0.23) 4.91 (0.54)8 1.15 (0.12) 1.63 (0.17) 2.38 (0.22) 3.91 (0.39)Mean (s. dev) 1.19 (0.09) 1.66 (0.08) 2.46 (0.10) 4.46 (0.46)

Table 2 The fitted dead times τ (µs) as a function of digital pulse width on thediscriminator/amplifier for 8 detectors in an eVS detector module.

The fitted dead times are seen to converge to around 1 µs for very short pulse widthswhile as the pulse width is extended the fitted dead time is found to be around 0.5 µslonger than the fixed pulse width. This would appear to confirm that there is a secondsource of dead time in the system, probably originating in the time-of-flight-scaler. Thesecondary dead time will be count rate dependent which would explain why thiscontribution to the total dead time becomes less significant as the digital pulse width isincreased.

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Effect of dead time on the time-of-flight difference spectra

The effects of dead time on the measured count rate can be corrected for using equation1. However, on Vesuvio the measured signal is split between two periodscorresponding to analyser foil in and analyser foil out of the scattered neutron beam. Adifference is taken between the foil in and foil out data allowing the final neutronenergy to be defined. In this section the effect of varying the digital pulse width (andhence the dead time) on the recoil scattering spectrum from a Pb sample is shown. Theenergy calibration procedures, which allow the energy resonance of the Au analyserfoils to be calibrated by fitting a Lorentzian to the peak in momentum space, were runon data corrected and uncorrected for dead time. The resonance is defined by an energy(derived from the shift in the peak in momentum space) and Lorentzian half width athalf maximum (derived from the width of the peak in momentum space). The results ofthe energy calibration for different digital pulse widths are listed in table 3.

Uncorrected Corrected

Pulse Width (µµs) E1 (meV) ∆∆E1 (meV) E1 (meV) ∆∆E1 (meV)

0.06 4903.0 (2.1) 118.6 (0.7) 4904.4 (2.1) 134.1 (1.7)

1.0 4902.2 (2.2) 114.5 (1.4) 4906.0 (0.78) 130.8 (1.4)

2.0 4907.8 (0.7) 109.4 (1.4) 4909.3 (0.7) 125.5 (0.5)

4.0 4923.1 (2.9) 88.23 (12.93) 4926.1 (0.21) 120.8 (0.3)

Table 3 Results of running the eVS energy calibration procedures on data correctedand uncorrected for dead time. The values are the mean values obtained for 8detectors in a single eVS detector module.

Figure 2 shows the corrected and uncorrected J(y) for a single detector with the digitalpulse width on the discriminator set to 4 µs. Analysis of the corrected and uncorrecteddata using the energy calibration procedures shows the 4 µs dead time introduces a shiftto the data which is not corrected by using expression (1).

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Figure 2 The dead time corrected and uncorrected Compton profiles measured in asingle detector with a digital pulse width of 4µs.

2.3 Training, testing and theoretical aspects

Three Post-Doctoral research fellows have been employed in the year 2001: Dr. A.Fielding (Liverpool Univ.), Dr. R. Senesi (INFM) and Dr. E. Degiorgi (INFM). Theyare being trained in the experimental and theoretical aspects of eV neutron scattering.This year a significant drive was made to improve the understanding of calibrationtechniques as used in the study of eV neutron scattering. As an example the developmentof simulation tools for DINS data and interpretation, systematic series of simulationsand measurements were performed for the evaluation of multiple scattering events, asoutlined below:

2.3.1 Monte Carlo simulations of multiple scattering and experimental tests

A Monte Carlo code DINSMS has been specifically developed to simulate theperformance of the eVS-VESUVIO spectrometer and has been applied in the presentwork to calculate multiple scattering contributions in Deep Inelastic Neutron Scattering(DINS) experiments. In the work described here a systematic test has been carried outon the capability of the code to predict the multiple scattering, as a function of thesample thickness and atomic mass.

-400 -200 0 2 0 0 4 0 0

0.000

0.001

0.002

0.003

0.004

0.005Corr. HWHM = 65.9 A

-1

Uncorr. HWHM = 53.4 A-1

Uncorrected J(y)

Uncorrected fit Corrected J(y)

Corrected fit

J(y)

(A

rb.

units

)

Momentum y (A-1

)

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Previous approaches to multiple scattering corrections, include those of Vinyard2 andSears3 for plane slab geometry, and Blech and Averbach4 for cylindrical samples.These authors gave a series of exact and approximate results for elastic isotropicscattering. Alternative phenomenological approaches have been used for multiplescattering corrections for hydrogenous samples in slab geometry, in the case of directgeometry time-of-flight chopper spectrometers 5,6. However the most widely usedapproaches, both in the case of steady state sources7 and in the pulsed source-time offlight case8,9 , make use of Monte Carlo procedures, which allow for a simulation of thereal experiment by following a given number of neutron histories.

Theory of Measurements

The analysis of data on eVS relies upon the assumption that at the high momentum andenergy transfers available on the instrument, the scattering can be calculated within theimpulse approximation (IA)10, which is exact when the momentum transfer

rq and energy

transfer ω are infinite11,12. The formal statement of the IA for an atom of mass M is

pdMqp

Mp

pnqSMrrrrr

∫

+−+=2

)(2

)(),(22

ωδω (2.1)

where ),( ωqSMr

is the incoherent dynamic structure factor, n p( )r

is the nuclearmomentum distribution, and

rp is the atomic momentum. The two essential features of

the IA are that the scattering is incoherent, (i.e. the neutron interacts with a singlenucleus in the sample) and that total kinetic energy of the nucleus and neutron isconserved during the interaction. The latter condition is expressed formally by the δfunction in equation 2.1. Using the identity axax )()( δδ = , gives

),ˆ(),( MMM yqJqM

qSrr

=ω (2.2)

where,

pdyqppnyqJ MMMrrrrr

)ˆ.()(),ˆ( −= ∫ ∂ (2.3)$rq is the unit vector along the direction of rq and

−=

Mq

qM

yM 2

2

ω (2.4)

