- Email: [email protected]
gamma pulse shape discrimination
Nuclear Instruments and Methods in Physics Research A 729 (2013) 522–526
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Analysis of the pulse shape mechanism in a plastic scintillator with efficient neutron/gamma pulse shape discrimination N.P. Hawkes n, G.C. Taylor National Physical Laboratory, Hampton Road, Teddington TW11 0LW, UK
art ic l e i nf o
a b s t r a c t
Article history: Received 7 February 2013 Received in revised form 19 July 2013 Accepted 23 July 2013 Available online 1 August 2013
A sample of the new plastic scintillator recently formulated by Zaitseva et al., and shown by them to have efficient pulse shape discrimination properties, was exposed to pure gamma and mixed neutron/gamma radiation from different sources, and the pulse shapes recorded by a digitising oscilloscope. Separate average neutron and gamma pulse shapes were derived, using pulse shape discrimination where necessary. A theoretical pulse shape formula, based on the conventional two-lifetime description of pulse shape formation in organic scintillators, was then fitted to these measured shapes to obtain numerical values for the lifetimes and proportions of the scintillator excitations. It is found that, although the conventional model explains much of the observed pattern of values, there are hints of behaviour that is not consistent with its assumptions. Crown Copyright & 2013 Published by Elsevier B.V. All rights reserved.
Keywords: Neutron detection Plastic scintillator Pulse shape Pulse shape discrimination Scintillator excitations
1. Introduction It has been known for a long time that certain organic scintillators produce a slightly different pulse shape in response to neutron interactions than they do in response to gamma rays, allowing the two to be distinguished [1]. One well-used pulse shape discrimination (PSD) technique is to integrate the pulse over two different intervals and compare the two integrals, the ‘long gate/short gate’ method [2]. Until recently, detailed studies of the shape of the very fast pulses from such scintillators were difficult to carry out, but with the advent of fast digital samplers it has become possible to record large numbers of pulses in nanosecond detail. The aim of the present work was to measure pulse shapes at this level of detail from a PSD-capable organic scintillator, and analyse them in terms of the excitation mechanisms that are understood to occur in such scintillators. Additional motivation for such studies was provided recently by Zaitseva et al. [3] of the Lawrence Livermore National Laboratory (LLNL), USA. This group successfully demonstrated efficient PSD in a plastic scintillator. Up to then, PSD had only been practical in liquids, with attendant problems of leakage, thermal expansion, and in many cases flammability. This development could considerably simplify the construction and use of PSD-capable counters. The Zaitseva group kindly provided a sample of an early formulation of the new scintillator to the National Physical Laboratory, UK,
n
Corresponding author. Tel.: +44 20 8943 7064. E-mail address: [email protected] (N.P. Hawkes).
where pulse shape measurements were carried out as part of an ongoing programme of research into novel detection methods for neutrons. The scope of the present work does not include a measurement of the quality of discrimination achievable with this scintillator, beyond a demonstration that it was effective for this study. 2. Experimental method The uncoated scintillator sample, identified by LLNL as number 885, is close to being cylindrical in shape (the circular faces being slightly dished) and measures 25 mm ∅ 10 mm. It was coupled with a generous application of optical grease directly to the end window of an ET Enterprises 9214KB linear focused photomultiplier, and held in place by lightweight packing material. The photomultiplier is 51 mm in diameter (48 mm nominal active diameter) and has 12 dynodes. It was fitted with a plug-on voltage divider type VD20E1-Neg, negative high voltage being preferred so that the anode would be near ground potential with no isolating capacitor needed for the signal connection. The high voltage was 1250 V. The anode of the photomultiplier was connected to the pulse digitiser by approximately 40 m of high bandwidth cable (Huber +Suhner SX 07262 BD). The digitiser, a Tektronix TDS5052 digital oscilloscope, has 8 bits of voltage resolution, and for the tests reported here it was set to 200 mV/div, 20 ns/div, 2.5 GS/s (400 ps/ sample), and 500 samples per trace. The trigger position was set so that the trace covered 20 ns to 180 ns. Traces were transferred over the General Purpose Interface Bus (GPIB) interface, under the
0168-9002/$ - see front matter Crown Copyright & 2013 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nima.2013.07.071
N.P. Hawkes, G.C. Taylor / Nuclear Instruments and Methods in Physics Research A 729 (2013) 522–526
control of a LabVIEW program, to a PC where they were written to a text file for off-line analysis. Measurements were carried out using a 22Na gamma source (producing gamma rays at 1.275 and 0.511 MeV) and an 241Am/Be neutron source (producing neutrons with a broad energy spectrum extending above 10 MeV, together with copious gamma rays). The 22 Na gamma source consists of a 1 mm diameter ion exchange bead at the centre of a solid plastic disc 3 mm thick and 25 mm in diameter [4], and had an activity of approximately 43 kBq at the time of the measurement. The neutron source has a nominal alpha activity of 1 Ci (37 GBq), and emits neutrons at a rate of approximately 2.4 106 s 1 into 4π. The active material is sealed in a cylindrical stainless steel capsule of the type designated X3 and measuring 22.4 mm in diameter by 31 mm in height. A lead cap approximately 2 mm thick was placed over the neutron source in order to reduce the low-energy gamma flux, which is particularly strong at 60 keV. For the measurements, the 22Na source was suspended in a low-mass enclosure at about 12.5 cm from the scintillator, while the neutron source was placed at approximately 90 cm. Measurement runs were restricted to 4000 traces at a time, in order to keep the text files to a manageable size, but two files were obtained for each measurement condition to give 8000 traces each, prior to rejection of clipped pulses as described in the next section.
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Fig. 1. Discrimination plot for the LLNL 885 scintillator. Black dots, 241Am/Be source; green crosses, 22Na source. There is marked PSD in the 241Am/Be data (even for unoptimised timings), and the 22Na data confirm which is the gamma branch. The solid red lines show the PSD criteria applied to the 241Am/Be data, events to the left of the vertical line being discarded. The dashed lines show the amplitude limits applied when deriving the average shape. Only those pulses between the applicable lines (black dashes, 241Am/Be; green dashes, 22Na) were used in the averaging process.
