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Monte Carlo calculation of energy response functions for a lithium glass scintillator for neutrons between 1 and 6 MeV
NUCLEAR
INSTRUMENTS
AND
METHODS
131
(i975) 5 2 9 - 5 3 3 ;
©
NORTH-HOLLAND
PUBLISHING
CO.
M O N T E C A R L O C A L C U L A T I O N OF E N E R G Y R E S P O N S E F U N C T I O N S F O R A L I T H I U M GLASS S C I N T I L L A T O R F O R N E U T R O N S B E T W E E N 1 AND 6 MeV D. R. W E A V E R
Birmingham Radiation Centre, University of Birmingham, P.O. Box 363, Birmingham B15 2TT, England Received 13 N o v e m b e r 1975 Energy response functions have been calculated for a cylinder o f NE905 lithium glass scintillator which was 44 m m in diameter a n d 25 m m long. T h e calculations were p e r f o r m e d by the M o n t e Carlo m e t h o d in the n e u t r o n energy range 1-6 MeV. T h e n e u t r o n
detection efficiency, as a function o f discriminator setting, h a s been derived f r o m the response functions a n d has been c o m p a r e d with experimental m e a s u r e m e n t s . R e a s o n s are given for the increase in efficiency above 2 MeV.
TABLE 1
1. Introduction
A lithium glass scintillator has been used by Khadduri 1) in the Department of Physics, University .of Birmingham, for the measurement of neutron spectra by time-of-flight. The spectra were those emitted by proton bombardment of medium weight nuclei and the purpose of producing them was to obtain quasiisotropic sources; consequently the energy range to be measured went up to several MeV. In order to convert the time-of-flight data to neutron energy spectra, it was necessary to know the detection efficiency of the scintillator as a function of neutron energy in the range up to 6 MeV. This was determined experimentally at A . E . R . E . , Harwell, using the IBIS accelerator and their long counter as a standard. It was expected from the work of Neiil et al. 2) that the efficiency of the detector would cease to follow the 6Li(n,~) crosssection downwards for neutron energies above 2 MeV, but would increase with increasing neutron energy. That result was confirmed by the IBIS experiments and the purpose of this work was to investigate the reasons for the increase. Neill 3) had found spectra which looked similar to g a m m a ray Compton scattering edges and had suggested that the detection of gammas from inelastic events in the counter would give such a spectrum, and that the integration of this shape above a discriminator level would lead to an increase in eJ~ciency with increasing neutron energy. 2. Calculation
2.1. DATA The composition of the NE905 was supplied by Nuclear Enterprises and the data are given in table 1. The detector itself is a cylinder of diameter 44 m m and length 25 mm, coupled to a 56AVP photomultiplier. E N D F / B neutron data sets were obtained from
C o m p o s i t i o n o f lithium glass scintillator NE905. Element
6Li 7Li Oxygen Magnesium Aluminium Silicon Cerium
% by weight
6.3 0.33 50.7 2.3 9.8 27.2 3.41
Density 2480 k g / m a
the Neutron Data Compilation Centre, Gif-sur-Yvette, for all of the elements in the counter except cerium, for which no evaluation was available. Cross-sections for cerium were obtained from Foster4), Gilboy 5) and Owens 6) and the assumption made, in view of the low concentration of the element, that only elastic scattering occurs. Since the resolution of the detector was about 19% at the thermal peak, the energy groups used in the calculation could be relatively coarse; the E N D F / B data were averaged over 1 MeV wide steps for each isotope, the first covering the range 6.5-5.5 MeV and the last 1.5-0.5 MeV. Few neutrons were found to scatter below the 0.5 MeV lower limit of the data set; consequently it was not necessary to generate a group to cater for these neutrons. Inelastic neutron scattering in some of the elements of the glass led to y-ray production. The tabulations of Storm and Israel 7) were used to calculate both the probability of y escape from the detector and the type of y event.