2 G H Vinyard Phys. Rev. 96 93,(1954)3 V. F. Sears, Adv. Phys. 24, p. 1 (1975).4 I A Blech and B L Averbach, Phys. Rev. A 137, 1113 (1965)5 C. Andreani, V. Merlo and M. A. Ricci, Nucl. Instr. and Meth. B36,p. 216 (1989);6 C. Andreani , V. Merlo, M.A. Ricci and D. Lepoire, Nucl. Instr. and Meth. B61, p. 123 (1991).7 J.R. D. Copley, Comput. Phys. Commun. 7, p. 289 (1974).8 R. C. Blasdell and R. O. Simmons, Nucl. Inst. and Meth. A 405, p. 71(1998).9 D. L. Price, J. M. Carpenter, J. Non-Cryst. Solids, 92, p.153 (1987).10 S. W. Lovesey, in Theory of Neutron Scattering from Condensed Matter(Oxford University Press, London, 1987).11 V. F. Sears Phys. Rev. B 30, 44 (1984)12 J. Mayers Phys. Rev. B 41,41 (1991)

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is the West scaling varaible13 ),ˆ( MM yqJr

is the probability that the atom has a

momentum component along the direction $rq with magnitude between My and

MM dyy + and due to its physical significance should be symmetric with a maximum at0=My . Equations 2.1- 2.4 thus imply that at constant

rq , S q( , )

rω consists of a single

peak centred at the 'recoil energy' ωRM q M=2 2 . The corresponding physical

interpretation is that a neutron scatters from a stationary atom with an energy transferω RM and Doppler broadening due to atomic motion produces a range of energytransfers centred at ω RM . For an isotropic sample there is no dependence of J q y( $, )

r on

the direction of $rq and )(),ˆ( yJyqJ MM =

r is the probability that an atom has a

momentum component of magnitude along an arbitrary direction in space. Thecorresponding partial differential cross-section for scattering from an atom of massM is

)(4

),(4 0

1

0

1

1

2

MMM

MMM yJ

q

M

k

kqS

k

k

E πσ

ωπ

σσ==

∂Ω∂∂

(2.5)

where Mσ is the bound scattering cross section for mass M . The corresponding countrate in a time channel of width t∆ at time of flight t is 14

( )∑ ∂Ω∂∂

∆Ω∆

∆=∆M

MM E

NEEtdt

dEEIttC

1

2

110

0 )()()(σ

η (2.6)

The first expression in parentheses is the intensity of incident neutrons with times offlight between t and tt ∆+ . The second expression is the product of the detectorefficiency η at the final energy 1E , the detector solid angle ∆Ω and the energyresolution 1E∆ , giving a constant factor determined by the instrument geometry and thetype of detector. The last term is MN , the number of atoms of mass M in the sample,multiplied by the partial differential cross-section. Taking into account the massdependent resolution function )( MM yR of the spectrometer by the approximation thatthis can be incorporated as a convolution with the intrinsic )(yJ M due to the sample,the count rate is

( ))()(4)()()/()( 2001101 MMMMM

MM yRyJbNdt

dEEIEEqvvtC ⊗

∆Ω∆= ∑ πη (2.7)

The terms in square brackets are sample independent and can be calculated from thecalibrated instrument parameters and the time of flight t. For harmonically bound atomsthe “neutron Compton profile” )(yJ M is a Gaussian

function15

−=2

2

2 2exp

2

1)(

MM

M

yyJ

σπσ(2.8)

and it is assumed that )(yJ M can be written in the form of equation 2.7 for the systemsstudied in this paper. Within this approximation, the mean atomic kinetic energy is

)2/(3 2 MMσ .

13 G. B. West, Phys. Rep., 18C, p. 264 (1975).14 C. Windsor “ Pulsed Neutron Scattering”, (Taylor and Francis, London,1981)15 See for example M. S. Nelkin and D. E. Parks,Phys. Rev. B, 119, p.1060 (1960).

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The energy transfer ω and momentum transfer rq on eVS, are calculated from the

neutron time of flight t . E1 is fixed by the resonance energy of the filter and the velocity

v1 of the scattered neutrons can be calculated from the relation E mv

1 1

22= where m is

the neutron mass. The velocity v0 of the incident neutron is determined from a

measurement of the neutron time of flight via the equation

01

1

0

0 tvL

vL

t ++= (2.9)

where L0 is the distance from source to sample and L

1 that from sample to detector and

t0 is an electronic time delay constant.The energy transfer is

( ) 2/2120 vvm −=ω (2.10)and the momentum transfer

( ) 21102021 cos2 θvvvvmq ++=(2.11)

where θ is the scattering angle.In the Monte-Carlo simulation, a series of neutron histories are followed and thesimulated data is a sum of the different neutron histories, weighted according to theprobabilities that they would occur in a real experiment. Two methods of assigning theappropriate weight to processes occurring during the neutron history are adopted in theprogram depending on convenience.(a) A neutron event is generated and given a statistical weight according the toprobablility distribution for the event(b) Neutron events are statistically generated with the frequency with which theywould actually occur.

a Comparison with Analytic Calculations

For scattering which is elastic and isotropic, analytic expressions have been calculatedfor an infinite plane slab by Vinyard2. These expressions provide a useful test of theprogram, since an elastic isotropic cross-section is obtained from the expression for theimpulse approximation for the differential scattering cross-section, in the limit

∞→M and 0→Mσ . The program was run for a fictitious mass of 2000 amu and35=Mσ Å

-1 , which closely approximates elastic isotropic scattering. The samplegeometry was a parallel plane slab of dimensions 100 x 100 cm, with the beamperpendicular to the slab face. The beam dimensions were set at 0.005 cm. Theprogram was used to calculate the ratio of second/first order scattering neutrons as afunction of the parameter tµ , where µ is the inverse attenuation length and t is the slabthickness. The results are shown as points below. The solid line is the analyticexpression due to Vineyard2. The program clearly agrees very well with the analyticexpressions.

