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A study of neutron detection efficiency of an organic scintillation detector through simulation of detection processes
Nuclear Instruments and Methods 176 (1980) 549-554 © North-Holland Publishing Company
A STUDY OF NEUTRON DETECTION EFFICIENCY OF AN ORGANIC SCINTILLATION DETECTOR
THROUGH SIMULATION OF DETECTION PROCESSES K. GUL Pakistan Institute of Nuclear Science and Technology, P.O. Nilore, Rawalpindi, Pakistan
Received 13 December 1979 and in revised form 28 April 1980
Neutron detection efficiency of an organic scintillation detector has been studied through Rawal Monte Carlo programm coded in FORTRAN IV for energies of 0-15 MeV. The contributions from multiple scattering, carbon break-up and light pile-up have been investigated. The effect of resonances in the total cross-section of carbon on neutron detection efficiency as a function of neutron energy dispersion has also been studied. The comparison of calculated efficiency with reported measurements indicates that evaluated ENDF/B-IV alpha emission cross-sections below 15 MeV are higher and the corresponding evaluation reported by Lachkar et al. leads to better agreement.
1. Introduction
cross-section of carbon on the neutron detection efficiency has been studied for resonances at 2.09 MeV and 6.3 MeV. The computed efficiency values have been compared with reported measurements and a good agreement between the computed values and measured values has been found in the vicinity of the neutron detection thresholds.
The ever increasing demand on accuracy of neutron data requires accurate knowledge of neutron detection efficiency of the detector used for data acquisition. Since efficiency measurements are confined to a limited energy range a computed curve is always required for extrapolation and interpolation. The neutron detection efficiency of hydrocarbon scintillators has been studied through approximate analytical methods [1,2]. With the availability of digital computers various studies of neutron detection efficiency for different energy regions have been reported through Monte Carlo codes [ 3 - 9 ] . Hermsdorf et al. [7] have studied the contributions of multiple scattering a n d carbon break-up reactions in the 0 - 1 5 MeV energy region and have carried out a comparison of Monte Carlo calculations with analytical calculations. Recently Cecil et al. [9] have reported improved predictions o f neutron detection efficiency for hydrocarbon scintillators from 1 MeV to about 300 MeV. However the agreement between their computed and measured efficiency values near the threshold is poor. In the present work we report on a study of neutron detection efficiency of the hydrocarbon scintillator for the energy range 0 - 1 5 MeV through a computer program coded in FORTRAN IV which includes explicitly the contribution from multiple scattering, carbon break-up and light pile-up in multiple scattering. The effect of resonances in the total
2. Physical basis A neutron is detected through the process of transfer of its energy to charged particles which induce scintillations in a scintillator. The scintillations fall on the photocathode of a photomultiplier tube resulting in photoelectrons whose stage by stage amplification culminates in an electricpulse. The pulses are amplified and processed electronically. In order to suppress noise inherent in electronics, only pulses above a suitable height defining the detection threshold are allowed to be counted. The detection threshold level is determined in a standard manner so as to be reproducible and correspond to a known neutron energy. Thus on o f the important parameters of neutron detection efficiency is the detection threshold level. The various possible nuclear processes that can take place with neutrons up to 15 MeV in the detector are shown in table 1. The reactions 12C(n, p)12B and 12C(n,d)llB have thresholds of 13.6 and 14.9 MeV and have small cross sections below 15 MeV. 549
550
K. Gul / Neutron detection efficiency
Table 1 Various possible nuclear processes taking place with 15 MeV neutrons in the scintillator 1H(n, n)lH 12C(n, n)l~C 12C(n, n'3,)l 2C
n-p scattering n-Celastic scattering n-C inelastic scattering
12C(n, 4He)9Be 12C(n, ~He)9Be,(2.43) 9*Be ~ B e + n 8Be ~ 24He or 9Be --->SHe+ 4He S H e e n + ~He 12C(n, n,)41' 2C* 1 2 , C --~ 32 He
n - a reaction
n-3c~ reaction
These reactions have been neglected. As gamma-neutron pulse shape discrimination is commonly used in neutron spectroscopy, the contribution of 12C(n, n'7)12C to neutron detection processes has been neglected. However the reaction has been considered as a mode of changing the velocity of a neutron. The following expressions for light output have been used as given by Batchelor et al. [10].
Lp
r0.215Ep + 0.028E~, ! L0.60Ep - 1.28,
(0 < E p < 8 MeV) ; (8 ~
For alphas: L a = 0.046E a + 0.007E~. For Be: Lne = 0.023EBe , and for carbon nuclei: Lc = 0.017Ec, Where all energies are in MeV.