3. Derivation of average pulse shape Once the digitiser is set up, its input voltage range is fixed, and any input pulse that exceeds the maximum is clipped at that level. In order to exclude any such clipped pulses from the analysis, a trace was rejected if any of its samples reached the maximum sample value in the file. Analysis was carried out using Excel spreadsheets and VBA macros. The PSD necessary to separate neutrons from gammas in the 241Am/Be measurement was based on the long gate/short gate technique, the long integral (actually just the sum of sample values) covering 0–180 ns, i.e. essentially the whole pulse, and the short integral 50–180 ns (the tail). The t ¼ 0 reference point for these timings was set for each trace separately to be 6 ns before the time point when the leading edge of the pulse reached 50% of its final amplitude. No prolonged effort was made to optimise these timing parameters, but as shown in Fig. 1 the separation of the events into neutron and gamma branches was sufficiently clear for further adjustment to be unnecessary. The result of applying the same analysis to the 22Na data is also shown in the figure, and confirms which branch corresponds to gammas. It is understood that the right-hand limits (i.e. the edges at large values of long integral) of both of the 241Am/Be branches are produced by the rejection of clipped pulses, and not by any feature in the source spectrum. Furthermore the difference in the Long Integral position of these boundaries is understood to be due to the difference in pulse shape, the gamma pulse being more peaked and therefore reaching the voltage limit sooner as the total area is increased. The spectra from the 241Am/Be source lack sharp features, and do not provide an energy calibration. The gamma rays from 22Na, however, produce Compton edges at 341 and 1062 keV. These are clearly visible when the gamma data are binned into a “pulse height” (actually Long Integral) spectrum (Fig. 2). There is no significant zero offset in the integrals, as any small offset in an individual pulse was determined from the first 25 samples and subtracted off, so this allows a long integral value of approximately 7.29 in the gamma branch to be associated with an electron energy of 341 keV and 25.9 with an electron energy of 1062 keV. This is consistent with the conventional assumption that electron light
Fig. 2. Pulse height spectrum for gamma rays from 22Na, obtained by binning the 22 Na long integral values from Fig. 1. The Compton edges at electron energies of 341 and 1062 keV are clearly visible.
output is proportional to the electron energy minus an offset, the offset here being approximately 59 keV. Also shown in Fig. 1 are the PSD criteria used to separate the neutron and gamma events in the 241Am/Be data. To reduce the risk of identifying events wrongly, those to the left of the vertical red line were discarded. The 22Na data were assumed to relate exclusively to gammas and were not subjected to any PSD process. Three average pulse shapes were derived, for 241Am/Be neutrons, 214Am/Be gammas, and 22Na gammas. In each case the average was built up one trace at a time by first normalising the trace to a standard area, and then adding its contribution in at the desired sequence of sample times, using linear interpolation where necessary to derive a sample value between actual samples. The time reference for each trace was the same as used for the PSD analysis, i.e. based on the 50% point on the leading edge. Finally the average pulse shapes were normalised to a standard area of 40 (in units of (amplitude units) (nanoseconds)). The validity of fitting a theoretical function to an average shape depends firstly on the acquisition process being free of significant distortion, and then on the pulse shapes remaining effectively constant with the energy deposited, at least over a limited energy range. In the present work, evidence that these conditions are met is provided by the Compton spectrum of Fig. 2 (where the edge positions are consistent with reasonable expectations of the electron
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N.P. Hawkes, G.C. Taylor / Nuclear Instruments and Methods in Physics Research A 729 (2013) 522–526
from the scintillator at subsequent times is proportional to B LðtÞ ¼ tA1 exp tt1 þ t 2 t t Z0 exp tt2 exp tt1 1 ¼0
Fig. 3. Average measured pulse shapes for neutrons and gammas. Each shape is plotted twice, once showing the entire trace and again at a magnification factor of 10 (see right-hand scale) so as to show the pulse tail in detail.
light output) and the discrimination plot of Fig. 1 (where the neutron and gamma branches show near linearity). The 8-bit amplitude resolution of the digitiser used in this experiment is ample for displaying traces on the screen, but not ideal when pulses have a low-amplitude region of interest (here the short integral) but must not be allowed to saturate at the peak. This problem was mitigated by including in the averages only those pulses with an areaZ 45% that of the largest non-clipped pulse in the measurement in question. In addition, an upper area limit was also applied (95% for 241Am/Be and 75% for 22Na), in case the shape of the largest pulses was in some way unusual. These criteria are shown as dotted vertical lines in Fig. 1, and are more stringent than the PSD limits, i.e. not all discriminated events were in fact used. After all selection criteria were applied, 689 traces contributed to the average pulse shape for 241Am/Be neutrons, 819 to that for 241 Am/Be gammas, and 823 to that for 22Na gammas. The three shapes are shown in Fig. 3. As one would expect, the two gamma shapes are very similar to each other, despite originating from markedly different sources, and the neutron shape differs noticeably from both (especially in the tail). Each of the pulse shapes in Fig. 3 shows amplitude fluctuations that the averaging process has not removed, for example the dip at approximately 88 ns. These are explicable in terms of nonstatistical processes, such as reflections due to the detailed configuration of the dynode chain and of the cable and its connectors. They may be responsible, at least in part, for the difficulties described below that were experienced in the fitting process.