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Figure 2. The solid line shows the ratio of first to second order scattering calculated by the analyticexpression for an infinite plane slab given by Vinyard2. The points were obtained from the Monte-Carlo progam.

bExperimental testsFor experimental tests of the program three different masses were chosen: hydrogenwhich has the lowest atomic mass of 1.0079 amu, Carbon which represents anintermediate case, with mass 12 and tin which is a heavy mass of 118.9 amu. Figures 3and 4 show measured and simulated data for a thickness of 0.059 mm of polythene at ascattering angle of 73° and 46° respectively. For this thickness, 11.0=dµ andprobability that the neutron will be scattered is )exp(1 dµ−− = 0.104. Figure 6 showsdata taken from a 100x100x 5mm slab of graphite as points, with errors bars. For thisthickness of graphite, 21.0=dµ and the probability of scattering is 0.19. The data wasa sum of 8 spectra at scattering angles between 45 and 60°. Figure 7 shows the data andsimulation from the same sample for scattering angles between 121° and 145°. Figure 8shows the ratio of secondary and primary scattering as a function of angle for threedifferent thicknesses of graphite. Figure 9 shows experimental and simulated data for a5 x 100 x 100 mm slab of tin, where 089.0=dµ and the probability of scattering is0.085. The data and simulations were a sum of eight spectra between scattering anglesof 125° and 145° . Figure 10 shows the sum of data and simulations for eight spectrabetweeen scattering angles of 32° and 54°.

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Figure 3 Data and simulation for 5 sheets of polythene at a scattering angle of 73°. The percentage of

multiply scattered neutrons is 0.15

Figure 4 . Data and simulation for 5 sheets of polythene at a scattering angle of 46°. The percentage

of multiply scattered neutrons is 0.07.

Figure 5 Ratio of 2cnd to 1st order scattering in Polyethene as function of scattering angle for three

different thicknesses: + = 0.0117 cm, * =.0351, o = 0.0585 cm

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Figure 6. Measurement and simulation for 5mm of graphite for the sum of 8 spectra, at scattering

angles between 45 and 60 degrees. The points are measured data, the solid line is the simulated data

and the dashed line is the multiple scattering contribution.

Figure 7 Data and simulation for 5 mm of graphite. Sum of angles between 121-143 degrees. The

points are measured data, the solid line is the simulated data and the dashed line is the multiple

scattering contribution.

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Figure 8. Calculated ratio of second to first order scattering as a function of scattering angle, for 3

thicknesses of graphite: oo-1mm, xx- 3mm, 5mm .

22

Measurements and Simulations of Tin

Figure 9 Experimental data for a 5 x 100 x 100 mm slab of tin is shown for scatering angles between

125° and 145° . The solid line is the simulated data generated by DINSMS, the dashed line is the

multiple scattering contribution.

It can be seen from Figures 6,7 and 9 that DINSMS accurately represent the measureddata and the degree of multiple scattering in graphite and tin. In the polythene sample itwas not possible to sum different spectra due to the large shift in the hydrogen peakwith angle and the statistical accuracy available from a single spectrum makes adetailed comparison of data and simulation difficult. However, the good agreementbetween the simulation and the graphite and tin data and the good agreement betweenthe results of the program suggests that DINSMS also accurately represents the multiplescattering in the case of hydrogen. It can be seen that in all three cases the multiplescattering peaks at smaller times of flight than the primary scattering. On an inversegeometry spectrometer such as eVS, this corresponds to a greater energy loss by theneutron. The peak shift is due to the fact when the neutron energy is much greater thanthe atomic kinetic energy, the neutron loses energy with every collision and multiplyscattered neutrons therefore lose more energy than singly scattered neutrons. The peakshift is greatest at small scattering angles, where the once scattered neutrons lose mostenergy.The calculated ratio of second to first order scattering increases with scattering anglefor all three masses is , with the largest angular dependence in small mass samples.This can be attributed to the decrease in the primary scattering cross-section withincreasing angle. This effect is largest in hydrogen where, for scattering in the impulseapproximation, the partial cross-section Ωdd /σ is proportional to the cosine of thescattering angle, going to zero at a scattering angle of 90°. In tin Ωdd /σ is almostindependent of angle, as is the ratio of primary to secondary scattering.

In summary, a Monte-Carlo program DINSMS, for calculating multiple scattering inDeep Inelastic Neutron Scattering has been described. Comparison of the programresults with data and analytic expressions shows that the program can be used toreliably correct DINS data.

23

2.4 Specific goals and tests in experimental physics reportsSome of the specific goals described in the original proposal have beenaddressed in previous annual reports. In the present reports we shalladdress the following:

I. Hydrogen momentum distribution .

II. Single particle dynamics in quantum fluids and solids .

III. Accurate study of simple molecular systems.

IV. Single particle dynamics in amorphous materials, polymers, catalysts andmetal hydrides.

A selection of experimental results is presented below following the order of topicsoutlined in the specific goals and experimental tests:

24

Specific goal I. Hydrogen momentum distribution.

• Deep inelastic neutron scattering from fluid hydrogen and deuterium: Fromvibrational excitations to the impulse approximation

Andreani C, Colognesi D, Pace E

PHYSICAL REVIEW B 60, 10008 (1999)

Experimental deep inelastic neutron-scattering data from fluid deuterium at atemperature of 20.7 K, collected over a wide range of momentum transfer q (28 Å–1

25

Specific goal I. Hydrogen momentum distribution.

• Single-particle dynamics in fluid hydrogen and deuterium

C Andreani, P Cipriani, D Colognesi and E Pace

J. PHYS.: CONDENS. MATTER 12 139 (2000)

Single-particle response functions for liquid D2 and H2 , obtained from previousinelastic neutron scattering measurements, are compared with an exact quantumcalculation for D2 and a Wentzel-Kramers-Brillouin (WKB) model for D2 and H2 . Theexact and WKB calculations both provide satisfactory descriptions of the experimentalresponse function of these fluids over a wide range of momentum and energy transfers,which spans from the roto-vibrational excitations up to the molecular dissociationregime.