3. Program description The details of mathematical and statistical theory can be found in refs. 3, 11 and 12. The logical flow chart is shown in fig. 1. The history of an incident neutron of a given energy is processed according to the following steps. a) The position coordinates of the neutron (x, y, z = 0) are determined and its direction cosines U =
Q=0 Q=0 Q = -4.433 MeV -7.656 MeV -9.63 MeV -10.84 MeV -11.83 MeV Q = -5.704 MeV Q = -8.134 MeV
Q = -7.276 MeV
V = O, W = 1 are fixed. b) From the total macroscopic cross section the fraction of the unit weight left unscattered is determined which is termed as current weight. c) The probability for the interaction of the neutron with proton is determined using n - p scattering cross section. d) The type of nucleus with which the neutron interacts is determined. For collisions with protons only elastic scattering occurs. If the collision is with carbon the various possible interactions are considered. The light output is calculated. e) The light output from the reaction is compared with that corresponding to threshold light output, i.e. light output due to a proton having energy equal to the threshold detection level. f) If the light output is equal to or greater than the threshold light output, the event is detected and the current weight is stored in a register. A new event is initiated if required by going to (a). g) If the light output is less than the threshold light output, the distance at which the collision took place is determined and the position coordinates are calculated. The new direction cosines are computed from the scattering angle of the neutron. The current weight is computed again. The steps from (b) to (h) are repeated till the event is detected or the energy of the neutron falls below the detection threshold or the current weight falls below a specified value. In the case of n - a reaction further collisions cannot be processed. In such a case a new entry of a neutron is initiated. The light outputs from multiple collisions are addded up if these occur within a specified time.
J
Read and p r i n t in -put data -Reset registers -compute threshold light out-put: L M -compute tegendre polynomials
-Set initial coordinates xjyj z = 0 direction cosln es U=O, V=O W=1 -reset registers -compute current weight Compute the probability of Interaction of the neutron with o proton, EFFD
J I J
n-¢
interaction
_>0 n-p scQ~I ¢* i n ~
I Determine the type of interaction -angle of scatter [ng and energy of neutron except in n-=~ reaction compute energy release to charged particles
t
Compute the light out-put I L
|
i
1
Compute scattering Qngle and energy loss of the neutron
J
Compute the light out-put ~L
I
1
I
>~o
O~
t
0<~~ = 0
-Determine the point of collision J-Compute the direction J cosines of new flight I path [-Compute current weight
Compute the efficiency and its various components
t
Compute the probability J of interaction of the J neutron with a proton, EFFDJ Fig. 1. Flow scheme of the code.
t
Print out the results I and plot the efficiency I
552
K. Gul / Neutron detection efficiency
4. Input data The total neutron-proton scattering cross section is calculated from the following expression given by Gammel [131 37r °n-P = 1.206E + (-1.86 + 0.09415E + 0.0001306E2) 2
1.206E + (0.4223 + 0.13E~ 2 ' where E is the energy of the neutron in MeV and n is in b. The following expression given by Gammel for anisotropic n - p scattering has been used for computation of the probability of scattering angle in the c.m. system. anp(O E) =°nP(g) X( 1 + b cos20) '
4
(1 + b / 3 )
'
with b = 2(E/90) 2 , where E and 0 are neutron energy (MeV) in laboratory and scattering angle in the c.m. system respectively. The total cross section of carbon below 2 MeV has been calculated from the following expression given by Lachkar et al. [14] o(E) = 4.725 - 3.251E + 1.316E 2 - 0.227E 3 , where the neutron energy E is in MeV and o is in b. All other data concerning carbon except the data pertaining to the angular distributions of scattered neutrons have been taken from ENDF/IV-B. For comparison data on carbon break-up have also been taken from Lachkar et al. [14]. The data on the elastically scattered neutrons have been taken from other published work [15-17]. Although the reaction ~2C(n, n'3,)~2C does not contribute to the detection of neutrons it changes the energy and direction cosines of the neutrons being processed for multiple collision. The inelastic scattering can arise from the 4.43, 7.65, 9.64, 10.84 (having about 3 MeV half-width) and 11.83 MeV states in carbon with cross sections of 215 -+ 15, 8.5 + 2, 62.5 + 5, 13.5 -+ 3 and 3.5 -+ 3 mb respectively for 14.1 MeV neutrons [18]. The 9.64, 10.84 and 11.83 MeV states decay predominently through alpha emission and thus thier excitation has been included by the consideration of 12C(n,a)gBe and 12C(n,n')3a reactions. As the cross section of
excitation of the 7.65 MeV state is small this has been neglected. The angular distribution of neutrons scattered from the 4.43 MeV state has been assumed to be isotropic in the c.m. system below 9 MeV and the data of Glasgow et al. [17] have been used above 9 MeV for the angular distribution of neutrons for this state. The energy distribution of neutrons from the reaction 12C(n, n')12"C, 12"C ~ 3~He has been calculated after Brinkley et al. [19] using the expression N(e) de = const. (1 - e) 2 x/~de ,
with e = E/Ema x ,
where E and Emax are the energy of neutron and maximum energy available to neutrons both taken in the c.m. system. The branching ratio between 12C(n, ~)gBe and 12C(n, a)9*Be (2.43) has been taken from refs. 20 and 21. In order to study the effect of resonances in the total cross section of carbon on the detection efficiency, the data on the total cross section of carbon was divided in to 13 energy regions each region being characterized by its own energy interval for which data were specified. The minimum energy interval was 5 keV for a sharp resonance and 200 keV for a region where the cross section variation was small.