4. A mathematical model of pulse shape To analyse the measured pulse shapes, a theoretical model was required, based on the actual processes believed to occur in the scintillator. Fitting this model to the measured shapes might then provide some quantitative insight into those processes. The response of a PSD-capable scintillator to a gamma ray or neutron has been described [5–7] in terms of the production of two types of excited entity, one significantly shorter-lived than the other. The short-lived type decays exponentially to give light, while the other decays to produce an entity of the short-lived type which then decays and gives light. (The decay of the long-lived type is understood to require a pair of excited molecules to interact, but for simplicity this pair will be considered as one ‘entity’.) PSD is possible because gamma and neutron interactions produce the two types in different proportions. If an interaction in a scintillator instantaneously produces A short-lived and B long-lived entities at time t ¼ 0, then the light
t o0
where t 1 is the time constant for the short-lived type and t 2 that for the long-lived type. The first term in this expression represents the decay of the initial population of the short-lived type, while the second comes from convoluting an exponential representing the decay of the long-lived type with another representing the decay of the new short-lived entities so produced. (The equations describing this process are very similar to the well-known equations describing two-stage radioactive decay.) It is convenient to re-write the t Z 0 expression in terms of total light N ¼ A þ B and the long-lived fraction f ¼ B=ðA þ BÞ 1 t 1 t LðtÞ ¼ ð1r ÞN exp þ rN exp t1 t1 t2 t2 where r ¼ ðt 2 f Þ=ðt 2 t 1 Þ For reasonable values of the parameters, the above function rises vertically at t ¼ 0, which is not realistic for an actual pulse shape as measured by an oscilloscope or digitiser. To produce a realistic shape, a signal transmission function must be convoluted with LðtÞ to represent the processes that distort the signal as it passes from the scintillator to the digitiser. For example, random variations in the transit time of electrons in the photomultiplier would introduce a random delay between the emission of light from a decay in the scintillator and the arrival of the corresponding signal contribution at the measuring device. A Gaussian transmission function would be a reasonable choice to represent such a process. For most purposes only the variation in the delay needs to be determined, and its average value can be regarded as arbitrary. Convoluting a Gaussian distribution with an exponential one produces a function known as an exponentially-modified Gaussian or ExGaussian [8–10]. Functions of this type arise, for example, in the field of physiology, where they can be used to represent reaction times. The ExGaussian function cðxÞ resulting from the convolution of the exponentially decaying function f ðxjx0 Þ ¼ x10 ex=x0
xZ0
¼0
xo0
(where x0 is the decay constant) with the Gaussian Þ2 1 r x r 1 g ðxjμ; sÞ ¼ sp1ffiffiffiffi exp ðxμ 2s2 2π (where μ is the mean and s the standard deviation) can be written as ! 1 s2 ðxμÞ ðxμÞ s cðxx0 ; μ; sÞ ¼ exp Φ 2 x0 x0 s x0 2x0 in which the vertical line is used to separate the function argument from the parameters, and ΦðvÞ is the cumulative area under a Gaussian distribution of zero mean and unit standard deviation, i.e. 1 ΦðvÞ ¼ pffiffiffiffiffiffi 2π
Z
2 u du exp 2 1 v
It is useful that the ExGaussian is expressible in terms of standard mathematical functions commonly provided by computational software.
N.P. Hawkes, G.C. Taylor / Nuclear Instruments and Methods in Physics Research A 729 (2013) 522–526
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The cumulative area under an ExGaussian can be evaluated by integration by parts, and is given by ! Z x s2 ðxμÞ cðujx0 ; μ; sÞdu ¼ exp C ðxjx0 ; μ; sÞ ¼ x0 2x20 1 ðxμÞ s xμ þΦ Φ s x0 s involving only the same standard functions as before. In the present context, this expression is useful for evaluating the integral under part of a pulse shape, e.g. the value of the long or short integral in a long gate/short gate PSD system. The final expression for the observed pulse shape L0 ðtÞ is therefore L0 ðtÞ ¼ ð1rÞNcðtjt 1 ; μ; sÞ þ rNcðtjt 2 ; μ; sÞ
1 r t r1
with the integral under the pulse shape given by substituting C for c. For notational convenience, the function has been left as positive-valued, even though voltage signals from photomultipliers are commonly negative. Pulse shape functions based on exponentials have been used previously by, for example, Marrone et al. [11] and Aspinall et al. [12], but these authors did not relate their function parameters explicitly to the decay of excited entities in the scintillator. In addition, they represented signal transmission effects using an exponential convolution rather than a Gaussian one, which does not produce a good match to the rising edge of the measured pulse, the model function being too steep. (The true form of the signal transmission function may be neither Gaussian nor exponential, but for the present work the use of a function more complicated than Gaussian was considered to introduce too many adjustable parameters.)
5. Fitting to the measured pulse shapes The pulse shape expression L0 ðtÞ was fitted to each of the shapes in Fig. 3 separately, the six parameters t 1 ; t 2 ; μ; s; N and f all being allowed to vary. The mean transmission time μ was included here, even though it is arbitrary, because its value is affected by the convention used for fixing the t ¼ 0 position on the time axis. The fitting was carried out by routine E04GZF of the NAG Fortran library [13], which minimises the sum of squared residuals resulting from a user-defined model. With this routine, the derivatives of the model function with respect to each of its parameters must be supplied, and these were calculated analytically. The same initial parameter values were used each time. Possibly because of the non-statistical amplitude fluctuations in the measured shapes (noted earlier), it was found difficult to obtain fits that were satisfactory in both the peak and the tail at the same time, even with a fitting routine that uses the function derivatives. A smoothing process appeared to be called for. This was achieved by summing the measured sample values together in groups of 11, and fitting these sums instead of individual samples. (Five samples, all from before the onset of the pulse, were discarded in order to produce exactly 45 groups.) This group size was chosen, somewhat arbitrarily, as achieving the desired effect without losing sensitivity to the peak of the pulse. With this process in place, the fitting routine E04GZF returned in each case with no reports of problems (status variable equal to 0). The fits are shown in Fig. 4 (with the original, ungrouped, measured shapes). In each case, the function is seen to reproduce the measured shape well, although the 10 zoom does show that the fit tends to undershoot the measurement after about t ¼ 120 to 140 ns. The parameter values determined by the fits are shown in Table 1. For the two gamma shapes, the parameter values are all
Fig. 4. The pulse shape function L0 ðtÞ fitted to the three average shapes of Fig. 3. (a) Neutrons from 241Am/Be, (b) Gammas from 241Am/Be, (c) Gammas from 22Na. As before, the shapes are also plotted at X10 zoom in order to show the details of the rising edge and the tail region.
very similar, reflecting the close similarity in shape already noted. For the neutron shape, the short time constant is very similar to that for the gammas, but both the long time constant and the long-lived fraction f show an increase over the corresponding gamma values. If for the long-lived state the entities in question are pairs of molecules, the fraction becomes 2f =ð1 þ f Þ in terms of individual molecules, and this value is also given in Table 1.