26

Specific goal II. Single particle dynamics in quantum fluidsand solids .

a) SOLID AND LIQUID HE-3

• Deep-inelastic neutron scattering determination of the single-particle kineticenergy in solid and liquid He-3

Senesi R, Andreani C, Colognesi D, Cunsolo A, Nardone MPHYSICAL REVIEW LETTERS

86 (20): 4584-4587 MAY 14 2001

For the first time, an experimental determination of the single-particle mean kineticenergies, , in

3He along the T=2.0 K isotherm in the dense liquid and in the solidhcp and bcc phases was reported. Deep inelastic neutron scattering measurements atexchanged wave-vectors ranging from 90.0 Å-1 to 140.0 Å-1 have been performed inorder to evaluate, within the framework of the impulse approximation, the molarvolume dependence of the single-particle mean kinetic energy. In the figure below themolar volume dependence of is plotted together with the same quantity evaluatedby both Diffusion Monte Carlo (DMC) calculations and Self Consistent Phonon method(SCP). We observe that the experimental values of are in remarkable agreementwith the DMC calculations for both liquid and solid phases. It has to be stressed that,among the various theoretical models, DMC seems to provide the most accurate results.As a matter of fact the Equation of State that this method yields for 3He in liquid, bccand hcp phases is in good agreement with the experiments. Such a broad-bandagreement has been attributed to the use of a recent ab-initio interatomic potentialwhich includes also some three-body terms. Other simulations, limited to the solidphases and based upon variational methods, have indeed obtained results for 4He,which are close to the experimental ones. Although, the agreement is surprisingly lessimpressive for crystalline 3He, in spite of the negligible energy contribution arising inthe solid from the different quantum statistics. As shown in the figure, the values of thesingle-particle mean kinetic energy obtained through the SCP calculations liesystematically lower than the experimental results. Indeed in this theoretical approachthe anharmonic contributions to are only approximately accounted for through acubic anharmonic term. A similar discrepancy between the , calculated via thisapproach, and the experiment, was also observed for solid 4He. This is not surprisinggiven the strong anharmonic character of these solids, i.e. the light atomic masscombined with the highly repulsive hard core of the interatomic potential. In particular,since the anharmonic contributions to are expected to be more relevant for thelighter isotope, the present experimental data further support the need of properlyincorporating these contributions within the theoretical framework.

27


The molar volume dependence of in 3He is plotted (black circles) together with the same

quantity evaluated by both Diffusion Monte Carlo calculations (red squares) and Self ConsistentPhonon method (dashed line).

28


• Momentum distribution of liquid 3 He: simulation of Deep Inelastic NeutronScattering experiments with the VESUVIO spectrometer

Senesi R , Andreani C and Colognesi DJOURNAL OF LOW TEMPERATURE PHYSICS

(IN PRESS - 2001)

The recent experimental determination of the 3 He single-particle mean ki-netic energies in solid hcp, bcc and dense liquid phases has allowed toperforman accurate test of the single-particle dynamical properties derived from theexisting theoretical models. A Monte Carlo simulation of a Filter-Differenceneutron spectrometer for Deep Inelastic Neutron Scattering with enhancedresolution performance is presented. It aims to study the feasibility of anaccurate experimental determination of the He-3 momentum distributions inpure liquid and in He-3/ He-4 liquid mixtures.

29


b) QUANTUM LIQUID MIXTURES

• Deep inelastic neutron scattering from H2-D2quantum mixtures Chatzidimitriou-Dreismann C A, Streffer R M F, Abdul-Redah T

ISIS ANNUAL REPORT 2001

Our neutron Compton scattering (NCS) experiments on liquid water and in H2O-D2Omixtures, which started 1995, provided first direct evidence for the existence of short-lived quantum entanglement (QE) of nuclei (protons and/or deuterons) at roomtemperature [1,2]. In the meantime, this new quantum effect has been also found to existin various systems, like metallic hydrides [3], polymers [4] and organic liquids.First experimental evidence of this effect in fluid H2 was very recently reported in Ref.[5]. Here we report the experimental NCS results from H2 and various H2-D2mixtures, see Figure. (xD denotes the D-molar fraction of these systems.) The fluids (atT ˜20 K) were in an Al can. We present here the ratio of the H signal area AH to the Alsignal area AAl, AH/AAl. To facilitate comparison of the data, for all samples thisratio is normalised to unity at the smaller available scattering angle. A striking strongdependence on the scattering angle is found, which is independent of the atomic H:Dcomposition of the samples. A similar “scattering angle dependence” wasalso found in some metallic hydrides [3], but not in various mixtures of liquid H-Benzene/D-Benzene, or H2O-D2O [1], or H-polymers [4]. This comparison indicatesthe fundamental difference of the relevant quantum dynamics of the protons invarious H- containing systems. Interestingly, the xD -independence of AH/AAldemonstrates that this effect is mainly of intramolecular origin. However, one mayobject that the observed effect might be due to “shadowing” (and/or “multiplescattering”) of the scattered neutrons at large scattering angles. This is conceivable,since the used Al can was flat and was put perpendicular to the incoming neutron beam,sothat the data of the detectors at higher scattering angles might be more affected thanthose of the lower angle detectors. To investigate this possibility, we performed againthe measurements using the same scattering geometry as previously, and then werepeated the measurements after rotating the flat Al can by ca. 20 degrees. Moreover,we repeated the measurements using a second experimental set-up, in which thedistance considerably to 100 cm. directly time effects” times intensity of the H-signal.The results of these measurements have fully confirmed the data presented in the Figure.In summary, all these new measurements have reproduced exactly thescattering angle dependence of AH/AAl shown in the Figure. Thus we conclude that the

30

effect shown represents a real phenomenon, which is of particular importance due tothe simplicity of the investigated system. Further data analysis in under way. Furtherrelated experiments are planned.

References:[1] C A C-Dreismann, T. Abdul-Redah, R. M. F. Streffer, and J. Mayers, Phys. Rev. Lett. 79, 2839(1997).[2] C A C-Dreismann et al., “Science Highlight” in: ISIS 2000 Annual Report, pp. 58-59.[3] E B Karlsson, et al., Europhys. Lett. 46, 617 (1999).[4] C A C-Dreismann et al., J. Chem. Phys. 113, 2784 (2000).[5] C A. C-Dreismann et al., Experimental Report, RB 10930, ISIS Report, 2000.

31



• Anomalous neutron Compton scattering in Nb hydride: Indications of protoncorrelations

Karlsson E. B., Chatzidimitriou-Dreismann C. A., Abdul-Redah T, Streffer R. M. F.,Hjörvarsson B. , Öhrmalm J. and Mayers J.

EUROPHYS. LETT, 46 (5), PP. 617-623 (1999)

Neutron Compton scattering probes properties of matter at time scales of the order of10-16-s. Very strong anomalies in the cross-sections for protons were observed forscattering on and . The effective proton cross-section was found to vary with the time ofobservation (first used as a parameter in the present experiments) being reduced by30% at times around but reaching its conventional value for times larger than . Noconventional explanation for this anomaly (which indicates some kind of very short-lived correlations) is known. A tentative explanation is that during such short timeintervals, nearby protons are quantum correlated (even at ambient temperatures) in sucha manner that their neutron cross-sections are modified.