530
D . R . WEAVER
2.2. DETECTOR RESPONSE TO GAMMA AND PARTICLE EVENTS
In scintillators it is well known that the light output from a 7 absorption is not the same as from a particle depositing the same amount of energy [Birksa)]; similarly particles of different masses may not produce the same output pulse for equal input energy. The Monte Carlo program is required to determine the size of the single light pulse which is the result of the contributions from the various energy depositing reactions caused by a single neutron in its passage through the scintillator. Therefore conversion factors for all the possible reaction products are required. In liquid organic scintillators there are plenty of data for the light output as a function of particle energy and mass. However, information is not available for NE905 and it is not clear what form it might take, so the simple relation was assumed that all particles produce a light pulse proportional to the energy deposited and no variation with particle mass was allowed. In the case of y-rays, subsidary experiments and calculations were
used to determine the relative effect of absorption of thermal neutrons and y-rays in the glass. The response to standard 7 sources (6°Co, Say, ZZNa and 43Mn) and to thermalised neutrons from an AmBe source was measured and the Monte Carlo program run with an incident 7 flux to provide a comparison with the y experiments. The y sources were of known activity so the efficiency of the counter could be determined absolutely. For example, in the case of a 6°Co source at a certain distance from the detector the calculation gave 3.30 counts in the peak channel for 1000 gammas incident while the experiment gave 3.26 counts/1000 y-rays; this agreement must be regarded as fortuitously good as the errors inherent in the Monte Carlo method were at least several percent. The experiments showed that 1 MeV deposited by 7 interaction was equivalent to (2.6_+0.2)MeV deposited by particle interaction. 2.3. THE PROGRAM A flow diagram is given in fig. 1. The neutron crosssection data were converted into probability density
Initialisation (i)Set neutron starting energy {ii) Read gamma and neutron probability densityfunctions from file (iii)Read Q values from file Calculate neutron transI i mission probability i
I Enough neutrons processed? l I Choose radius at which neutron enters I J Choose depth'at which it interacts I
IChoose interaction type
I
]
I •
I
[ absorphon
.
I etashc I
I
[ ~nela-~'tic i
If 6Li,o~ygen or silicon use angular scattering data Otherwise assume sotropic ~)
I
Multiply by reso uhon funct on
J
Output response funct on J
J Calculateenergy~" ] C~ I Choose whether I ~" escapes
tculate new t neutron ir t on ]
Catcutate new neutron energy 1 K Choose whether I neutr°n ,ascapes J L
t°electricl
Pl3r
1ch~ose r~wl
Calculate I [Calculate total¥ interactionl ~energydeposited I Ipositional
Calculate, total J energy aeposlted l in th,s eveit I
I
Determine tight I [(3otoB pulse heighl and Lrecord in hstogram
J
I Oo to D I
I
Fig. I. Flow diagram of the Monte Carlo program.
production J
I
~o.o~, J nnihilation~
ENERGY RESPONSE FUNCTIONS
functions such that a 1 MeV wide neutron group was broken into 49 sub-units, this number being required to accommodate the seven isotopes and the seven reactions considered [elastic, (n,p), (n,c0 and four levels of inelastic scatter]. The width of the sub-unit corresponded to the relative probability of each reaction; hence, if a reaction did not occur, the subunit had zero width. The Monte Carlo program did not need to refer to the cross-section data, only to the probability density functions, so these were calculated once, stored in a file and accessed at each initiation of the program together with total cross-sections and Qvalues. Neutrons were considered to be incident normal to the fiat face of the scintillator because this was the geometry used by Khadduri. In this geometry it was possible to employ the symmetry of the detector about the cylindrical axis as all neutrons entering the detector at the same radius were equivalent. The probability of transmission without interaction was known from the total cross-section, so it was not necessary to calculate that from the Monte Carlo method. A probability density function was therefore constructed which forced all neutrons to interact at some depth in the glass, and the absolute efficiency was obtained by weighting the Monte Carlo results by the probability that the incident neutrons did indeed react within the glass. When the reaction type had been chosen, the program path divided depending on whether the event was an absorption or an elastic or inelastic scatter. In the case of an absorption, the energy deposited was converted to light units and the event was recorded in a pulse height histogram. For elastic scatters the new neutron direction was chosen using, in the cases of 6Li, oxygen and silicon, the E N D F / B angular distribution data and for all other isotopes an isotropic distribution. This was not too severe an approximation since there was little 7Li in the glass, and scattering from the remaining elements produced only small energy degradation. In the case of inelastic scattering, the 7-rays were followed until they were lost or absorbed. It was not possible to store all the branching ratios for the excited levels; however, it was found that the majority of the transitions of the most important inelastic reactions involved ~ decay to the ground state so this was assumed for all cases. The exception was the 3-body break-up reaction 6Li(n,n')d,~, when no ~ was emitted; the low concentration of 7Li in the glass made the multibody break-up 7Li(n,n')ctt an unlikely event. When the tracking of y-ray paths was complete, the