6. Conclusions The theoretical shape function used in this work is seen to be capable of producing good fits to scintillator pulse shapes, including the leading edge. As this function and its integral are relatively
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N.P. Hawkes, G.C. Taylor / Nuclear Instruments and Methods in Physics Research A 729 (2013) 522–526
Table 1 Parameter values determined by fitting the pulse shape function to the three measured average shapes. The spread given in the last column is the standard deviation of the relevant values (with ðn1Þ divisor) divided by the mean. Parameter description
Symbol
Initial guess
Fitted values 241
Short time constant (ns) Long time constant (ns) Mean transmission time (ns) St. dev. of transmission time (ns) Normalisation Fraction excited into long-lived state Fraction in terms of individual molecules a
t1 t2 μ s N f 2f 1þf
5.5 67.0 6.2 1.6 40.0 0.200
Am/Be neutrons
4.737 47.278 6.374 1.708 39.730 0.255 0.407
241
Am/Be gammas
4.527 32.078 6.486 1.773 39.350 0.188 0.317
Mean
Spread (%)
4.57 37.28 6.41 1.74 39.47 0.19a 0.32a
3.3 23.2 1.0 1.9 0.6 1.6a 1.4a
22
Na gammas
4.450 32.487 6.384 1.728 39.339 0.193 0.323
The average and spread figures for f and its derived value refer to the gamma data only.
straightforward to evaluate, it may have wider applications in pulse shape studies. If the conventional 2-lifetime description of pulse shape formation applies, one would expect the two gamma shapes to have the same values of the short and long excitation time constants t 1 and t 2 , and also of the fraction f of entities excited into the long-lived state. The fitted values of these parameters bear this out. Further, one would expect the neutron shape to show the same time constants and differ only in an increased value for the fraction f . The fitted value of f for the neutron shape is indeed larger than those for the gamma shapes, but the fitting process has additionally produced a larger value of the long time constant t 2 . Moreover it is seen in Fig. 4 that the fitted curve struggles to match the measurement at long times. These features could be due simply to variability in the fitting process. However, the formulation of the Zaitseva et al. scintillator comprises multiple chemical components [3], and it is possible that a third time constant (which will not necessarily be the longest one) needs to be introduced into the pulse shape formula to describe the transfer of energy between components. In so far as the 2-lifetime description does apply, and assuming that the shape function adequately includes the effects of signal transmission, one can assign values of approximately 4.6 ns and 37 ns to the short and long time constants for the scintillator used, and values of 0.26 and 0.19 to the long-lived fraction f for neutrons and gammas respectively (0.41 and 0.32 in terms of individual molecules). The parameter s, corresponding to the standard deviation of the transmission delay, is found to be approximately 1.7 ns, which is small compared with the total duration of the pulse but significant in terms of the pulse rise time. It is presumably determined by a combination of factors such as the scintillator size, the consistency of electron transit times in the photomultiplier, and the nature of the connection between the photomultiplier and the digitiser. It is possible that the fitted excitation lifetimes include a residual contribution from any such signal transmission effects not completely accounted for by the Gaussian convolution, an effect that could usefully be studied by making measurements with larger scintillators, different photomultipliers, etc.
The effect of the relatively low (8-bit) resolution of the digitiser used in this work is hard to quantify. Digitisation errors could conceivably result in either an under- or over-estimation of the pulse tail, and random noise might complicate the issue further. Additional measurements should be carried out when a greater amplitude resolution becomes available.
Acknowledgements The authors are grateful to Natalia Zaitseva and her co-workers for providing the scintillator and to David Thomas for his helpful comments on the manuscript. The financial support of the National Measurement Office (an Executive Agency of the UK government's Department for Business, Innovation and Skills) is acknowledged with gratitude. References [1] F.D. Brooks, Nuclear Instruments and Methods 4 (1959) 151. [2] J.M. Adams, G. White, Nuclear Instruments and Methods 156 (1978) 459. [3] N. Zaitseva, B.L. Rupert, I. Pawełczak, A. Glenn, H.P. Martinez, L. Carman, M. Faust, N. Cherepy, S. Payne, Nuclear Instruments and Methods in Physics Research A 668 (2012) 88. [4] High Technology Sources Ltd., 〈http://www.hightechsource.co.uk〉. [5] J.B. Birks, The Theory and Practice of Scintillation Counting, Pergamon Press, London, 1964. [6] F.D. Brooks, Nuclear Instruments and Methods 162 (1979) 477. [7] N. Zaitseva, A. Glenn, L. Carman, R. Hatarik, S. Hamel, M. Faust, B. Schabes, N. Cherepy, S. Payne, IEEE Transactions on Nuclear Science NS-58 (6) (2011) 3411. [8] M.R.W. Dawson, Behavior Research Methods, Instruments and Computers 20 (1) (1988) 54. [9] T. Van Zandt, Psychonomic Bulletin and Review 7 (3) (2000) 424. [10] J.T. Townsend, C. Honey, Journal of Mathematical Psychology 51 (4) (2007) 242. [11] S. Marrone, D. Cano-Ott, N. Colonna, C. Domingo, F. Gramegna, E.M. Gonzales, F. Gunsing, M. Heil, F. Käppeler, P.F. Mastinu, P.M. Milazzo, T. Papaevangelou, P. Pavlopoulos, R. Plag, R. Reifarth, G. Tagliente, J.L. Tain, K. Wisshak, Nuclear Instruments and Methods in Physics Research A 490 (2002) 299. [12] M.D. Aspinall, B. D’Mellow, R.O. Mackin, M.J. Joyce, Z. Jarrah, A.J. Peyton, Nuclear Instruments and Methods in Physics Research A 578 (2007) 261. [13] Numerical Algorithms Group, 〈http://www.nag.co.uk/〉.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
Analysis of the pulse shape mechanism in a plastic scintillator with efficient neutron/gamma pulse shape discrimination N.P. Hawkes n, G.C. Taylor National Physical Laboratory, Hampton Road, Teddington TW11 0LW, UK
art ic l e i nf o
a b s t r a c t
Article history: Received 7 February 2013 Received in revised form 19 July 2013 Accepted 23 July 2013 Available online 1 August 2013
A sample of the new plastic scintillator recently formulated by Zaitseva et al., and shown by them to have efficient pulse shape discrimination properties, was exposed to pure gamma and mixed neutron/gamma radiation from different sources, and the pulse shapes recorded by a digitising oscilloscope. Separate average neutron and gamma pulse shapes were derived, using pulse shape discrimination where necessary. A theoretical pulse shape formula, based on the conventional two-lifetime description of pulse shape formation in organic scintillators, was then fitted to these measured shapes to obtain numerical values for the lifetimes and proportions of the scintillator excitations. It is found that, although the conventional model explains much of the observed pattern of values, there are hints of behaviour that is not consistent with its assumptions. Crown Copyright & 2013 Published by Elsevier B.V. All rights reserved.
