Impact of the Detected Scintillation Light Intensity on Neutron-Gamma Discrimination

This article reports the method and the results of a study on the impact of the detected light intensity on gamma-neutron discrimination. In particular, the minimum number of photons required to achieve a statistically significant separation was measured and shown to be stable against a variation of the photon detection efficiency (PDE) of the system under study. The method, developed using an EJ-276 scintillator bar coupled to a silicon photomultiplier (SiPM), is of general interest. For this specific system, the minimum statistic was measured to be 317 ± 16 photons, corresponding to different values of the deposited energy, as the PDE was changed.


Impact of the Detected Scintillation Light Intensity on Neutron-Gamma Discrimination
Massimo Caccia , Marco Galoppo, Luca Malinverno, Pietro Monti-Guarnieri , and Romualdo Santoro Abstract-This article reports the method and the results of a study on the impact of the detected light intensity on gammaneutron discrimination. In particular, the minimum number of photons required to achieve a statistically significant separation was measured and shown to be stable against a variation of the photon detection efficiency (PDE) of the system under study. The method, developed using an EJ-276 scintillator bar coupled to a silicon photomultiplier (SiPM), is of general interest. For this specific system, the minimum statistic was measured to be 317 ± 16 photons, corresponding to different values of the deposited energy, as the PDE was changed.

I. INTRODUCTION
S ILICON photomultipliers (SiPMs hereafter) are compact solid-state light detectors with single photon sensitivity, photon counting capability, low bias voltage, and low power consumption. In the last decade, SiPMs have been used in a variety of fields, such as particle and nuclear physics, medical imaging, and homeland security [1], [2], [3]. It has been shown that SiPMs, coupled to specifically engineered scintillators with sensitivity to both fast and slow neutrons, represent a viable solution for the discrimination of light pulses originated by gamma rays against neutrons [4]. The enabling feature of this class of scintillators is the different light emission time in response to interactions of neutrons or gamma rays. Hence, a pulse shape analysis is usually implemented by defining a pulse shape discrimination (PSD) observable [5], [6], [7], [8], [9], [10], [11]. For every detection system used for particle identification there exists a critical condition for which the signal produced by the impinging radiation does not convey enough information to achieve particle discrimination. This effect usually manifests itself through the existence of a system-specific energy deposit threshold below which the identification capability is lost. In the case of a scintillator coupled to a light sensor, the energy deposit and thus the information carried by the signal is directly related to the intensity of the scintillation light. The idea behind this study is to investigate the correlation between the minimum amount of information required for particle discrimination and the photon statistics.
The results of the investigation reported here stems from a system based on a plastic scintillator (EJ-276, by Eljen Technologies) coupled to a SiPM, where the response and sensitivity were changed by varying the photon detection efficiency (PDE) of the SiPM, acting on the biasing voltage. The outcome of this study is the definition of a procedure having a general applicability that not only sheds light on the correlation between the photon statistics and the information conveyed by the signal but also yields the minimum photon statistics required for neutron-gamma discrimination.

II. MATERIALS AND METHODS
The analysis is based on a 6 mm × 6 mm area SiPM produced by HAMAMATSU Photonics (model S13360-6050PE), with the main features reported in Table I, as of the vendor's specifications [12].
The sensor was coupled through optical grease to a 5 cm × 1 cm × 1 cm EJ-276 scintillator bar produced by Eljen Technologies, where pulse shape neutron-gamma discrimination is made possible by the differences in the scintillating time decay constants, as reported in Table II [13]. The bar was wrapped with Teflon tape diffuser to maximize light collection and the assembly was operated in a light-tight box to prevent contamination from ambient light.
The energy calibration was performed exploiting the Compton spectrum shoulder for a series of gamma emitting isotopes   133 Ba, and 137 Cs). Neutron-gamma discrimination was instead investigated using a 252 Cf source.
The system response in terms of detected photons per pulse was measured after a calibration performed by illuminating the sensor with an ultrafast blue LED emitting at 420 nm, pulsed by a PicoQuant PDL-800B unit.
For γ and neutron detection, the signal produced by the SiPM was directly digitized with a CAEN DT5720 Desktop Digitizer (sampling frequency 250 mega-samples/s, 12-bit resolution, 2-V input range). For the calibration in photoelectrons, the signals were amplified using the CAEN SP5600 unit, featuring a variable gain in the 0-50-dB range.