32



• Comment on "Precision Neutron Interferometric Search for Evidence ofNuclear Quantum Entanglement in Liquid H2O-D2O Mixtures"

Chatzidimitriou-Dreismann C. A., Abdul-Redah T, Streffer R. M. F., Hessmo B

PHYSICAL REVIEW LETTERS 84, P. 2036 (2000)

A Comment on the Letter by A. Ioffe et al., Phys. Rev. Lett. 82, 2322 (1999). Theauthors of the Letter offer a Reply

33



• Mean kinetic energy of helium single atoms in H2-He and D2-He liquidmixtures

Andreani C, Colognesi D, Degiorgi EISIS ANNUAL REPORT 2001

We have carried out deep inelastic neutron scattering measurements on supercriticalmixtures of helium-four and normal hydrogen (i.e. H2 with no ortho-para conversion)along an approximated isothermal-isochoric line (T= 35 K, n=26 nm-3 ) for differentmolecular compositions including also a lead calibration run at T= 290 K.These states, close to the hydrogen critical temperature (Tc=32.98 K), were chosen inorder to investigate the quantum behaviour of the He mean kinetic energy, as afunction of the mixture composition, i.e. changing the He-atom mean field and theaverage mass of its neighbour atoms.The quantity can be extracted from the measured neutron Compton profiles Theseappear like two separated recoil peaks, weighted by the different cross-sections andconcentrations of 4He and Al (from the sample cell) and are localised at distinct time-of-flight values. The hydrogen recoil peak was not visible since all thedetectors were placed in back scattering (2 >90 deg).The single atom mean kineticenergy is then simply related to the properly normalised peak second moment, once data are transformed in y using the mass, M, of 4He (4.0026 a.m.u.):In addition, Path Integral Monte Carlo quantum simulations (PIMC) of the 4He-nH2mixture in all the thermodynamic conditions of the experiment are in progress.

34

Specific Goal III. Accurate study of simple molecularsystems.

a) H2O

• Proton dynamics in supercritical waterAndreani C, Colognesi D, Degiorgi E, Ricci M A

JOURNAL OF CHEMICAL PHYSICS 115 (2001)

An inelastic neutron scattering experiment has been performed on supercritical water athigh momentum transfer, up to q=90 Å-1, in order to study the short-time single protondynamics. The value of the proton mean kinetic energy, H, has been extracted inthe framework of the impulse approximation and then compared with the predictions ofa harmonic model, devised under the assumptions of total decoupling amongtranslational, rotational and vibrational degrees of freedom. In Panel a of the figurebelow typical spectrum together with the data best fit and the resolution component areshown. In panel (b) we report the present DINS determination of the proton meankinetic energy in supercritical water (full diamond), together with the calculated valuesfor an isolated water molecule (dot-dashed line), and for the dense fluid up to thesupercritical states (solid circles with the solid line as an eye-guide). In order to derivethe proton mean kinetic energy in the whole temperature range of interest, the internalvibrational and the roto-translational frequencies have been taken from opticalspectroscopy studies found in the literature, for both the isolated molecule and thedense fluid along the coexistence curve up to the supercritical state. It is evident that thecalculated value of the mean kinetic energy for supercritical water is in good agreementwith our experimental result. As far as the predicted density and temperaturedependences are concerned, differences between the H values for the isolatedmolecule and the dense fluid are visible only at temperatures lower than 400 K. Thispeculiar effect can be explained considering that the intra-molecular stretching modesbecome softer, while the external modes (mainly hindered rotations and librations)become harder as the density increases. These two changes seem to compensate eachother almost in an exact way. Our results show that when the dependence on thethermodynamic state of the frequencies of both internal and external modes is properlytaken into account, DINS experiments give a very satisfactory agreement withtheoretical predictions. Indeed, the evolution with the thermodynamic conditions of thehydrogen bond network in water is reflected on DINS results through the changes of thevibrational frequencies.

In our study the possibility of an Anisotropic Proton Momentum Distribution (APMD)inside a single water molecule, which, instead of a simple Gaussian distribution, isexpected to provide a better description of the experimental response function inmolecular systems, was also discussed. Unfortunately, due to statistical uncertainties ofour data, we can only assess a compatibility between the experimental responsefunction and that obtained from an APMD. Nevertheless, this confirms the importanceof taking into account the anisotropy induced by the molecular bonds, when an accurateextraction of the single atom mean kinetic energy is needed, as

35

Specific Goal III. Accurate study of simple molecularsystems

previously demonstrated in the H2S case. In conclusion, data from a DINS measurementon water in the supercritical state have been presented and the meankinetic energy of the proton inside a H2O molecule extracted. This is well described bya semi-classical harmonic model making use of the optical spectroscopic dataavailable in literature. The agreement between the experimental results and thetheoretical predictions implies that the hypothesis of both the harmonic approximationand the negligible interaction among translational, librational and vibrational degreesof freedom can be reasonably assumed, at least in the supercritical state of water. Thiswork will be published on Journal of Chemical Physics, volume 115, number 24(2001).

FIG. 4. Panel (a): experimental (error bars) and fitted (full line) response functions of supercriticalwater from DINS measurements for the scattering angle 2θ =27.88o. Resolution contribution (dashedline) is also plotted. Panel (b): proton mean kinetic energy as a function of temperature. Valuesobtained from optical data are represented as a dot-dashed line for an isolated water molecule and assolid circles for the dense fluid along the coexistence curve and the supercritical state (solid line isan eye-guide). The result of the present experiment is reported as a full diamond.

36


a) H2O

• Inelastic neutron scattering study of water in the subcritical andsupercritical region

C. H. Uffindell, A. I. Kolesnikov, J-C. Li, and J. Mayers

PHYSICAL REVIEW B 62, 5492 (2000)

Inelastic neutron scattering measurements have been carried out at high-energy transferson H2O water in the subcritical and supercritical region. The

results were compared toestimated values of the kinetic energy of a hydrogen atom in a water molecule in the gasand liquid states. It was found that the increase in kinetic energy with temperature wasmore than expected from the harmonic approximation. It is concluded that about half thehydrogen bonds in water with density of = 0.85 g/cm3 are broken at 400 °C. It was alsofound that there was a further decrease in the number of hydrogen bonds on decreasingthe density at 400 °C.