Keywords: Neutron detection Plastic scintillator Pulse shape Pulse shape discrimination Scintillator excitations
1. Introduction It has been known for a long time that certain organic scintillators produce a slightly different pulse shape in response to neutron interactions than they do in response to gamma rays, allowing the two to be distinguished [1]. One well-used pulse shape discrimination (PSD) technique is to integrate the pulse over two different intervals and compare the two integrals, the ‘long gate/short gate’ method [2]. Until recently, detailed studies of the shape of the very fast pulses from such scintillators were difficult to carry out, but with the advent of fast digital samplers it has become possible to record large numbers of pulses in nanosecond detail. The aim of the present work was to measure pulse shapes at this level of detail from a PSD-capable organic scintillator, and analyse them in terms of the excitation mechanisms that are understood to occur in such scintillators. Additional motivation for such studies was provided recently by Zaitseva et al. [3] of the Lawrence Livermore National Laboratory (LLNL), USA. This group successfully demonstrated efficient PSD in a plastic scintillator. Up to then, PSD had only been practical in liquids, with attendant problems of leakage, thermal expansion, and in many cases flammability. This development could considerably simplify the construction and use of PSD-capable counters. The Zaitseva group kindly provided a sample of an early formulation of the new scintillator to the National Physical Laboratory, UK,
n
Corresponding author. Tel.: +44 20 8943 7064. E-mail address: [email protected] (N.P. Hawkes).
where pulse shape measurements were carried out as part of an ongoing programme of research into novel detection methods for neutrons. The scope of the present work does not include a measurement of the quality of discrimination achievable with this scintillator, beyond a demonstration that it was effective for this study. 2. Experimental method The uncoated scintillator sample, identified by LLNL as number 885, is close to being cylindrical in shape (the circular faces being slightly dished) and measures 25 mm ∅ 10 mm. It was coupled with a generous application of optical grease directly to the end window of an ET Enterprises 9214KB linear focused photomultiplier, and held in place by lightweight packing material. The photomultiplier is 51 mm in diameter (48 mm nominal active diameter) and has 12 dynodes. It was fitted with a plug-on voltage divider type VD20E1-Neg, negative high voltage being preferred so that the anode would be near ground potential with no isolating capacitor needed for the signal connection. The high voltage was 1250 V. The anode of the photomultiplier was connected to the pulse digitiser by approximately 40 m of high bandwidth cable (Huber +Suhner SX 07262 BD). The digitiser, a Tektronix TDS5052 digital oscilloscope, has 8 bits of voltage resolution, and for the tests reported here it was set to 200 mV/div, 20 ns/div, 2.5 GS/s (400 ps/ sample), and 500 samples per trace. The trigger position was set so that the trace covered 20 ns to 180 ns. Traces were transferred over the General Purpose Interface Bus (GPIB) interface, under the
0168-9002/$ - see front matter Crown Copyright & 2013 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nima.2013.07.071
N.P. Hawkes, G.C. Taylor / Nuclear Instruments and Methods in Physics Research A 729 (2013) 522–526
control of a LabVIEW program, to a PC where they were written to a text file for off-line analysis. Measurements were carried out using a 22Na gamma source (producing gamma rays at 1.275 and 0.511 MeV) and an 241Am/Be neutron source (producing neutrons with a broad energy spectrum extending above 10 MeV, together with copious gamma rays). The 22 Na gamma source consists of a 1 mm diameter ion exchange bead at the centre of a solid plastic disc 3 mm thick and 25 mm in diameter [4], and had an activity of approximately 43 kBq at the time of the measurement. The neutron source has a nominal alpha activity of 1 Ci (37 GBq), and emits neutrons at a rate of approximately 2.4 106 s 1 into 4π. The active material is sealed in a cylindrical stainless steel capsule of the type designated X3 and measuring 22.4 mm in diameter by 31 mm in height. A lead cap approximately 2 mm thick was placed over the neutron source in order to reduce the low-energy gamma flux, which is particularly strong at 60 keV. For the measurements, the 22Na source was suspended in a low-mass enclosure at about 12.5 cm from the scintillator, while the neutron source was placed at approximately 90 cm. Measurement runs were restricted to 4000 traces at a time, in order to keep the text files to a manageable size, but two files were obtained for each measurement condition to give 8000 traces each, prior to rejection of clipped pulses as described in the next section.