5. Results and discussion
The neutron detection efficiency of three NE213 liquid scintillation detectors of different sizes and detection thresholds has been studied with the Rawal Code. Fig. 2 shows the efficiency calculated through the present code of a NE213 liquid scintillator of 3.8 cm diameter and 10 cm thickness for a detection threshold of 0.81 MeV proton equivalent energy. Efficiency calculations by Hermsdorf et al. [7] for this detector are also shown in this figure for comparison. The two calculations are in good agreement with each other. The slight difference between the two results could be attributed to a difference in the carbon data used in these calculations. Two different sets of evaluated data for alpha-emission cross sections of carbon have been used which clearly shows the dependence of neutron detection efficiency on the data used for carbon. The contribution to the detection efficiency from alpha-emission for 15 MeV neutrons in this particular case amounts to about 27% if one uses the
K. Gul/ Neutron detection efficiency
553
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Monte CQrlo Ccalculotion ( Present Work ) } MeQsurernents by HOOUQI et a l .
.< "5
I
I
--
En(MeVI
En(MeV}
Fig. 2. Comparison of the present work with that of Hermsdoff et al.
Fig. 3. Comparison of the present calculations with the measurements reported by Haouat et al.
evaluated data of Lachkar et al. [14] and to 40% for the data from ENDF/B-IV. In fig. 3 we show a comparison between the calculated efficiency and measured efficiency of a liquid NE213 scintillator of 12.7 cm diameter and 5 cm thickness operated at 2.5 MeV proton equivalent detection threshold energy. The measurement for this detector efficiency have been reported by Haouat et al. [22]. The contribution of carbon break-up below 15 MeV at the 2.5 MeV bias to neutron detection efficiency is negligible. In fig. 4 we show efficiency calculations for a liquid scintillator NE213 of 12 cm diameter and 5.6 cm thickness for 0.256 MeV electron equivalent bias (1.15 MeV proton equivalent bias). The figure also shows neutron detection efficiency measurements by Drosg [23], which were taken from Cecil et al. [9]. The data on alpha emission for carbon from ENDF/B-IV
give higher neutron detection efficiency than that obtained by using the data of Lachkar et al. [14] which results in better agreement with the measured efficiency. The role of light pile-up in neutron detection has been investigated for obtaining insight into the neutron detection process in the scintillator. It has been found that light pile-up plays a role in neutron detection only near the threshold of detection. As the neutron energy increases the energy loss suffered by neutrons in the last collision is enough to produce pulses with their heights above the threshold of detection. For example, for the last neutron detector operated at 1.15 MeV bias the total neutron detection efficiency at 2.5 MeV is 0.336 of which 0.224 comes from n - p scattering and of the rest of 0.112 arising from multiple scattering, 0.045 is due to light pile-up.
---,--O--'MEASUREMENTS
ENERGY DISPERSION 0 KEV
.... Y~--- ENERGY DISPERSION 1OOKEV
BY M. DROSG
MONIE CARLO CALCULATEON (PRESENT WORK)
0.4
--~
0.5
'~
o.~.
¢u
0.3
zLu 0
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0.3
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et al
0.1
0.I
2
/.
6
8
I0
112
i I~
i
16
En(MIv)
Fig. 4. Comparison of the present calculations with measurements reported by Drosg.
I :~05
I 2.O?
I 2.09
I 2.11
--~f/
I 6.2
I 6.25
I 6.3
I 6-35
En(Mev)
Fig. 5. Effect of energy dispersion of neutrons on the detection efficiency for resonances at 2.09 and 6.3 MeV in the total cross section of carbon.