531
secondary neutron was followed as for an elastic scattering event. At the end of each case the energy deposited in the glass was converted to light units, using the normalisation determined earlier to bring ~,-ray energy to the same scale as particle energy, and the individual contributions were summed. The resultant light pulse was recorded in the output histogram and the program went on to the next case. The final response function was obtained by multiplying the histogram by the resolution function of the counter when all the neutrons had been processed. F r o m experiment, the thermal neutron peak had a fwhm of 18.6%, but no information was available for the variation of resolution with incident neutron energy so an assumption of fwhm proportional to the square root of the energy deposited was made. 2.4.
RANDOM NUMBER GENERATION
Random numbers between 0 and 1 were generated within the Hewlett-Packard computer used in this work. It was found that care had to be taken in the selection of the random numbers; for example, each neutron case entailed the determination of the position of entry of the neutron on the front face, the depth at which it interacted, with which isotope, and so on. This led to the depth calculation being frequently every sixth random number, and while the whole series was found to be uniformly distributed, a selection from the series at fixed intervals was not. Therefore, individual random number generators, employing the same algorithm but randomised starting points, were used for each type of event. 3. Results
The response functions obtained are given in fig. 2; except for those produced by thermal neutrons, they have been normalised so that the same number of neutrons is incident at each energy. The thermal neutron cases have been arbitrarily normalised and are shown to indicate the position of the peak resulting from the 4.786 MeV Q-value of the 6Li(n,~) reaction. Fig. 3 gives the efficiencies obtained by summing the response functions above a chosen discriminator level; also plotted are the results of Khadduri 1) and of Neill 2) who used a different size of counter; all the results are normalised at 1 MeV. The rapid rise in efficiency has been reproduced by the calculation, although the rise begins at a higher energy than suggested by the data of Khadduri and rises faster; this behaviour could be explained by assuming a non-linear variation of light
532
D.R.
output with deposited energy. However, there is sufficient correspondence for a number of observations to be made. The decrease in efficiency between 1 and 2 MeV coincides with the decrease in the 6Li(n, ~) cross-section shown by the lower number of counts in the peak. At 3 and 4 MeV there are structures like Compton edges in the response function which cause the efficiency to rise a little, but its massive rise at 5 and 6 MeV is due to the appearance, above the discriminator, of the high count rate in the low energy channels. This has the effect that up to 3 MeV the discriminator setting has little effect on efficiency, but above 4 MeV the discriminator level causes increasingly large changes, indicating the care that is required in setting the discriminator when using detectors of this type.
.•...
6MeV
3MeV
5 MeV
WEAVER
Fig. 4 shows the response functions at 6 MeV and 4 MeV when the )'-rays have been excluded. This was done in order to investigate Neill's proposal that the Compton-like edges were due to ),-rays. At 6 MeV it can be seen that the low pulse height event rate is little affected by the exclusion of the 7's but that the region between this and the neutron peak is decreased to zero. At 4 MeV the " C o m p t o n edge" structure disappears, so it is clear that inelastic events do produce sufficient )'-rays to cause changes in the spectra. However, the major contributors to the rise in efficiency at higher energies are not )'-rays; this work has shown that recoil particles from elastic and inelastic events bear the greatest responsibility. To demonstrate the point the program was run for 6 MeV neutrons, but recoil particle energy was not added to the spectrum. Fig. 5 compares this case with the normal 6 MeV response function; the full energy peak is not affected, but the low energy pulses are much
2 MeV °°% i
u
',
" 0
4MeV
6 MeV
IMeV
•
•O•Oo _.o°°'~•,1
,o•
~with
%1
3"
. . . . without "A" Thermal
Thermal
°% • • .="
,% . o
"%
.="
Pulse Height
%1 Pulse
Height
Fig. 2. Response functions for the lithium glass scintillator.