37


b) H2S

• Single particle dynamics in liquid and solid hydrogen sulphide: aninelastic neutron scattering study

Andreani C, Degiorgi E, Senesi R, Cilloco F, Colognesi D, Mayers J, Nardone M,Pace E

JOURNAL OF CHEMICAL PHYSICS 114, pag 387 (2001)

Inelastic neutron scattering experiments were performed at intermediate and highmomentum transfer, up to 88.2 Å–1, to study the temperature dependence of singlehydrogen mean kinetic energy in polycrystalline and liquid hydrogen sulphide (H2S),

inthe temperature range 16–206 K. Values of the hydrogen mean kinetic energy wereextracted, within the impulse approximation, by fitting to the high momentum transferdata a model response function, obtained from a momentum distribution which is theorientational average of a multivariate Gaussian function. The extracted kinetic energiesare compared with a harmonic model for the vibrational and roto-translationaldynamics. The model makes use of the hydrogen-projected density of states workedout from intermediate momentum transfer data, as well as of optical frequenciesdetermined from Raman and infrared (IR) spectroscopy. A fairly good agreement isobtained in the whole temperature range, while noticeably lower values for the kineticenergy are found if a single atom momentum distribution of isotropic Gaussian shape isassumed in the model response function.

38

Specific goal IV. Single particle dynamics in amorphousmaterials, polymers, catalysts and metal hydrides.

a) AMORPHOUS MATERIALS, POLYMERS

Study of the anisotropy in the atomic momentum distributions in a Kapton filmNemirovsky D, Moreh R, Finkelstein Y, Mayers J

JOURNAL OF PHYSICS-CONDENSED MATTER13 (22): 5053-5063 JUN 4 2001

The molecular anisotropy of polymide layers occurring in Kapton (C22H10N2O5)films was studied using neutron Compton scattering (NCS) by employing the pulsedneutron source (ISIS) at the Rutherford Appleton Laboratory (UK). The widths ofatomic momentum distributions along and normal to the Kapton film surface, sigma (p)and sigma (c) of the H and C atoms were obtained together with the correspondingeffective temperatures T-p and T-c and the anisotropy ratio T-p/T-c. The results areinterpreted in terms of the in-plane and out-of-plane zero-point motions of the H and Catoms relative to the film surface. The data reveal an anisotropy ratio of T-p/T-csimilar to 1.1 which is far lower than that deduced when assuming a rigid planarKapton molecule, where the ratio is similar to1.7. The results are in qualitativeagreement with calculations based on the AM1 semi-empirical method included in theGAUSSIAN98 package.

39


Multiple scattering in deep inelastic neutron scattering:Monte Carlo simulationsand experiments at the ISIS eVS inverse geometry spectrometer

Mayers J, Fielding A L, Senesi RNUCLEAR INSTRUMENTS AND METHODS IN PHYSICS RESEARCH A

In press (2001)

A procedure for the evaluation of multiple scattering contributions is described,fordeep inelastic neutron scattering (DINS)studies using an inverse geometry time-of-flightspectrometer.The accuracy of a Monte Carlo code DINSMS, used to calculate themultiple scattering,is tested by comparison with analytic expressions and withexperimental data collected from polythene,polycrystalline graphite and tin samples.Itis shown that the Monte Carlo code gives an accurate representation of the measureddata and can therefore be used to reliably correct DINS data.

40


b) AMORPHOUS MATERIALS, METAL HYDRIDES

Calibration of the electron Volt spectrometer, a deep inelasticneutron scattering spectrometer at the ISIS pulsed neutron

spallation sourceFielding A L,Mayers J

NUCLEAR INSTRUMENTS AND METHODS IN PHYSICS RESEARCH AIn press (2001)

The electron Volt spectrometer (eVS) is an inverse geometry filter differencespectrometer that has been optimised to measure the single atom properties ofcondensed matter systems using a technique known as neutron Compton scattering(NCS) or deep inelastic neutron scattering (DINS). The spectrometer utilises the highflux of epithermal neutrons that are produced by the ISIS neutron spallation sourceenabling the direct measurement of atomic momentum distributions and ground statekinetic energies. In this paper the procedure that is used to calibrate the spectrometer isdescribed . This includes details of the method used to determine detector positions andneutron flight path lengths as well as the determination of the instrument resolution.Examples of measurements on 3 different samples are shown, ZrH2,

4He and Sn whichshow the self-consistency of the calibration procedure.

H I G H L I G H T S O F

S C I E N C EI S I S

58

The measurement of proton momentum

distributions by neutron scattering is

analogous to the measurement of electron

momentum distributions by Compton

scattering and is known as Neutron

Compton scattering (NCS). NCS

measurements on protons have only

become possible since the construction of

intense accelerator sources such as ISIS,

which allow inelastic neutron scattering

measurements with energy transfers in the

electron volt (eV) region. The eVS

spectrometer at ISIS has been performing

measurements of proton momentum

distributions in isotropic samples for a

number of years and the technique has

now been extended to exploit the much

more detailed behaviour on proton

dynamics which can be obtained from

single crystal data.

Compton scattering, and its neutron

equivalent, both rely upon the fact that when

the momentum transferred to the target

particle is much greater than the initial

momentum of the particle, the impulse

approximation (IA) can be used to interpret

the data. In the IA, the total momentum and

kinetic energy of the neutron and proton are

conserved during the collision process. From

a measurement of the change in energy and

momentum of the neutron, the initial

momentum of the proton along the direction

of the momentum transfer can be

determined.

Measurements of the proton momentum

distribution n(p), can provide very detailed

information about the microscopic

dynamics. According to elementary

quantum mechanics, n(p) is related by

Fourier transform to the proton wave

function. This relation is formally identical

to that between a diffraction pattern and

scattering density, so that if n(p) can be

measured, the proton wave function can be

reconstructed by crystallographic

techniques. For example figure F16.1 shows

a model of a proton wave function in a

hydrogen bond, where the wavefunction is

distributed unevenly between two sites

separated by a distance 2a=1Å. Simulated

eVS data for momentum transfer along the

bond is shown in the lower plot of figure

F16.1. The tails on the data in the region 10-

20 Å-1 are due to ‘interference effects’

between components of the wavefunction in

the two wells.

