Experiment setup

The neutron emission rate of the ²⁵²Cf source was greater than 10⁵ n/s in the entire experiment period. The Silicon Carbide (SiC) detector for measuring fission fragments to obtain source neutron information and the take-off signal detector were positioned close to the source. The layout of the experimental platform is illustrated in Fig. 2. The experiments were performed using a spherical sample with the source located at the center of the sphere. This placement method is closer to practical application conditions, and it ensures that the nuclear reaction is carried out evenly in all directions and reduces the influence of the boundary effect. Thus, relevant information regarding the interaction between the neutrons emitted by the source at an angle of $4\pi$ and the sample can be effectively obtained. The EJ309 detector with a diameter and thickness of 2 in was purchased from SCIONIX Holland BV, and the energy resolution at Eγ = 662, keV was <7% FWHM. The CLYC detector (⁶Li to > 95%) with a diameter and thickness of 2 in was manufactured by Radiation Monitoring Devices, Inc. (RMD). It is characterized by a high density and good energy resolution (<5% at Eγ = 662, keV)[30]. This detector is suitable for thermal neutron and low-energy neutron detection via the ⁶Li(n, t) αreaction [31]. The EJ309 detector was positioned 200 cm away from the center of the ²⁵²Cf fission source, and the CLYC detector was located 100 cm away. Both the ²⁵²Cf source and the detector were placed 130 cm above the ground to reduce the impact of neutron scattering from the surrounding walls and ground.

Fig. 2Full-screen View

(Color online) Experimental arrangement for measuring the neutron leakage time-of-flight (TOF) spectrum

All wave signals were acquired using a CAEN DT5730SB digitizer (14-bit, 500MS/s, 5.12MS/ch) because of its faster signal processing capability and the provided digital pulse processing-pulse shape discrimination (DPP-PSD) software for online pulse shape discrimination (PSD) analysis. When the online analysis is insufficient, the digitized signals can be stored for offline processing [33].

Take-off signal tagging

The measurement principle of the TOF method is expressed in Eq. (1). $t=\frac{72.306L}{\sqrt{E}}$ (1) where t is the time of flight (ns), E is the neutron energy (MeV), and L is the flight-path distance (m). In the case of a fixed distance between the fission source and detector, the only variable is the time from the fission event to the neutron recorded by the neutron detector. Hence, determining the take-off signal is crucial. For this measurement, the accompanying γ-rays emitted by fission were used to determine the timing of the fission events. Because the take-off signal detector was close to the neutron source in the experiment, the flight time of the γ-ray to this detector was practically negligible compared to that of the neutron to the second detector. The feasibility of this approach was demonstrated by Blain et al. who reproduced the prompt fission neutron spectrum (PFNS) using the γ tagging method [33]. Owing to the advantages of a fast response time, high detection efficiency for γ-rays, and low detection sensitivity for neutrons, the BaF₂ detector with a diameter and thickness of 1 in was used to identify the take-off time in this measurement.

Coincidence model

The coincidence mode allows for the setting of a variable length time window. When a pulse is detected in one channel, the window is initiated; if a pulse is detected in the other channel during this period, a coincidence event is logged. The possible types of coincidences that may have occurred during the experimental process are listed in Table 1. Detector 1 was used to measure the take-off signal, whereas detector 2 measured the flight termination signal.

In addition to the γ-n events, the γ-γ coincidence and accidental coincident events still existed in this measurement. Because γ-rays travel at the speed of light, the flight time difference between two coincident γ-rays can reach 6 ns. Regardless of the detector at which they arrive, γ-rays arrive first, following the corresponding fission event. As shown in Fig. 3, all γ–γ coincidence events still fall within the gamma peak region. This initial peak in the TOF spectrum represents double γ-ray events: either a single photon scattered between the detectors or two correlated prompt photons. Therefore, the neutron peak is not affected by the γ–γ coincidence events. Accidentally coincident events can be corrected by taking the average count of the bins that represent the arriving coincidences.

Fig. 3Full-screen View

The TOF spectrum was measured from a ²⁵²Cf fission source using EJ309. The Gamma peak seen on the left contains coincident gamma detections. Events involving neutrons form a “hump” produced by the range of arrival times for neutrons of different energies. The initial flight time needs to be redetermined based on γ peak information

Neutron detection Efficiency determination

The neutron detector efficiency is a vital parameter that directly affects the accuracy of the simulated TOF spectra. Therefore, for the EJ309 neutron detector, the neutron detection efficiency was accurately obtained using the Monte Carlo code NEFF under different detection thresholds [34]. The reliability of the calculated efficiency curves was experimentally calibrated. The absolute efficiencies of the EJ309 detector were determined by the D-D and D-T neutron generators in CIAE using the TOF method, and the relative detection efficiencies were measured by the ²⁵²Cf source. The experimental detection efficiencies are in good agreement with the calculated results of the NEFF code in the range of uncertainty, as shown in Fig. 4.

Fig. 4Full-screen View

(Color online) Detection efficiency of EJ309 calculated by the NEFF code compared with experimental values in different thresholds

The detection efficiency curve of the CLYC detector was simulated using the MCNP-4C code. This method has been previously confirmed as feasible, for example, in [35]. The relative detection efficiencies were measured by the ²⁵²Cf source using the TOF method. As shown in Fig. 5, the calculated results are consistent with the experimental results within the uncertainty range.