40
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60
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3IX / Discriminator • Channel 16 ]r~ermol neutron x C h a n n e l 18 |peak occurs ,n + ChQnne[
20£
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0
4 MeV
,"
/ ,"./ ," /j , ,
I
1
I
I
I
I
2 3 4 5 Neutron Energy [MeVI
I
6
Fig. 3. Efficiency o f the scintillator as a function o f neutron energy and discriminator level.
2O
4O
6C) Channd Number
Fig. 4. Response functions with g a m m a response excluded.
ENERGY RESPONSE F U N C T I O N S
DDO
6 MeV
ee
"**
_~.e
* *%°
.
6MeV recoil energy excluded
OQOQ
20
40
60 ChannelNumber
Pulse Height
Fig. 5. Response functions with recoil energy excluded. reduced when recoils are neglected. In fact, the peak due to 29Si(n,p) and 160(n,a) about channel 18 can now be seen as can the smaller contribution o f 25Mg(n ' ct) about channel 30. A few cases were run, using a different r a n d o m n u m b e r generator, with double the n u m b e r o f incident neutrons. N o variations in the response functions were seen outside the statistics o f the Monte Carlo process, which gave about + 8 % at the peak of the 3 MeV neutron case. N o allowance was made in the p r o g r a m for edge effect, i.e. the loss o f energy to the region outside the scintillator. F o r the neutron absorption or scattering events the m a x i m u m energy acquired by a charged particle is a few MeV and its range in the scintillator will be a small fraction o f a millimeter. The probability of losing any of this energy is therefore very small. In the case of ~ interactions, electrons o f several MeV can be produced. Consulting the curves for electron range in Marion and Young9), it can be seen that the electrons travel almost 1 cm at 2 MeV in the NE905 material. The results o f the p r o g r a m show that the majority of V interactions are C o m p t o n scatters at
533
energies o f 2 MeV and below. Taking 2 MeV electrons, therefore, as an upper limit of likely electron energy, an estimate has been made of the fraction o f energy lost to the counter. The stopping powers shown by M a r i o n and Y o u n g have been used to obtain, when all possible paths within the scintillator were averaged, a figure o f 10% for the fraction o f the energy lost by a 3 MeV electron. With this as an upper limit it can be seen that no serious distortion o f the spectra has occurred because the calculation of electron trajectory has been omitted; however, for detectors of m u c h smaller size, b o u n d a r y corrections would have to be computed.
4. Conclusions The Monte Carlo analysis of the lithium glass scintillator has shown that the rise in efficiency o f the detector above 2 MeV is largely due to the energy deposited in the glass by the recoil nuclei f r o m elastic and inelastic reactions. The charged particles arising f r o m (n, ~) and (n, p) events produce a contribution to the rise in efficiency as do the g a m m a rays from inelastic scatters, but the effects are much smaller than that of the recoil particles largely due to the fact that scatters occur an order of magnitude more frequently than do other events. The results show the care that has to be exercised in setting discriminator levels for work with these counters at neutron energies o f several MeV. References 1) I.Y. Khadduri, P h . D . Thesis (Birmingham University, Department of Physics, 1973). 2) j. M. Neill, D. Huffman, C.A. Preskitt and J.C. Young, Nucl. Instr. and Meth. 82 (1970) 162. a) j. M. Neill, private communication. 4) D. G. Foster and D. W. Glasgow, Phys. Rev. C. 3 (1971) 576. ~) W. B. Gilboy and J. H. Towle, Nucl. Phys. 42 (1963) 86. 6) R. O. Owens and J. H. Towle, Nucl. Phys. 112 (1968) 337. 7) E. Storm and H. I. Israel, Nucl. Data Tables A 7, no. 6 (1970) 565. s) j. B. Birks, The theory and practice of scintillation counters (Pergamon Press, New York, 1964). 9) j.B. Marion and F.C. Young, Nuclear reaction analysis (North-Holland Publ. Co., Amsterdam, 1968).