In fact NCS provides information only

about the component of p along the

scattering vector, measuring the ‘Radon

transform’ of n(p). The problem of inverting

the Radon transform and reconstructing

n(p) from NCS data is similar to the

reconstruction of 3-D images from, for

example, NMR scans, and was solved

mathematically a number of years ago.

Programs for analysing eVS data on single

crystal samples were installed last year and

can now be used to reconstruct n(p). The

Momentum distribution spectroscopy byneutron Compton scattering

Figure F16.1. Top:

model of the

proton

wavefunction in a

hydrogen bond.

Bottom: simulated

eVS data for

momentum

transfer along the

bond.

ro senesiISIS ANNUAL REPORT 1999

H I G H L I G H T S O F

S C I E N C EI S I S

59

procedure consists of fitting the data to a

complete set of Hermite polynomials and

spherical harmonics, convoluted with the

instrument resolution function. Typically 20

coefficients are sufficient to accurately fit a

data set. An advantageous by-product of the

procedure is that instrumental effects are

removed and a data set of typically 105

numbers can be reduced to 20 coefficients.

The momentum distribution can be

reconstructed from the coefficients,

essentially by replacing the Hermite

polynomials in the expansion by Laguerre

polynomials. The lower plot of figure F16.1

shows an example of the procedure. It was

obtained by fitting the simulated eVS data,

and using 20 fit coefficients to reconstruct

n(p). The differences between the

reconstruction and the analytic n(p) are too

small to be seen.

A real eVS data set on a single crystal of

oxalic acid (KHC2O4) is shown in figure

F16.2. The plot was constructed by

superimposing measurements along all

directions in a single plane of the crystal.

Three similar measurements of

perpendicular planes were made and fitted

simultaneously. A particular advantage of

the data analysis procedure is that if the

potential is harmonic, then only the

coefficient of lowest order Hermite

polynomial will be non-zero. The presence

of higher order coefficients indicates that the

potential energy well is anharmonic. Figure

F16.3 shows the anharmonic components of

the momentum distribution of KHC2O4 in

the same plane of the crystal.

Unique features of the technique are that

information on the ground state is obtained

directly, whereas conventional spectroscopy

measures transitions between the ground

state and excited states. A reconstruction of

the wave function allows the determination

of the spatial distribution of the proton on

very short time scales, whereas diffraction

techniques determine an average spatial

distribution over much longer time scales.

In combination with diffraction

measurements, the NCS technique can

distinguish between static disorder and

dynamic disorder due to quantum

tunnelling. There are many areas of

technological and scientific interest to which

this new technique can be applied, such as

the study of hydrogen bonds, which are

essential for biological processes and the

study of metal hydrides, which have great

potential for clean energy storage.

G R e i t e r ( U n i v e r s i t y o f H o u s t o n ) , J M a y e r s ( I S I S ) ,J N o r e l a n d , R D e l a p l a n e ( U n i v e r s i t y o f U p p s a l a )

Figure F16.3. Anharmonic components of the momentum distribution of

KHC2O4.

Figure

F16.2. eVS

data set

from oxalic

acid.

Highlights of ISIS Science- ISIS 2000 ISIS FacilityAnnual Report 1999-2000 RAL-TR-2000-050August 2000

Neutron scattering reveals short-lived quantumentanglement of protons in condensed matter

The concept of quantum entanglement (QE) plays a pivotal role in present-day quantum theory. Based on previous theoretical investigations, we haverecently carried out a series of neutron Compton scattering (NCS)experiments on eVS, aiming to detect a predicted `anomalous' NCScomponent caused by entanglement of protons (or H-bonds) or of otherlight particles in condensed matter at ambient conditions. The experiments(e.g. on water and metallic hydrides) have confirmed these predictions,revealing a striking decrease of the total cross-section per proton in somecases as large as 30%. This effect may represent a new fundamental featureof quantum dynamics in many-body systems. It appears to be of quitegeneral nature and may have important consequences.

Figure H15.1. Dependence of sH/sD of H2O-D2O mixtures at room temperature on the deuteroncontent (molar fraction) XD . The full line represents the conventionally expected value sH/sD=10.7. Red (and blue) symbols represent data determined with the Au-foil (and U-foil)analyser. For each sample, the sH/sD anomaly was constant (within experimental error) overthe available range of scattering times tscatt.


The nonclassical effect of QE between two or more quantum systems — and the associated non-local Einstein-Podolsky-Rosen (EPR) correlations — has always been considered to representone of the most fundamental features of quantum theory. Nowadays, multiparticle QE and itscharacteristic dynamics (called decoherence or dephasing) are the focus of several experimentaland theoretical fields of physics and engineering (e.g. quantum optics, quantum computation andquantum cryptography).These investigations usually deal with pairs of quantum particles (photons, atoms, ions, etc.)which are carefully isolated from their environment. In condensed systems at ambientexperimental conditions QE is usually considered to be unimportant and/or not accessible byexperiment, due to its extremely fast decoherence.In contrast, our theoretical investigations of quantum dynamics in condensed systems —proceeding beyond the `traditional' methods, like the Born-Oppenheimer approximation —showed the possible existence of short-lived QE of protons (and other light particles) even incondensed systems. We proposed to test this effect by applying sufficiently `fast' scatteringtechniques. Using the neutron Compton scattering (NCS) method on liquid water and H2O-D2Omixtures at room temperature, we observed a strong anomalous decrease in the total cross sectionof the proton, for some mixtures amounting to 30 % of the well-known value of about 82barns/proton.This result provided, for the first time, a direct evidence of the QE of protons (or H-bonds) on thefemtosecond timescale.Extending these investigations, our experiments on other systems (e.g. metallic hydrides,benzene, polystyrene) have clearly confirmed the existence of this new effect, and alsodemonstrated that it is not limited to particular substances.Our NCS experiments have been carried out at the eVS instrument which, due to the intense fluxof epithermal neutrons, provides a unique opportunity to measure the present effects.

Figure H15.2. The ratio sH/sNb of the metallic hydride NbH0.85 at two different temperatures,exhibiting a strong dependence on the scattering time tscatt. The Au-foil analyser has beenused. The full line represents the conventionally expected value s H/sNb=13.1.