554
K. Gul / Neutron detection efficiency
At 8 MeV the neutron detection efficiency is about 0.252 of which 0.195 is from n - p scattering. Out of the rest of 0.057 the contribution due to light pile-up is 0.002. This contribution goes down with increase in neutron energy. In order to investigate the effect of resonances in the total cross section of carbon, the neutron detection efficiency for the first detector discussed in the present work has been calculated for energies lying on the resonances at 2.09 MeV and 6.3 MeV. The calculations have been carried otit for different energy dispersions where energy dispersion is defined as full width at half-maximum o f the spectrum o f the incident beam assuming a Gaussian shape. These calculations are shown in fig. 5. For the 2.09 MeV resonance the maximum difference between the efficiencies for no dispersion and a dispersion o f 70 keV amounts to 5 - 6 % . For the resonance at 6.3 MeV the difference is 3 - 4 % for no dispersion and a dispersion of 100 keV. These results show the dependence of neutron detection efficiency on sharp resonances in the total cross section of carbon for different energy dispersions Of the neutrons detected by the detector. The accuracy of computed neutron detection efficiency is decided by the accuracy of the data used in the calculations. The errors on the total cross sections of hydrogen are less than 1% while those on the total cross sections of carbon are less than 3% below 15 MeV. However the errors on the carbon break-up cross sections are about 10-15%. For higher threshold values ( > 2 MeV) the contribution from carbon break-up to the detection efficiency is negligible and thus it is possible to calculate neutron detection efficiency with about 4% error below 15 MeV. The author acknowledges the interest o f Dr. N.A. Khan, Director o f PINSTECH in the present work and wishes to express his gratitude to Nuclear Data Section of IAEA for providing data on carbon from ENDF/B-IV.
References [1] J.E. Hardy, Rev. Sci. Instr. 29 (1958) 705. [2] C.D. Swaztz and G.E. Owen, in Fast neutron physics,
vol 1 (eds. J.B. Marion and J.L. Fowler; Interscience Publ., New York, London, 1963). [3] B. Gustafsson and O. Aspelund, Nucl. Instr. and Meth. 48 (1967) 77. [4] H.J. KeUermann and R. Langkau, Nuel. Instr. and Meth. 94 (1971) 137. [5] W.W. Lindstrom and B.D. Anderson, Nucl. Instr. and Meth. 98 (1972) 413. [6] B.T. Thornton and J.R. Smith, Nucl. Instr. and Meth. 96 (1971) 551. [71 D. Hermsdorf, K. Pasieka and D. Seeliger, Nucl. Instr. and Meth. 107 (1973) 259. [8] R.E. Textor and V.V. Verbinski "05 S, a Monte Carlo Code", ORNL-4160, Oak Ridge National Laboratory (1968). [9] R.A. Cecil, B.D. Anderson and R. Madey, Nucl. Instr. and Meth. 161 (1979) 439. [10] R. Batchelor, W.B. Gilboy, J.B. Parker and J.H. Towle, Nucl. Instr. and Meth. 13 (1961) 70. [ 11 ] E.D. Cash Well and C.J. Everett, Practical manual on the Monte Carlo method for random walk problems (Pergamon Press, London, 1959). [12] K. Gul, The Rawal Monte Carlo Code for computation of neutron detection efficiency of a scintillation detector, PINSTECH Report 15 (NPD). [13] J.L, Gammel, in Fast neutron physics, vol 2 (eds. J.B. Marion and J.L. Fowler; Interscience Publ., New York, 1963). [14] J. Lachkar, F. Cocu, G. Haouat, P. le Floch, Y. Patin and J. Sigaud, NEANDC (E) 168 "L" - INDC (FR) 7/L, Nuclear Energy Agency, Nuclear Data Committee (1975). [15] M.D. Goldberg, V.M. May and J.R. Stehn, BNL 400 (1962). [16] D.I. Garber, L.G. Stromberg, M.D. Goldberg, D.E. Cullen and V.M. May, BNL 400 (1970). [17] D.W. Glasgow, F.O. Purser, H. Hogue, J.C. Clement, K. Stelzer, G. Mack, J.R. Boyce, D.H. Epperson, S.G. Buccino, P.W. Lisowski, S.G. Glendinning, E.G. Bilpuch, H.W. Newson and C.R. Gould, Nucl. Sci. Eng. 61 (1976) 521. [18] G.A. Grin, B. Vaucher, J.C. Aider and C. Joseph, Heir. Phys. Acta. 42 (1969) 990. [19] T.A. Brinkley, B.A. Robson and E.W. Titterton, Proc. Phys. Soc. (London) 84 (1964) 201. [20] R.A.Ai-Kital and R.A. Peck, Jr. Phys. Rev. 130 (1963) 1500. [21] E.R. Graves and R.W. Davis, Phys. Rev. 97 (1955) 1205. [22] G. Haouat, J. Lachkar, J. Sigaud, Y. Patin and F. Cosu, Nucl. Sci. Eng. 65 (1978) 331. [23] M. Drosg, Nucl. Instr. and Meth. 105 (1972) 573.