A. Energy Calibration
Due to the low Z and density of the plastic scintillator, the gamma rays rarely interact through photoelectric effect. Hence, calibrations relied on the Compton spectrum shoulders. The energy associated with the edge of a shoulder, E edge , can be derived from the theory of the Compton scattering [14] and is given by where m e c 2 is the energy of the electron at rest and E γ is the γ ray energy or the weighted mean of multiple lines not resolved in the experimental spectrum (with the weights being the emission branching ratios). The edge shoulders used in the calibration are reported in Table III. For these measurements, the DT5720 unit was self-triggered and signals exceeding a fixed threshold were sampled and digitized over a 8 μs long window, with the signal peak located 2 μs after the digitization gate opening. For every run at different conditions, about 250 000 pulses were recorded. For the duration of all experiments and the measurements of the main sensor figures, the SiPM was maintained at constant temperature of 18.0 • C ± 0.1 • C. The calibration was repeated for every SiPM biasing voltage used to evaluate the impact of a PDE variation, namely from 3 to 6.5 V above the breakdown voltage, at 0.5 V steps.
During data processing, the signal baseline was calculated for every waveform over 400 ns (100 points) before the trigger and then subtracted. The occasional occurrence of a spurious pulse dark count during the baseline calculation was identified by an anomalous standard deviation of the data points; moreover, piled-up events in the digitization window following the trigger were spotted by identifying a second signal peak. Whenever a waveform featured one of these anomalies, it was flagged and removed from the dataset.
The Compton edges were modeled as step functions, appearing in the spectra as complementary error functions due to their convolution with the response function of the detector which is assumed to be Gaussian. An exemplary spectrum of the 22 Na source, obtained by biasing the sensor at 55.5 V (which corresponds to 4 V above the breakdown voltage), is reported in Fig. 1. A typical calibration line at a fixed bias is shown in Fig. 2.