60

R Senesi (INFM, Italy),

C Andreani (University of

Rome ‘Tor Vergata’ and

INFM, Italy), D Colognesi

(CNR, Italy, and ISIS)

Single particle kinetic energy in solid and denseliquid 3He

For many years the dense phases of the light

helium isotope have attracted the interest of

both theoretical and experimental physicists, it

being a prototype system for the understand-

ing of quantum many body physics. Indeed,

thanks to the accurate knowledge of the inter-

particle potential, and to the non-relativistic

dynamical regime involved, a detailed,

quantitative comparison can be made between

theory and experiment which is not generally

feasible for other quantum many-body systems.

Despite this advantage, 3He still appears to

challenge the efforts of theoreticians, because

of the intrinsic difficulty in dealing with a

many-body anti-symmetric wave-function in

computer simulations. From the experimental

point of view the study of 3He dynamics by

thermal neutron spectroscopy has been

limited by the large neutron absorption cross

section which results in a striking lack of

experimental data. However, recently we have

been able to overcome this experimental

constraint by using epithermal neutrons with

energy in excess of 1 eV and to derive, for the

first time, unique information on single-

particle mean kinetic energies, , in the

solid and high density liquid phases of 3He.

The results of this experimental work have

been successfully compared with the most

advanced ground-state simulation techniques.

It is worth noticing that the single-particle

mean kinetic energy is a quantity which

strongly characterises dense quantum systems,

being substantially different according to the

system investigated and/or the approximations

adopted (e.g. the classical Maxwellian regime,

the quantum Boltzmann liquid regime, the

Debye-like anharmonic crystal , the Bose

condensates, the Fermi liquids etc.). Further-

more, epithermal neutron scattering has

proved to be the only reliable technique

providing direct access to its determination.

The experiment was performed on the eVS

spectrometer, where an intense flux of

incident neutrons in the 1-100 eV spectral

range and high momentum transfer, 90-140 Å-1,

are available. In this scattering regime the

Impulse approximation (IA) can be invoked

and the dynamical structure factor S(q,ω), is

simply related to the single particle momen-

tum distribution. The experiment was per-

formed at a constant temperature T=2 K

varying the applied pressure in order to obtain

a high density liquid sample (molar volume v =

23.8 cm3/mole), a body centred cubic (bcc)

sample (molar volume v = 20.1 cm3/mole) and

a hexagonal close packed (hcp) sample (molar

volume v = 18.8 cm3/mole) of 3He. In order to

Solid 3He at low

temperature is a quantum

crystal in which the effects

of both atomic localization

and strong anharmonicity

result in a large excess of

single-particle kinetic

energy. Deep Inelastic

Neutron Scattering (DINS)

measurements using eVS

have provided the first

experimental

determination of the

single-particle mean

kinetic energy of this

system in the solid hcp

and bcc phases, and in the

high density liquid near

the melting transition.

ÙFig. H22.1 Scaling scattering function F(y) for the bcc

solid sample. Data (full circles); best fit (purple line);

resolution function of eVS (red line); simulated resolution

function expected for VESUVIO (pink line).

F (Y

)(Å

)

-6 -4 -2 20 4 6Y (Å-1)

0.00

0.04

0.08

0.12

0.16


HIGHLIGHTS OF ISIS SCIENCE THE ISIS FACILITY

61

(K

)

2015 3025 35 40v (cm3/mole)

10

20

30

40

50

Solid

Liquid

DINS experiment

DMC - solid

DMC - liquid

SCP calculations

minimise the absorption of the sample it was

vital to perform the experiment using the

highest available incident neutron energies.

The inelastic neutron spectrum has been

determined using the filter difference tech-

nique measuring the time of flight of the

neutrons absorbed by the 4.908 eV resonance

of the Au foil filter. Under this experimental

condition the average ratio between the

sample absorption and scattering cross section

was about 30, to be compared with a ratio of

about 1000 for thermal neutrons.

Within the IA, the dynamic response of

the sample, S(q,ω), can be expressed in terms

of the single particle momentum distribution

of the initial state, n(p), (i.e. the state of each

particle before the collision with the incident

neutron),

∫⋅−−= pd

M

pq

M

qpnqS

rrr

rr)

2()(),(

2ωδω

The dynamic response function in the IA can

also be described in terms of a scaling function

F(y)=q/M S(q,ω), where

)2

(2

M

q

q

My −= ω

and M is the 3He mass. The second moment of

F(y) is proportional to the single particle mean

kinetic energy and, due to the scaling proper-

ties, a single response function resulting from

an average over all the 32 detectors was derived.

An example of the scaling function is reported

in Fig. H22.1 for the bcc sample. The values of

were obtained from this function

assuming a Gaussian function for the helium

momentum distribution, n(p), and exploiting

the second moment sum rule.

In Fig. H22.2 the molar volume depen-

dence of derived from the DINS experi-

ment is plotted together with the same quantity

evaluated by both Diffusion Monte Carlo

(DMC) calculations and by the self-consistent

phonon method. We observe that the experi-

mental values of are in remarkable

agreement with the DMC calculations for both

liquid and solid phases. It has to be stressed

that, among theoretical models, the DMC

simulations seem to provide the most accurate

results. Such a broad-band agreement has

been attributed to the use of a recent ab initio

interatomic potential which also includes

three-body terms. As shown in Fig. H22.1,

values of the single particle mean kinetic

energy obtained through the self-consistent

phonon calculation lie systematically lower

than the experimental results. Indeed in this

theoretical approach the anharmonic contri-

butions to are only approximately

accounted for through the introduction of a

cubic anharmonic term. These results repre-

sent the first experimental determination of

in solid 3He and the demonstration that

epithermal neutron scattering is the ideal

quantitative probe for the study of single

particle dynamic properties. ×Fig. H22.2 Molar volume

dependence of : present DINS

measurements (blue circles);

Diffusion Monte Carlo calculations

for the solid phase by Moroni et al.

(red circles): Diffusion Monte Carlo

calculations for the liquid phase by

Casulleras et al. (red triangles):

Self- Consistent Phonon

calculations by Moleko et al.

(continuous line); the vertical line

represents the solid-liquid boundary

at T=2 K.

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