A STUDY OF NEUTRON DETECTION EFFICIENCY OF AN ORGANIC SCINTILLATION DETECTOR
THROUGH SIMULATION OF DETECTION PROCESSES K. GUL Pakistan Institute of Nuclear Science and Technology, P.O. Nilore, Rawalpindi, Pakistan
Received 13 December 1979 and in revised form 28 April 1980
Neutron detection efficiency of an organic scintillation detector has been studied through Rawal Monte Carlo programm coded in FORTRAN IV for energies of 0-15 MeV. The contributions from multiple scattering, carbon break-up and light pile-up have been investigated. The effect of resonances in the total cross-section of carbon on neutron detection efficiency as a function of neutron energy dispersion has also been studied. The comparison of calculated efficiency with reported measurements indicates that evaluated ENDF/B-IV alpha emission cross-sections below 15 MeV are higher and the corresponding evaluation reported by Lachkar et al. leads to better agreement.
1. Introduction
cross-section of carbon on the neutron detection efficiency has been studied for resonances at 2.09 MeV and 6.3 MeV. The computed efficiency values have been compared with reported measurements and a good agreement between the computed values and measured values has been found in the vicinity of the neutron detection thresholds.
The ever increasing demand on accuracy of neutron data requires accurate knowledge of neutron detection efficiency of the detector used for data acquisition. Since efficiency measurements are confined to a limited energy range a computed curve is always required for extrapolation and interpolation. The neutron detection efficiency of hydrocarbon scintillators has been studied through approximate analytical methods [1,2]. With the availability of digital computers various studies of neutron detection efficiency for different energy regions have been reported through Monte Carlo codes [ 3 - 9 ] . Hermsdorf et al. [7] have studied the contributions of multiple scattering a n d carbon break-up reactions in the 0 - 1 5 MeV energy region and have carried out a comparison of Monte Carlo calculations with analytical calculations. Recently Cecil et al. [9] have reported improved predictions o f neutron detection efficiency for hydrocarbon scintillators from 1 MeV to about 300 MeV. However the agreement between their computed and measured efficiency values near the threshold is poor. In the present work we report on a study of neutron detection efficiency of the hydrocarbon scintillator for the energy range 0 - 1 5 MeV through a computer program coded in FORTRAN IV which includes explicitly the contribution from multiple scattering, carbon break-up and light pile-up in multiple scattering. The effect of resonances in the total
2. Physical basis A neutron is detected through the process of transfer of its energy to charged particles which induce scintillations in a scintillator. The scintillations fall on the photocathode of a photomultiplier tube resulting in photoelectrons whose stage by stage amplification culminates in an electricpulse. The pulses are amplified and processed electronically. In order to suppress noise inherent in electronics, only pulses above a suitable height defining the detection threshold are allowed to be counted. The detection threshold level is determined in a standard manner so as to be reproducible and correspond to a known neutron energy. Thus on o f the important parameters of neutron detection efficiency is the detection threshold level. The various possible nuclear processes that can take place with neutrons up to 15 MeV in the detector are shown in table 1. The reactions 12C(n, p)12B and 12C(n,d)llB have thresholds of 13.6 and 14.9 MeV and have small cross sections below 15 MeV. 549
550
K. Gul / Neutron detection efficiency
Table 1 Various possible nuclear processes taking place with 15 MeV neutrons in the scintillator 1H(n, n)lH 12C(n, n)l~C 12C(n, n'3,)l 2C
n-p scattering n-Celastic scattering n-C inelastic scattering
12C(n, 4He)9Be 12C(n, ~He)9Be,(2.43) 9*Be ~ B e + n 8Be ~ 24He or 9Be --->SHe+ 4He S H e e n + ~He 12C(n, n,)41' 2C* 1 2 , C --~ 32 He
n - a reaction
n-3c~ reaction
These reactions have been neglected. As gamma-neutron pulse shape discrimination is commonly used in neutron spectroscopy, the contribution of 12C(n, n'7)12C to neutron detection processes has been neglected. However the reaction has been considered as a mode of changing the velocity of a neutron. The following expressions for light output have been used as given by Batchelor et al. [10].