INSTRUMENTS
AND
METHODS
131
(i975) 5 2 9 - 5 3 3 ;
©
NORTH-HOLLAND
PUBLISHING
CO.
M O N T E C A R L O C A L C U L A T I O N OF E N E R G Y R E S P O N S E F U N C T I O N S F O R A L I T H I U M GLASS S C I N T I L L A T O R F O R N E U T R O N S B E T W E E N 1 AND 6 MeV D. R. W E A V E R
Birmingham Radiation Centre, University of Birmingham, P.O. Box 363, Birmingham B15 2TT, England Received 13 N o v e m b e r 1975 Energy response functions have been calculated for a cylinder o f NE905 lithium glass scintillator which was 44 m m in diameter a n d 25 m m long. T h e calculations were p e r f o r m e d by the M o n t e Carlo m e t h o d in the n e u t r o n energy range 1-6 MeV. T h e n e u t r o n
detection efficiency, as a function o f discriminator setting, h a s been derived f r o m the response functions a n d has been c o m p a r e d with experimental m e a s u r e m e n t s . R e a s o n s are given for the increase in efficiency above 2 MeV.
TABLE 1
1. Introduction
A lithium glass scintillator has been used by Khadduri 1) in the Department of Physics, University .of Birmingham, for the measurement of neutron spectra by time-of-flight. The spectra were those emitted by proton bombardment of medium weight nuclei and the purpose of producing them was to obtain quasiisotropic sources; consequently the energy range to be measured went up to several MeV. In order to convert the time-of-flight data to neutron energy spectra, it was necessary to know the detection efficiency of the scintillator as a function of neutron energy in the range up to 6 MeV. This was determined experimentally at A . E . R . E . , Harwell, using the IBIS accelerator and their long counter as a standard. It was expected from the work of Neiil et al. 2) that the efficiency of the detector would cease to follow the 6Li(n,~) crosssection downwards for neutron energies above 2 MeV, but would increase with increasing neutron energy. That result was confirmed by the IBIS experiments and the purpose of this work was to investigate the reasons for the increase. Neill 3) had found spectra which looked similar to g a m m a ray Compton scattering edges and had suggested that the detection of gammas from inelastic events in the counter would give such a spectrum, and that the integration of this shape above a discriminator level would lead to an increase in eJ~ciency with increasing neutron energy. 2. Calculation
2.1. DATA The composition of the NE905 was supplied by Nuclear Enterprises and the data are given in table 1. The detector itself is a cylinder of diameter 44 m m and length 25 mm, coupled to a 56AVP photomultiplier. E N D F / B neutron data sets were obtained from
C o m p o s i t i o n o f lithium glass scintillator NE905. Element
6Li 7Li Oxygen Magnesium Aluminium Silicon Cerium
% by weight
6.3 0.33 50.7 2.3 9.8 27.2 3.41
Density 2480 k g / m a
the Neutron Data Compilation Centre, Gif-sur-Yvette, for all of the elements in the counter except cerium, for which no evaluation was available. Cross-sections for cerium were obtained from Foster4), Gilboy 5) and Owens 6) and the assumption made, in view of the low concentration of the element, that only elastic scattering occurs. Since the resolution of the detector was about 19% at the thermal peak, the energy groups used in the calculation could be relatively coarse; the E N D F / B data were averaged over 1 MeV wide steps for each isotope, the first covering the range 6.5-5.5 MeV and the last 1.5-0.5 MeV. Few neutrons were found to scatter below the 0.5 MeV lower limit of the data set; consequently it was not necessary to generate a group to cater for these neutrons. Inelastic neutron scattering in some of the elements of the glass led to y-ray production. The tabulations of Storm and Israel 7) were used to calculate both the probability of y escape from the detector and the type of y event.