B. Photoelectron Calibration
The charge corresponding to the avalanche generated in the silicon matrix by a single initial photoelectron depends on the gain of the SiPM, which is linked to the excess voltage, and the external amplification stage. It was measured by analyzing for each specific setting the multiphoton spectrum, namely the histogram characterizing the sensor response to a low plurality of photons emitted by the ultrafast blue LED pulsed by the PicoQuant unit. An exemplary spectrum is shown in Fig. 3, where peaks correspond to the number of fired cells for every pulse, determined by the detected photons and the prompt optical crosstalk, while the significant background between the peaks is connected to delayed optical crosstalk, after pulsing and occasional spurious pulses (dark counts) occurring within the integration window. The shape of the histogram results from the convolution of the Poissonian distribution of emitted  Table III. photons and the probability distributions of crosstalk and after pulsing. Since the main goal of the procedure is determining the calibration of the sensor response in photoelectrons (number of fired cells), the quantity of interest here is the peak-to-peak distance ( pp ), providing the single pulse charge in ADC channel at the specified voltage and amplification gain. The single photon signal at gain G = 1 ( 1 pp ) and at fixed bias V, namely the condition in use for gamma and neutron detection, was measured by extrapolating the values of pp at different amplification settings, as shown for instance in Fig. 4, again for the reference bias of 55.5 V (4 V above the breakdown voltage). A residual difference between digitization and integration of the direct output of the SiPM, dc coupled to the input of the digitizer, and the gain 1 setting of the ac coupled amplifier in the SP5600 unit was measured comparing the most probable value of the response of the system in the two configurations to a high light intensity pulsed illumination. This procedure lead to a final scaling factor Fig. 4.
Variation of the delta peak-to-peak pp as a function of the amplification gain G, for fixed biasing voltage 55.5 V. Linear extrapolation in the form pp = m · G + q, with m = 7.67 ± 0.03, and q = 1.96 ± 1.49. k ac/dc = 0.8830 ± 0.0001, taken into account when calibrating the energy response in photoelectrons.
Moreover, the multiphoton spectrum offers the possibility to measure the following.
• The optical crosstalk, fitting the spectrum with the convolution of the Poisson probability describing photon emission by a pulsed light source and the geometrical distribution for the crosstalk [15]. This figure is required to extract the statistics of primary photoelectrons in pulses originated by gamma and neutrons. • The relative PDE by a variation of the mean number of detected photons in a pulse at constant illumination for different SiPM biasing voltages [16]. As by-product of this analysis, the breakdown voltage of the sensor was also calculated as the value of V where pp is null.
For these measurements, the data acquisition was synchronous to the PicoQuant pulsing, and signals were digitized over a 4 μs long window, with the peak of the signal located 2 μs after its opening. For every run at different conditions, about 150 000 pulses were digitized, recorded, integrated, and histogrammed. A multi-Gaussian function was fit over every spectrum, in order to calculate pp , defined as the mean distance between adjacent peaks. This procedure was repeated for amplification gains ranging from 24 to 38 dB with step 2 dB and biasing voltages ranging from 54.5 V (3 V above the breakdown voltage) to 58 V (6.5 V above the breakdown voltage). By the end of this analysis, an extrapolation of pp values obtained at different voltages and gain 32 dB returned a breakdown voltage V bd = 51.42 ± 0.04 V.
The optical crosstalk and the variation of the PDE with the biasing voltage were extracted by the same dataset. However, it was instrumental to process the data to produce multiphoton spectra based on the use of the peak value of every waveform rather than the integral, since detector-related spurious effects, notably after pulses, delayed crosstalk and dark counts are expected not to come into play. This is evident in the Once pp is known, the average value of the amplitude distribution can be converted into number of fired cells (μ exp ). This value accounts for the number of detected photons μ 0 and the effective optical crosstalk X, with a dependence that can be modeled as [17] Under the assumption of a Poissonian distribution of emitted photons, the value of μ 0 can be obtained as where P 0 , the probability of having 0 fired cells, can be simply calculated as the fraction of the events with a pulse height ≤ 0.5 × pp . Experimentally, crosstalk probabilities ranging from 13% to 25% were measured, corresponding to biasing voltages ranging from 3 to 6.5 V above the breakdown voltage.
Since μ 0 is proportional to the PDE of the sensor, its trend against biasing voltage variations actually maps changes in the PDE. Results are shown in Fig. 6, normalized according to the producer's specifications, namely PDE = 40% at V ov = 3 V.

C. Neutron-Gamma Discrimination
As of the characterization reported in [3] and the comparative analysis performed in [18], neutron-gamma discrimination was based on a PSD variable corresponding to the energy deposited in the tail of the signal, normalized to the pulse height where S(t) is the digitized signal, t s marks the beginning of the tail, and t w its length. The optimal limits for the tail   7. Variation of the FOM, as a function of the PSD parameters t s ("distance from the peak") and t w ("tail window"), as used in (4). The FOM was calculated, for every set of parameters, by means of (5).
integration were identified by scanning the parameter space and identifying the region with the highest discrimination power, quantified by a figure of merit (FOM) defined as [14] FOM = PSD n − PSD γ FWHM n + FWHMγ (5) where PSD n and PSD γ correspond to the mean values of the PSD distributions for gamma rays and neutrons, respectively, while FWHM n and FWHM γ are their full-width at half-maximum. Discrimination is assumed to be statistically relevant when FOM > 1.27, corresponding to a 3σ separation between the distributions of the PSD variables for neutrons and gammas, presumed to be Gaussians. For each biasing voltage, on average, 500 000 events were recorded, digitized, and analyzed. Fig. 7 shows an exemplary outcome of the optimization procedure of the algorithm, showing the variation of the FOM against the PSDs parameters  t s , t w (data recorded at the reference bias of 55.5 V). Fig. 8 shows an exemplary 2-D histogram of the PSD values against the deposited energy in response to 252 Cf: here gammas and neutrons form two clearly separated regions, for energies above 1 MeV. An exemplary distribution of the PSD values in the [1, 1.5] MeV range of deposited energy is shown in Fig. 9.