Lp
r0.215Ep + 0.028E~, ! L0.60Ep - 1.28,
(0 < E p < 8 MeV) ; (8 ~
For alphas: L a = 0.046E a + 0.007E~. For Be: Lne = 0.023EBe , and for carbon nuclei: Lc = 0.017Ec, Where all energies are in MeV.
3. Program description The details of mathematical and statistical theory can be found in refs. 3, 11 and 12. The logical flow chart is shown in fig. 1. The history of an incident neutron of a given energy is processed according to the following steps. a) The position coordinates of the neutron (x, y, z = 0) are determined and its direction cosines U =
Q=0 Q=0 Q = -4.433 MeV -7.656 MeV -9.63 MeV -10.84 MeV -11.83 MeV Q = -5.704 MeV Q = -8.134 MeV
Q = -7.276 MeV
V = O, W = 1 are fixed. b) From the total macroscopic cross section the fraction of the unit weight left unscattered is determined which is termed as current weight. c) The probability for the interaction of the neutron with proton is determined using n - p scattering cross section. d) The type of nucleus with which the neutron interacts is determined. For collisions with protons only elastic scattering occurs. If the collision is with carbon the various possible interactions are considered. The light output is calculated. e) The light output from the reaction is compared with that corresponding to threshold light output, i.e. light output due to a proton having energy equal to the threshold detection level. f) If the light output is equal to or greater than the threshold light output, the event is detected and the current weight is stored in a register. A new event is initiated if required by going to (a). g) If the light output is less than the threshold light output, the distance at which the collision took place is determined and the position coordinates are calculated. The new direction cosines are computed from the scattering angle of the neutron. The current weight is computed again. The steps from (b) to (h) are repeated till the event is detected or the energy of the neutron falls below the detection threshold or the current weight falls below a specified value. In the case of n - a reaction further collisions cannot be processed. In such a case a new entry of a neutron is initiated. The light outputs from multiple collisions are addded up if these occur within a specified time.
J
Read and p r i n t in -put data -Reset registers -compute threshold light out-put: L M -compute tegendre polynomials
-Set initial coordinates xjyj z = 0 direction cosln es U=O, V=O W=1 -reset registers -compute current weight Compute the probability of Interaction of the neutron with o proton, EFFD
J I J
n-¢
interaction
_>0 n-p scQ~I ¢* i n ~
I Determine the type of interaction -angle of scatter [ng and energy of neutron except in n-=~ reaction compute energy release to charged particles
t
Compute the light out-put I L
|
i
1
Compute scattering Qngle and energy loss of the neutron
J
Compute the light out-put ~L
I
1
I
>~o
O~
t
0<~~ = 0
-Determine the point of collision J-Compute the direction J cosines of new flight I path [-Compute current weight
Compute the efficiency and its various components
t
Compute the probability J of interaction of the J neutron with a proton, EFFDJ Fig. 1. Flow scheme of the code.
t
Print out the results I and plot the efficiency I
552
K. Gul / Neutron detection efficiency
4. Input data The total neutron-proton scattering cross section is calculated from the following expression given by Gammel [131 37r °n-P = 1.206E + (-1.86 + 0.09415E + 0.0001306E2) 2
1.206E + (0.4223 + 0.13E~ 2 ' where E is the energy of the neutron in MeV and n is in b. The following expression given by Gammel for anisotropic n - p scattering has been used for computation of the probability of scattering angle in the c.m. system. anp(O E) =°nP(g) X( 1 + b cos20) '
4
(1 + b / 3 )
'
with b = 2(E/90) 2 , where E and 0 are neutron energy (MeV) in laboratory and scattering angle in the c.m. system respectively. The total cross section of carbon below 2 MeV has been calculated from the following expression given by Lachkar et al. [14] o(E) = 4.725 - 3.251E + 1.316E 2 - 0.227E 3 , where the neutron energy E is in MeV and o is in b. All other data concerning carbon except the data pertaining to the angular distributions of scattered neutrons have been taken from ENDF/IV-B. For comparison data on carbon break-up have also been taken from Lachkar et al. [14]. The data on the elastically scattered neutrons have been taken from other published work [15-17]. Although the reaction ~2C(n, n'3,)~2C does not contribute to the detection of neutrons it changes the energy and direction cosines of the neutrons being processed for multiple collision. The inelastic scattering can arise from the 4.43, 7.65, 9.64, 10.84 (having about 3 MeV half-width) and 11.83 MeV states in carbon with cross sections of 215 -+ 15, 8.5 + 2, 62.5 + 5, 13.5 -+ 3 and 3.5 -+ 3 mb respectively for 14.1 MeV neutrons [18]. The 9.64, 10.84 and 11.83 MeV states decay predominently through alpha emission and thus thier excitation has been included by the consideration of 12C(n,a)gBe and 12C(n,n')3a reactions. As the cross section of