530
D . R . WEAVER
2.2. DETECTOR RESPONSE TO GAMMA AND PARTICLE EVENTS
In scintillators it is well known that the light output from a 7 absorption is not the same as from a particle depositing the same amount of energy [Birksa)]; similarly particles of different masses may not produce the same output pulse for equal input energy. The Monte Carlo program is required to determine the size of the single light pulse which is the result of the contributions from the various energy depositing reactions caused by a single neutron in its passage through the scintillator. Therefore conversion factors for all the possible reaction products are required. In liquid organic scintillators there are plenty of data for the light output as a function of particle energy and mass. However, information is not available for NE905 and it is not clear what form it might take, so the simple relation was assumed that all particles produce a light pulse proportional to the energy deposited and no variation with particle mass was allowed. In the case of y-rays, subsidary experiments and calculations were
used to determine the relative effect of absorption of thermal neutrons and y-rays in the glass. The response to standard 7 sources (6°Co, Say, ZZNa and 43Mn) and to thermalised neutrons from an AmBe source was measured and the Monte Carlo program run with an incident 7 flux to provide a comparison with the y experiments. The y sources were of known activity so the efficiency of the counter could be determined absolutely. For example, in the case of a 6°Co source at a certain distance from the detector the calculation gave 3.30 counts in the peak channel for 1000 gammas incident while the experiment gave 3.26 counts/1000 y-rays; this agreement must be regarded as fortuitously good as the errors inherent in the Monte Carlo method were at least several percent. The experiments showed that 1 MeV deposited by 7 interaction was equivalent to (2.6_+0.2)MeV deposited by particle interaction. 2.3. THE PROGRAM A flow diagram is given in fig. 1. The neutron crosssection data were converted into probability density
Initialisation (i)Set neutron starting energy {ii) Read gamma and neutron probability densityfunctions from file (iii)Read Q values from file Calculate neutron transI i mission probability i
I Enough neutrons processed? l I Choose radius at which neutron enters I J Choose depth'at which it interacts I
IChoose interaction type
I
]
I •
I
[ absorphon
.
I etashc I
I
[ ~nela-~'tic i
If 6Li,o~ygen or silicon use angular scattering data Otherwise assume sotropic ~)
I
Multiply by reso uhon funct on
J
Output response funct on J
J Calculateenergy~" ] C~ I Choose whether I ~" escapes
tculate new t neutron ir t on ]
Catcutate new neutron energy 1 K Choose whether I neutr°n ,ascapes J L
t°electricl
Pl3r
1ch~ose r~wl
Calculate I [Calculate total¥ interactionl ~energydeposited I Ipositional
Calculate, total J energy aeposlted l in th,s eveit I
I
Determine tight I [(3otoB pulse heighl and Lrecord in hstogram
J
I Oo to D I
I
Fig. I. Flow diagram of the Monte Carlo program.
production J
I
~o.o~, J nnihilation~
ENERGY RESPONSE FUNCTIONS
functions such that a 1 MeV wide neutron group was broken into 49 sub-units, this number being required to accommodate the seven isotopes and the seven reactions considered [elastic, (n,p), (n,c0 and four levels of inelastic scatter]. The width of the sub-unit corresponded to the relative probability of each reaction; hence, if a reaction did not occur, the subunit had zero width. The Monte Carlo program did not need to refer to the cross-section data, only to the probability density functions, so these were calculated once, stored in a file and accessed at each initiation of the program together with total cross-sections and Qvalues. Neutrons were considered to be incident normal to the fiat face of the scintillator because this was the geometry used by Khadduri. In this geometry it was possible to employ the symmetry of the detector about the cylindrical axis as all neutrons entering the detector at the same radius were equivalent. The probability of transmission without interaction was known from the total cross-section, so it was not necessary to calculate that from the Monte Carlo method. A probability density function was therefore constructed which forced all neutrons to interact at some depth in the glass, and the absolute efficiency was obtained by weighting the Monte Carlo results by the probability that the incident neutrons did indeed react within the glass. When the reaction type had been chosen, the program path divided depending on whether the event was an absorption or an elastic or inelastic scatter. In the case of an absorption, the energy deposited was converted to light units and the event was recorded in a pulse height histogram. For elastic scatters the new neutron direction was chosen using, in the cases of 6Li, oxygen and silicon, the E N D F / B angular distribution data and for all other isotopes an isotropic distribution. This was not too severe an approximation since there was little 7Li in the glass, and scattering from the remaining elements produced only small energy degradation. In the case of inelastic scattering, the 7-rays were followed until they were lost or absorbed. It was not possible to store all the branching ratios for the excited levels; however, it was found that the majority of the transitions of the most important inelastic reactions involved ~ decay to the ground state so this was assumed for all cases. The exception was the 3-body break-up reaction 6Li(n,n')d,~, when no ~ was emitted; the low concentration of 7Li in the glass made the multibody break-up 7Li(n,n')ctt an unlikely event. When the tracking of y-ray paths was complete, the