III. EXPERIMENTAL RESULTS
For every excess voltage, namely for every PDE, the value of the deposited energy required to achieve FOM = 1.27 was estimated by analyzing the PSD variable distribution in different deposited energy bins, initially 100 keV wide for edges ranging from 150 keV to 1 MeV. Subsequently, the width was doubled at every bin, in order to compensate for the smaller  size of the sample as the energy increased. The minimum energy necessary to reach FOM = 1.27 (E 1.27 ) was calculated by fitting the variation of the FOM with respect to the energy by means of an exponential function An exemplary trend of the FOM variation at the 55.5 V reference voltage is shown in Fig. 10. The minimum number of photoelectrons corresponding to an energy deposit of E 1.27 , namely N 1.27 , can be derived through the calibration of the deposited energy in photoelectrons taking into account the effective crosstalk and k ac/dc , namely whereas 1 pp is the pp extrapolated at linear gain G = 1 and m, q are the energy calibration coefficients.  shown as a function of the number of photoelectrons extracted per keV of energy deposit. The label "2021 data" refers to the first dataset analyzed in the article, i.e., the one with an EJ-276 bar without aging effects. The label "2019 data" refers to the higher light yield dataset. The line is simply meant to guide the eye.
The variation of E 1.27 as a function of the over-voltage of the sensor (V ov ) is shown in Fig. 11, with a statistically significant decreasing trend as expected by the PDE variation. However, when E 1.27 values are turned into photoelectrons, experimental data correspond to the results shown in Fig. 12, where the hypothesis of a constant "minimum amount of information," corresponding to 316 ± 19 photoelectrons is statistically acceptable.
In order to verify this conclusion, data presented so far were complemented by a different set, coupling a bar of the same EJ-276 scintillator with a higher light yield to a SiPM from the same family. Difference in the light yield was possibly due to aging in the scintillation properties, with the two bars tested right after the delivery by the producer and after three years on the shelf. Since the two detectors were tested at different over-voltages and featured differences in the PDE, data were displayed against number of photoelectrons per keV of deposited energy. Data on the trend of E 1.27 are shown in Fig. 13, where the dependence on the system sensitivity is made stronger, while the corresponding number N 1.27 of photoelectrons is shown in Fig. 14. The weighted mean number of photoelectrons required to reach FOM = 1.27 was found to be, in the two datasets N a 1.27 = 316 ± 19 N b 1.27 = 314 ± 35. The statistical compatibility of the results confirms the hypothesis of linking the minimum value of deposited energy for discriminating gamma from neutrons to the photoelectron statistics, with a combined value for the specific system under study of N 1.27 = 316 ± 17.

IV. CONCLUSION
A neutron-sensitive plastic scintillator bar (EJ-276 by Eljen Technologies) coupled to an SiPM has been used to investigate the impact of the detected light intensity on neutron-gamma discrimination based on pulse shape analysis. The single photon sensitivity of SiPM has been exploited to go from a qualification based on a macroscopic observable, the minimum deposited energy for a statistically relevant discrimination, to the corresponding microscopic quantity, namely the number of detected scintillation photons. For the system under study and the implemented algorithm, based on the ratio between the signal peak value and the integral in the tail of the pulse over an optimal window, 316 ± 17 photoelectrons are required to discriminate pulses originated from gamma rays and neutrons. The value was shown to correspond to different deposited energy values as the PDE was changed in a controlled way for the sake of the investigation.
Apart from quantifying the rather obvious need for a high light yield material and optimal coupling to a highly sensitive photon detector, the method sheds light on the possibility to compare different gamma-neutron discrimination algorithms and procedures, qualified according to the efficiency in extracting information from the available statistics of photons and robustness against statistical fluctuations.