excitation of the 7.65 MeV state is small this has been neglected. The angular distribution of neutrons scattered from the 4.43 MeV state has been assumed to be isotropic in the c.m. system below 9 MeV and the data of Glasgow et al. [17] have been used above 9 MeV for the angular distribution of neutrons for this state. The energy distribution of neutrons from the reaction 12C(n, n')12"C, 12"C ~ 3~He has been calculated after Brinkley et al. [19] using the expression N(e) de = const. (1 - e) 2 x/~de ,
with e = E/Ema x ,
where E and Emax are the energy of neutron and maximum energy available to neutrons both taken in the c.m. system. The branching ratio between 12C(n, ~)gBe and 12C(n, a)9*Be (2.43) has been taken from refs. 20 and 21. In order to study the effect of resonances in the total cross section of carbon on the detection efficiency, the data on the total cross section of carbon was divided in to 13 energy regions each region being characterized by its own energy interval for which data were specified. The minimum energy interval was 5 keV for a sharp resonance and 200 keV for a region where the cross section variation was small.
5. Results and discussion
The neutron detection efficiency of three NE213 liquid scintillation detectors of different sizes and detection thresholds has been studied with the Rawal Code. Fig. 2 shows the efficiency calculated through the present code of a NE213 liquid scintillator of 3.8 cm diameter and 10 cm thickness for a detection threshold of 0.81 MeV proton equivalent energy. Efficiency calculations by Hermsdorf et al. [7] for this detector are also shown in this figure for comparison. The two calculations are in good agreement with each other. The slight difference between the two results could be attributed to a difference in the carbon data used in these calculations. Two different sets of evaluated data for alpha-emission cross sections of carbon have been used which clearly shows the dependence of neutron detection efficiency on the data used for carbon. The contribution to the detection efficiency from alpha-emission for 15 MeV neutrons in this particular case amounts to about 27% if one uses the
K. Gul/ Neutron detection efficiency
553
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Fig. 3. Comparison of the present calculations with the measurements reported by Haouat et al.
evaluated data of Lachkar et al. [14] and to 40% for the data from ENDF/B-IV. In fig. 3 we show a comparison between the calculated efficiency and measured efficiency of a liquid NE213 scintillator of 12.7 cm diameter and 5 cm thickness operated at 2.5 MeV proton equivalent detection threshold energy. The measurement for this detector efficiency have been reported by Haouat et al. [22]. The contribution of carbon break-up below 15 MeV at the 2.5 MeV bias to neutron detection efficiency is negligible. In fig. 4 we show efficiency calculations for a liquid scintillator NE213 of 12 cm diameter and 5.6 cm thickness for 0.256 MeV electron equivalent bias (1.15 MeV proton equivalent bias). The figure also shows neutron detection efficiency measurements by Drosg [23], which were taken from Cecil et al. [9]. The data on alpha emission for carbon from ENDF/B-IV
give higher neutron detection efficiency than that obtained by using the data of Lachkar et al. [14] which results in better agreement with the measured efficiency. The role of light pile-up in neutron detection has been investigated for obtaining insight into the neutron detection process in the scintillator. It has been found that light pile-up plays a role in neutron detection only near the threshold of detection. As the neutron energy increases the energy loss suffered by neutrons in the last collision is enough to produce pulses with their heights above the threshold of detection. For example, for the last neutron detector operated at 1.15 MeV bias the total neutron detection efficiency at 2.5 MeV is 0.336 of which 0.224 comes from n - p scattering and of the rest of 0.112 arising from multiple scattering, 0.045 is due to light pile-up.