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Fig. 1. Discrimination plot for the LLNL 885 scintillator. Black dots, 241Am/Be source; green crosses, 22Na source. There is marked PSD in the 241Am/Be data (even for unoptimised timings), and the 22Na data confirm which is the gamma branch. The solid red lines show the PSD criteria applied to the 241Am/Be data, events to the left of the vertical line being discarded. The dashed lines show the amplitude limits applied when deriving the average shape. Only those pulses between the applicable lines (black dashes, 241Am/Be; green dashes, 22Na) were used in the averaging process.
3. Derivation of average pulse shape Once the digitiser is set up, its input voltage range is fixed, and any input pulse that exceeds the maximum is clipped at that level. In order to exclude any such clipped pulses from the analysis, a trace was rejected if any of its samples reached the maximum sample value in the file. Analysis was carried out using Excel spreadsheets and VBA macros. The PSD necessary to separate neutrons from gammas in the 241Am/Be measurement was based on the long gate/short gate technique, the long integral (actually just the sum of sample values) covering 0–180 ns, i.e. essentially the whole pulse, and the short integral 50–180 ns (the tail). The t ¼ 0 reference point for these timings was set for each trace separately to be 6 ns before the time point when the leading edge of the pulse reached 50% of its final amplitude. No prolonged effort was made to optimise these timing parameters, but as shown in Fig. 1 the separation of the events into neutron and gamma branches was sufficiently clear for further adjustment to be unnecessary. The result of applying the same analysis to the 22Na data is also shown in the figure, and confirms which branch corresponds to gammas. It is understood that the right-hand limits (i.e. the edges at large values of long integral) of both of the 241Am/Be branches are produced by the rejection of clipped pulses, and not by any feature in the source spectrum. Furthermore the difference in the Long Integral position of these boundaries is understood to be due to the difference in pulse shape, the gamma pulse being more peaked and therefore reaching the voltage limit sooner as the total area is increased. The spectra from the 241Am/Be source lack sharp features, and do not provide an energy calibration. The gamma rays from 22Na, however, produce Compton edges at 341 and 1062 keV. These are clearly visible when the gamma data are binned into a “pulse height” (actually Long Integral) spectrum (Fig. 2). There is no significant zero offset in the integrals, as any small offset in an individual pulse was determined from the first 25 samples and subtracted off, so this allows a long integral value of approximately 7.29 in the gamma branch to be associated with an electron energy of 341 keV and 25.9 with an electron energy of 1062 keV. This is consistent with the conventional assumption that electron light
Fig. 2. Pulse height spectrum for gamma rays from 22Na, obtained by binning the 22 Na long integral values from Fig. 1. The Compton edges at electron energies of 341 and 1062 keV are clearly visible.
output is proportional to the electron energy minus an offset, the offset here being approximately 59 keV. Also shown in Fig. 1 are the PSD criteria used to separate the neutron and gamma events in the 241Am/Be data. To reduce the risk of identifying events wrongly, those to the left of the vertical red line were discarded. The 22Na data were assumed to relate exclusively to gammas and were not subjected to any PSD process. Three average pulse shapes were derived, for 241Am/Be neutrons, 214Am/Be gammas, and 22Na gammas. In each case the average was built up one trace at a time by first normalising the trace to a standard area, and then adding its contribution in at the desired sequence of sample times, using linear interpolation where necessary to derive a sample value between actual samples. The time reference for each trace was the same as used for the PSD analysis, i.e. based on the 50% point on the leading edge. Finally the average pulse shapes were normalised to a standard area of 40 (in units of (amplitude units) (nanoseconds)). The validity of fitting a theoretical function to an average shape depends firstly on the acquisition process being free of significant distortion, and then on the pulse shapes remaining effectively constant with the energy deposited, at least over a limited energy range. In the present work, evidence that these conditions are met is provided by the Compton spectrum of Fig. 2 (where the edge positions are consistent with reasonable expectations of the electron
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from the scintillator at subsequent times is proportional to B LðtÞ ¼ tA1 exp tt1 þ t 2 t t Z0 exp tt2 exp tt1 1 ¼0
Fig. 3. Average measured pulse shapes for neutrons and gammas. Each shape is plotted twice, once showing the entire trace and again at a magnification factor of 10 (see right-hand scale) so as to show the pulse tail in detail.
light output) and the discrimination plot of Fig. 1 (where the neutron and gamma branches show near linearity). The 8-bit amplitude resolution of the digitiser used in this experiment is ample for displaying traces on the screen, but not ideal when pulses have a low-amplitude region of interest (here the short integral) but must not be allowed to saturate at the peak. This problem was mitigated by including in the averages only those pulses with an areaZ 45% that of the largest non-clipped pulse in the measurement in question. In addition, an upper area limit was also applied (95% for 241Am/Be and 75% for 22Na), in case the shape of the largest pulses was in some way unusual. These criteria are shown as dotted vertical lines in Fig. 1, and are more stringent than the PSD limits, i.e. not all discriminated events were in fact used. After all selection criteria were applied, 689 traces contributed to the average pulse shape for 241Am/Be neutrons, 819 to that for 241 Am/Be gammas, and 823 to that for 22Na gammas. The three shapes are shown in Fig. 3. As one would expect, the two gamma shapes are very similar to each other, despite originating from markedly different sources, and the neutron shape differs noticeably from both (especially in the tail). Each of the pulse shapes in Fig. 3 shows amplitude fluctuations that the averaging process has not removed, for example the dip at approximately 88 ns. These are explicable in terms of nonstatistical processes, such as reflections due to the detailed configuration of the dynode chain and of the cable and its connectors. They may be responsible, at least in part, for the difficulties described below that were experienced in the fitting process.