531
secondary neutron was followed as for an elastic scattering event. At the end of each case the energy deposited in the glass was converted to light units, using the normalisation determined earlier to bring ~,-ray energy to the same scale as particle energy, and the individual contributions were summed. The resultant light pulse was recorded in the output histogram and the program went on to the next case. The final response function was obtained by multiplying the histogram by the resolution function of the counter when all the neutrons had been processed. F r o m experiment, the thermal neutron peak had a fwhm of 18.6%, but no information was available for the variation of resolution with incident neutron energy so an assumption of fwhm proportional to the square root of the energy deposited was made. 2.4.
RANDOM NUMBER GENERATION
Random numbers between 0 and 1 were generated within the Hewlett-Packard computer used in this work. It was found that care had to be taken in the selection of the random numbers; for example, each neutron case entailed the determination of the position of entry of the neutron on the front face, the depth at which it interacted, with which isotope, and so on. This led to the depth calculation being frequently every sixth random number, and while the whole series was found to be uniformly distributed, a selection from the series at fixed intervals was not. Therefore, individual random number generators, employing the same algorithm but randomised starting points, were used for each type of event. 3. Results
The response functions obtained are given in fig. 2; except for those produced by thermal neutrons, they have been normalised so that the same number of neutrons is incident at each energy. The thermal neutron cases have been arbitrarily normalised and are shown to indicate the position of the peak resulting from the 4.786 MeV Q-value of the 6Li(n,~) reaction. Fig. 3 gives the efficiencies obtained by summing the response functions above a chosen discriminator level; also plotted are the results of Khadduri 1) and of Neill 2) who used a different size of counter; all the results are normalised at 1 MeV. The rapid rise in efficiency has been reproduced by the calculation, although the rise begins at a higher energy than suggested by the data of Khadduri and rises faster; this behaviour could be explained by assuming a non-linear variation of light
532
D.R.
output with deposited energy. However, there is sufficient correspondence for a number of observations to be made. The decrease in efficiency between 1 and 2 MeV coincides with the decrease in the 6Li(n, ~) cross-section shown by the lower number of counts in the peak. At 3 and 4 MeV there are structures like Compton edges in the response function which cause the efficiency to rise a little, but its massive rise at 5 and 6 MeV is due to the appearance, above the discriminator, of the high count rate in the low energy channels. This has the effect that up to 3 MeV the discriminator setting has little effect on efficiency, but above 4 MeV the discriminator level causes increasingly large changes, indicating the care that is required in setting the discriminator when using detectors of this type.
.•...
6MeV
3MeV
5 MeV
WEAVER
Fig. 4 shows the response functions at 6 MeV and 4 MeV when the )'-rays have been excluded. This was done in order to investigate Neill's proposal that the Compton-like edges were due to ),-rays. At 6 MeV it can be seen that the low pulse height event rate is little affected by the exclusion of the 7's but that the region between this and the neutron peak is decreased to zero. At 4 MeV the " C o m p t o n edge" structure disappears, so it is clear that inelastic events do produce sufficient )'-rays to cause changes in the spectra. However, the major contributors to the rise in efficiency at higher energies are not )'-rays; this work has shown that recoil particles from elastic and inelastic events bear the greatest responsibility. To demonstrate the point the program was run for 6 MeV neutrons, but recoil particle energy was not added to the spectrum. Fig. 5 compares this case with the normal 6 MeV response function; the full energy peak is not affected, but the low energy pulses are much
2 MeV °°% i
u
',
" 0
4MeV
6 MeV
IMeV
•
•O•Oo _.o°°'~•,1
,o•
~with
%1
3"
. . . . without "A" Thermal
Thermal
°% • • .="
,% . o
"%
.="
Pulse Height
%1 Pulse
Height
Fig. 2. Response functions for the lithium glass scintillator.