---,--O--'MEASUREMENTS
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554
K. Gul / Neutron detection efficiency
At 8 MeV the neutron detection efficiency is about 0.252 of which 0.195 is from n - p scattering. Out of the rest of 0.057 the contribution due to light pile-up is 0.002. This contribution goes down with increase in neutron energy. In order to investigate the effect of resonances in the total cross section of carbon, the neutron detection efficiency for the first detector discussed in the present work has been calculated for energies lying on the resonances at 2.09 MeV and 6.3 MeV. The calculations have been carried otit for different energy dispersions where energy dispersion is defined as full width at half-maximum o f the spectrum o f the incident beam assuming a Gaussian shape. These calculations are shown in fig. 5. For the 2.09 MeV resonance the maximum difference between the efficiencies for no dispersion and a dispersion o f 70 keV amounts to 5 - 6 % . For the resonance at 6.3 MeV the difference is 3 - 4 % for no dispersion and a dispersion of 100 keV. These results show the dependence of neutron detection efficiency on sharp resonances in the total cross section of carbon for different energy dispersions Of the neutrons detected by the detector. The accuracy of computed neutron detection efficiency is decided by the accuracy of the data used in the calculations. The errors on the total cross sections of hydrogen are less than 1% while those on the total cross sections of carbon are less than 3% below 15 MeV. However the errors on the carbon break-up cross sections are about 10-15%. For higher threshold values ( > 2 MeV) the contribution from carbon break-up to the detection efficiency is negligible and thus it is possible to calculate neutron detection efficiency with about 4% error below 15 MeV. The author acknowledges the interest o f Dr. N.A. Khan, Director o f PINSTECH in the present work and wishes to express his gratitude to Nuclear Data Section of IAEA for providing data on carbon from ENDF/B-IV.
References [1] J.E. Hardy, Rev. Sci. Instr. 29 (1958) 705. [2] C.D. Swaztz and G.E. Owen, in Fast neutron physics,
vol 1 (eds. J.B. Marion and J.L. Fowler; Interscience Publ., New York, London, 1963). [3] B. Gustafsson and O. Aspelund, Nucl. Instr. and Meth. 48 (1967) 77. [4] H.J. KeUermann and R. Langkau, Nuel. Instr. and Meth. 94 (1971) 137. [5] W.W. Lindstrom and B.D. Anderson, Nucl. Instr. and Meth. 98 (1972) 413. [6] B.T. Thornton and J.R. Smith, Nucl. Instr. and Meth. 96 (1971) 551. [71 D. Hermsdorf, K. Pasieka and D. Seeliger, Nucl. Instr. and Meth. 107 (1973) 259. [8] R.E. Textor and V.V. Verbinski "05 S, a Monte Carlo Code", ORNL-4160, Oak Ridge National Laboratory (1968). [9] R.A. Cecil, B.D. Anderson and R. Madey, Nucl. Instr. and Meth. 161 (1979) 439. [10] R. Batchelor, W.B. Gilboy, J.B. Parker and J.H. Towle, Nucl. Instr. and Meth. 13 (1961) 70. [ 11 ] E.D. Cash Well and C.J. Everett, Practical manual on the Monte Carlo method for random walk problems (Pergamon Press, London, 1959). [12] K. Gul, The Rawal Monte Carlo Code for computation of neutron detection efficiency of a scintillation detector, PINSTECH Report 15 (NPD). [13] J.L, Gammel, in Fast neutron physics, vol 2 (eds. J.B. Marion and J.L. Fowler; Interscience Publ., New York, 1963). [14] J. Lachkar, F. Cocu, G. Haouat, P. le Floch, Y. Patin and J. Sigaud, NEANDC (E) 168 "L" - INDC (FR) 7/L, Nuclear Energy Agency, Nuclear Data Committee (1975). [15] M.D. Goldberg, V.M. May and J.R. Stehn, BNL 400 (1962). [16] D.I. Garber, L.G. Stromberg, M.D. Goldberg, D.E. Cullen and V.M. May, BNL 400 (1970). [17] D.W. Glasgow, F.O. Purser, H. Hogue, J.C. Clement, K. Stelzer, G. Mack, J.R. Boyce, D.H. Epperson, S.G. Buccino, P.W. Lisowski, S.G. Glendinning, E.G. Bilpuch, H.W. Newson and C.R. Gould, Nucl. Sci. Eng. 61 (1976) 521. [18] G.A. Grin, B. Vaucher, J.C. Aider and C. Joseph, Heir. Phys. Acta. 42 (1969) 990. [19] T.A. Brinkley, B.A. Robson and E.W. Titterton, Proc. Phys. Soc. (London) 84 (1964) 201. [20] R.A.Ai-Kital and R.A. Peck, Jr. Phys. Rev. 130 (1963) 1500. [21] E.R. Graves and R.W. Davis, Phys. Rev. 97 (1955) 1205. [22] G. Haouat, J. Lachkar, J. Sigaud, Y. Patin and F. Cosu, Nucl. Sci. Eng. 65 (1978) 331. [23] M. Drosg, Nucl. Instr. and Meth. 105 (1972) 573.