4. A mathematical model of pulse shape To analyse the measured pulse shapes, a theoretical model was required, based on the actual processes believed to occur in the scintillator. Fitting this model to the measured shapes might then provide some quantitative insight into those processes. The response of a PSD-capable scintillator to a gamma ray or neutron has been described [5–7] in terms of the production of two types of excited entity, one significantly shorter-lived than the other. The short-lived type decays exponentially to give light, while the other decays to produce an entity of the short-lived type which then decays and gives light. (The decay of the long-lived type is understood to require a pair of excited molecules to interact, but for simplicity this pair will be considered as one ‘entity’.) PSD is possible because gamma and neutron interactions produce the two types in different proportions. If an interaction in a scintillator instantaneously produces A short-lived and B long-lived entities at time t ¼ 0, then the light
t o0
where t 1 is the time constant for the short-lived type and t 2 that for the long-lived type. The first term in this expression represents the decay of the initial population of the short-lived type, while the second comes from convoluting an exponential representing the decay of the long-lived type with another representing the decay of the new short-lived entities so produced. (The equations describing this process are very similar to the well-known equations describing two-stage radioactive decay.) It is convenient to re-write the t Z 0 expression in terms of total light N ¼ A þ B and the long-lived fraction f ¼ B=ðA þ BÞ 1 t 1 t LðtÞ ¼ ð1r ÞN exp þ rN exp t1 t1 t2 t2 where r ¼ ðt 2 f Þ=ðt 2 t 1 Þ For reasonable values of the parameters, the above function rises vertically at t ¼ 0, which is not realistic for an actual pulse shape as measured by an oscilloscope or digitiser. To produce a realistic shape, a signal transmission function must be convoluted with LðtÞ to represent the processes that distort the signal as it passes from the scintillator to the digitiser. For example, random variations in the transit time of electrons in the photomultiplier would introduce a random delay between the emission of light from a decay in the scintillator and the arrival of the corresponding signal contribution at the measuring device. A Gaussian transmission function would be a reasonable choice to represent such a process. For most purposes only the variation in the delay needs to be determined, and its average value can be regarded as arbitrary. Convoluting a Gaussian distribution with an exponential one produces a function known as an exponentially-modified Gaussian or ExGaussian [8–10]. Functions of this type arise, for example, in the field of physiology, where they can be used to represent reaction times. The ExGaussian function cðxÞ resulting from the convolution of the exponentially decaying function f ðxjx0 Þ ¼ x10 ex=x0
xZ0
¼0
xo0
(where x0 is the decay constant) with the Gaussian Þ2 1 r x r 1 g ðxjμ; sÞ ¼ sp1ffiffiffiffi exp ðxμ 2s2 2π (where μ is the mean and s the standard deviation) can be written as ! 1 s2 ðxμÞ ðxμÞ s cðxx0 ; μ; sÞ ¼ exp Φ 2 x0 x0 s x0 2x0 in which the vertical line is used to separate the function argument from the parameters, and ΦðvÞ is the cumulative area under a Gaussian distribution of zero mean and unit standard deviation, i.e. 1 ΦðvÞ ¼ pffiffiffiffiffiffi 2π
Z
2 u du exp 2 1 v
It is useful that the ExGaussian is expressible in terms of standard mathematical functions commonly provided by computational software.
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The cumulative area under an ExGaussian can be evaluated by integration by parts, and is given by ! Z x s2 ðxμÞ cðujx0 ; μ; sÞdu ¼ exp C ðxjx0 ; μ; sÞ ¼ x0 2x20 1 ðxμÞ s xμ þΦ Φ s x0 s involving only the same standard functions as before. In the present context, this expression is useful for evaluating the integral under part of a pulse shape, e.g. the value of the long or short integral in a long gate/short gate PSD system. The final expression for the observed pulse shape L0 ðtÞ is therefore L0 ðtÞ ¼ ð1rÞNcðtjt 1 ; μ; sÞ þ rNcðtjt 2 ; μ; sÞ
1 r t r1
with the integral under the pulse shape given by substituting C for c. For notational convenience, the function has been left as positive-valued, even though voltage signals from photomultipliers are commonly negative. Pulse shape functions based on exponentials have been used previously by, for example, Marrone et al. [11] and Aspinall et al. [12], but these authors did not relate their function parameters explicitly to the decay of excited entities in the scintillator. In addition, they represented signal transmission effects using an exponential convolution rather than a Gaussian one, which does not produce a good match to the rising edge of the measured pulse, the model function being too steep. (The true form of the signal transmission function may be neither Gaussian nor exponential, but for the present work the use of a function more complicated than Gaussian was considered to introduce too many adjustable parameters.)
5. Fitting to the measured pulse shapes The pulse shape expression L0 ðtÞ was fitted to each of the shapes in Fig. 3 separately, the six parameters t 1 ; t 2 ; μ; s; N and f all being allowed to vary. The mean transmission time μ was included here, even though it is arbitrary, because its value is affected by the convention used for fixing the t ¼ 0 position on the time axis. The fitting was carried out by routine E04GZF of the NAG Fortran library [13], which minimises the sum of squared residuals resulting from a user-defined model. With this routine, the derivatives of the model function with respect to each of its parameters must be supplied, and these were calculated analytically. The same initial parameter values were used each time. Possibly because of the non-statistical amplitude fluctuations in the measured shapes (noted earlier), it was found difficult to obtain fits that were satisfactory in both the peak and the tail at the same time, even with a fitting routine that uses the function derivatives. A smoothing process appeared to be called for. This was achieved by summing the measured sample values together in groups of 11, and fitting these sums instead of individual samples. (Five samples, all from before the onset of the pulse, were discarded in order to produce exactly 45 groups.) This group size was chosen, somewhat arbitrarily, as achieving the desired effect without losing sensitivity to the peak of the pulse. With this process in place, the fitting routine E04GZF returned in each case with no reports of problems (status variable equal to 0). The fits are shown in Fig. 4 (with the original, ungrouped, measured shapes). In each case, the function is seen to reproduce the measured shape well, although the 10 zoom does show that the fit tends to undershoot the measurement after about t ¼ 120 to 140 ns. The parameter values determined by the fits are shown in Table 1. For the two gamma shapes, the parameter values are all
Fig. 4. The pulse shape function L0 ðtÞ fitted to the three average shapes of Fig. 3. (a) Neutrons from 241Am/Be, (b) Gammas from 241Am/Be, (c) Gammas from 22Na. As before, the shapes are also plotted at X10 zoom in order to show the details of the rising edge and the tail region.
very similar, reflecting the close similarity in shape already noted. For the neutron shape, the short time constant is very similar to that for the gammas, but both the long time constant and the long-lived fraction f show an increase over the corresponding gamma values. If for the long-lived state the entities in question are pairs of molecules, the fraction becomes 2f =ð1 þ f Þ in terms of individual molecules, and this value is also given in Table 1.