40
t
60
/
3IX / Discriminator • Channel 16 ]r~ermol neutron x C h a n n e l 18 |peak occurs ,n + ChQnne[
20£
/ / ,'
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Fig. 4. Response functions with g a m m a response excluded.
ENERGY RESPONSE F U N C T I O N S
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Fig. 5. Response functions with recoil energy excluded. reduced when recoils are neglected. In fact, the peak due to 29Si(n,p) and 160(n,a) about channel 18 can now be seen as can the smaller contribution o f 25Mg(n ' ct) about channel 30. A few cases were run, using a different r a n d o m n u m b e r generator, with double the n u m b e r o f incident neutrons. N o variations in the response functions were seen outside the statistics o f the Monte Carlo process, which gave about + 8 % at the peak of the 3 MeV neutron case. N o allowance was made in the p r o g r a m for edge effect, i.e. the loss o f energy to the region outside the scintillator. F o r the neutron absorption or scattering events the m a x i m u m energy acquired by a charged particle is a few MeV and its range in the scintillator will be a small fraction o f a millimeter. The probability of losing any of this energy is therefore very small. In the case of ~ interactions, electrons o f several MeV can be produced. Consulting the curves for electron range in Marion and Young9), it can be seen that the electrons travel almost 1 cm at 2 MeV in the NE905 material. The results o f the p r o g r a m show that the majority of V interactions are C o m p t o n scatters at
533
energies o f 2 MeV and below. Taking 2 MeV electrons, therefore, as an upper limit of likely electron energy, an estimate has been made of the fraction o f energy lost to the counter. The stopping powers shown by M a r i o n and Y o u n g have been used to obtain, when all possible paths within the scintillator were averaged, a figure o f 10% for the fraction o f the energy lost by a 3 MeV electron. With this as an upper limit it can be seen that no serious distortion o f the spectra has occurred because the calculation of electron trajectory has been omitted; however, for detectors of m u c h smaller size, b o u n d a r y corrections would have to be computed.
4. Conclusions The Monte Carlo analysis of the lithium glass scintillator has shown that the rise in efficiency o f the detector above 2 MeV is largely due to the energy deposited in the glass by the recoil nuclei f r o m elastic and inelastic reactions. The charged particles arising f r o m (n, ~) and (n, p) events produce a contribution to the rise in efficiency as do the g a m m a rays from inelastic scatters, but the effects are much smaller than that of the recoil particles largely due to the fact that scatters occur an order of magnitude more frequently than do other events. The results show the care that has to be exercised in setting discriminator levels for work with these counters at neutron energies o f several MeV. References 1) I.Y. Khadduri, P h . D . Thesis (Birmingham University, Department of Physics, 1973). 2) j. M. Neill, D. Huffman, C.A. Preskitt and J.C. Young, Nucl. Instr. and Meth. 82 (1970) 162. a) j. M. Neill, private communication. 4) D. G. Foster and D. W. Glasgow, Phys. Rev. C. 3 (1971) 576. ~) W. B. Gilboy and J. H. Towle, Nucl. Phys. 42 (1963) 86. 6) R. O. Owens and J. H. Towle, Nucl. Phys. 112 (1968) 337. 7) E. Storm and H. I. Israel, Nucl. Data Tables A 7, no. 6 (1970) 565. s) j. B. Birks, The theory and practice of scintillation counters (Pergamon Press, New York, 1964). 9) j.B. Marion and F.C. Young, Nuclear reaction analysis (North-Holland Publ. Co., Amsterdam, 1968).