6. Conclusions The theoretical shape function used in this work is seen to be capable of producing good fits to scintillator pulse shapes, including the leading edge. As this function and its integral are relatively
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Table 1 Parameter values determined by fitting the pulse shape function to the three measured average shapes. The spread given in the last column is the standard deviation of the relevant values (with ðn1Þ divisor) divided by the mean. Parameter description
Symbol
Initial guess
Fitted values 241
Short time constant (ns) Long time constant (ns) Mean transmission time (ns) St. dev. of transmission time (ns) Normalisation Fraction excited into long-lived state Fraction in terms of individual molecules a
t1 t2 μ s N f 2f 1þf
5.5 67.0 6.2 1.6 40.0 0.200
Am/Be neutrons
4.737 47.278 6.374 1.708 39.730 0.255 0.407
241
Am/Be gammas
4.527 32.078 6.486 1.773 39.350 0.188 0.317
Mean
Spread (%)
4.57 37.28 6.41 1.74 39.47 0.19a 0.32a
3.3 23.2 1.0 1.9 0.6 1.6a 1.4a
22
Na gammas
4.450 32.487 6.384 1.728 39.339 0.193 0.323
The average and spread figures for f and its derived value refer to the gamma data only.
straightforward to evaluate, it may have wider applications in pulse shape studies. If the conventional 2-lifetime description of pulse shape formation applies, one would expect the two gamma shapes to have the same values of the short and long excitation time constants t 1 and t 2 , and also of the fraction f of entities excited into the long-lived state. The fitted values of these parameters bear this out. Further, one would expect the neutron shape to show the same time constants and differ only in an increased value for the fraction f . The fitted value of f for the neutron shape is indeed larger than those for the gamma shapes, but the fitting process has additionally produced a larger value of the long time constant t 2 . Moreover it is seen in Fig. 4 that the fitted curve struggles to match the measurement at long times. These features could be due simply to variability in the fitting process. However, the formulation of the Zaitseva et al. scintillator comprises multiple chemical components [3], and it is possible that a third time constant (which will not necessarily be the longest one) needs to be introduced into the pulse shape formula to describe the transfer of energy between components. In so far as the 2-lifetime description does apply, and assuming that the shape function adequately includes the effects of signal transmission, one can assign values of approximately 4.6 ns and 37 ns to the short and long time constants for the scintillator used, and values of 0.26 and 0.19 to the long-lived fraction f for neutrons and gammas respectively (0.41 and 0.32 in terms of individual molecules). The parameter s, corresponding to the standard deviation of the transmission delay, is found to be approximately 1.7 ns, which is small compared with the total duration of the pulse but significant in terms of the pulse rise time. It is presumably determined by a combination of factors such as the scintillator size, the consistency of electron transit times in the photomultiplier, and the nature of the connection between the photomultiplier and the digitiser. It is possible that the fitted excitation lifetimes include a residual contribution from any such signal transmission effects not completely accounted for by the Gaussian convolution, an effect that could usefully be studied by making measurements with larger scintillators, different photomultipliers, etc.
The effect of the relatively low (8-bit) resolution of the digitiser used in this work is hard to quantify. Digitisation errors could conceivably result in either an under- or over-estimation of the pulse tail, and random noise might complicate the issue further. Additional measurements should be carried out when a greater amplitude resolution becomes available.
Acknowledgements The authors are grateful to Natalia Zaitseva and her co-workers for providing the scintillator and to David Thomas for his helpful comments on the manuscript. The financial support of the National Measurement Office (an Executive Agency of the UK government's Department for Business, Innovation and Skills) is acknowledged with gratitude. References [1] F.D. Brooks, Nuclear Instruments and Methods 4 (1959) 151. [2] J.M. Adams, G. White, Nuclear Instruments and Methods 156 (1978) 459. [3] N. Zaitseva, B.L. Rupert, I. Pawełczak, A. Glenn, H.P. Martinez, L. Carman, M. Faust, N. Cherepy, S. Payne, Nuclear Instruments and Methods in Physics Research A 668 (2012) 88. [4] High Technology Sources Ltd., 〈http://www.hightechsource.co.uk〉. [5] J.B. Birks, The Theory and Practice of Scintillation Counting, Pergamon Press, London, 1964. [6] F.D. Brooks, Nuclear Instruments and Methods 162 (1979) 477. [7] N. Zaitseva, A. Glenn, L. Carman, R. Hatarik, S. Hamel, M. Faust, B. Schabes, N. Cherepy, S. Payne, IEEE Transactions on Nuclear Science NS-58 (6) (2011) 3411. [8] M.R.W. Dawson, Behavior Research Methods, Instruments and Computers 20 (1) (1988) 54. [9] T. Van Zandt, Psychonomic Bulletin and Review 7 (3) (2000) 424. [10] J.T. Townsend, C. Honey, Journal of Mathematical Psychology 51 (4) (2007) 242. [11] S. Marrone, D. Cano-Ott, N. Colonna, C. Domingo, F. Gramegna, E.M. Gonzales, F. Gunsing, M. Heil, F. Käppeler, P.F. Mastinu, P.M. Milazzo, T. Papaevangelou, P. Pavlopoulos, R. Plag, R. Reifarth, G. Tagliente, J.L. Tain, K. Wisshak, Nuclear Instruments and Methods in Physics Research A 490 (2002) 299. [12] M.D. Aspinall, B. D’Mellow, R.O. Mackin, M.J. Joyce, Z. Jarrah, A.J. Peyton, Nuclear Instruments and Methods in Physics Research A 578 (2007) 261. [13] Numerical Algorithms Group, 〈http://www.nag.co.uk/〉.