Fig. 5Full-screen View

The detection efficiency curve of the CLYC detector simulated by MCNP-4C compared with experimental values

Pulse shape discrimination

To distinguish between the neutrons and γ-ray pulses, a pulse shape discrimination (PSD) technique was performed using the charge integration method [37, 38]. In this experiment, when the TOF spectrum based on ²⁵²Cf was measured, the PSD information was obtained by analyzing the data through the waveform acquisition method. The neutron TOF spectra were derived by selecting neutron events, as shown in Fig. 7.

Fig. 7Full-screen View

(Color online) 2D plots of pulse shape discrimination (PSD) versus QDC for the (a) EJ309 and (b)CLYC detectors of the neutron signals from a ²⁵²Cf source. The graph shows the ability of detectors to distinguish these two types of radiation. The areas framed by red lines are neutron events

Background correction

Background correction is crucial for processing the data of the TOF spectrum. This study had three background components: time-independent background, time-dependent neutron background, and time-dependent γ background. The easiest determination was that of the time-independent background, which arose from random events that did not correlate with the fission process occurring in the measurement window. This is shown in Fig. 3, where the count rate flattens at a long TOF spectrum. This background component was eliminated by subtracting the count rate from each channel in the average 210–300 ns region.

The second background component, the time-dependent γ background, originated primarily from the γ decay of fission fragments [38]. This background is not present in the EJ309 and CLYC detectors because PSD can remove the background from γ-rays.

The third background component is the time-dependent neutron background. This affected both the EJ309 and CLYC detectors and primarily originated from prompt fission neutrons scattering off the surrounding structures and scattering back to the neutron detectors. To determine the impact of neutron scattering, the background TOF spectrum was experimentally measured using shadow cones, as shown in Fig. 8. The effect/background ratio measured by the EJ309 detector was greater than 7, and the CLYC detector demonstrated a ratio exceeding 4. Once all these background components were corrected from the experimental signal, a pure TOF spectrum was obtained.

Fig. 8Full-screen View

Background spectra measured by the (a) EJ309 detector and (b) CLYC detector

Uncertainties analysis

The uncertainties of the present experiment mainly come from the statistical and systematic uncertainty, as presented in Table 2. Statistical uncertainty includes the uncertainties of neutron counting and ²⁵²Cf source neutron counting (used for data normalization). The systematic uncertainty is caused by angle ambiguity and relative error of the detector efficiency.

It can be observed that the neutron counting uncertainty is the most significant contributor to the overall uncertainty. For more than 80% of the data points, the statistical uncertainties in the neutron counts measured by the EJ309 detector in the range of 0.8–8.0 MeV were below 3%. Meanwhile, the uncertainties in neutron counts measured by the CLYC detector in the range of 0.15–0.8 MeV were approximately 8%. During the experiment, source neutron counts were obtained by monitoring the information of the fission fragment ²⁵²Cf. Therefore, the uncertainty of the ²⁵²Cf source neutron counting arose from fission fragment counting, which was 1.31% and 1.22%, respectively, in the two experiments. The angular uncertainty induced by deviations in the positioning of the samples and detectors was relatively small at approximately 0.1%. The uncertainty in the detection efficiency stemmed from discrepancies between the experimental and simulated results.

Capability of the neutron spectrum measurement system

To verify the capability of the constructed TOF spectrum measurement system, measurements were first performed without samples.

4.1.1

Time-of-flight spectrum of the EJ309 detector without sample

After the data were processed as shown in Fig. 6, the final TOF spectrum was obtained, as shown in Fig. 9. The TOF spectrum simulated by MCNP-4C was compared with the experimental spectrum. The TOF spectrum simulated showed good agreement with the measured spectrum in the 50–162 ns (0.8–8 MeV) range.

Fig. 9Full-screen View

TOF spectrum measured by the EJ309 detector without sample compared with the simulated spectrum

To assess the measurement accuracy of the TOF spectrum platform, the data were converted from the time domain to the energy domain using Eq. (1) and compared with the ²⁵²Cf standard spectrum from ISO:8529-1. Owing to the deviation between the Maxwellian standard spectrum at a nuclear temperature of 1.42 MeV and the ²⁵²Cf experimental spectrum, the standard spectrum was folded using the detection efficiency curve[39]. Figure 10 shows the effect of detector efficiency on the ²⁵²Cf standard spectrum. Then, the experimental spectrum was compared with the folded standard spectrum, as shown in Fig. 11. The experimental spectra were consistent with the standard spectrum in the uncertainty range. Although good consistency was observed across most of the measured data, the high-energy bins of the spectrum were somewhat higher than expected, and the peak value moved towards the high-energy region. This conclusion is similar to that of Becchetti, Blainand, and Alexander [20, 40, 41]. Two reasons may explain this. First, this could be a systematic error stemming from the assumption that prompt neutrons and γ-rays are simultaneously produced at the same moment in the measurement system. Typically, prompt fission γ-rays are emitted within a nanosecond after the fission event. However, some fission fragments exist in metastable states that decay over longer periods [42]. For short flight times, even minor delays in the gamma emission times would lead to an overestimation of the neutron energy, resulting in an overpopulation of the high-energy bins [41]. Second, the ²⁵⁰Cf in the Cf source also has a certain probability of spontaneous fission, as presented in Table 3. When the ²⁵²Cf source was produced, the atomic number ratio of ²⁵²Cf to ²⁵⁰Cf was approximately 5:1, the decay constant ratio was approximately 5:1, and the spontaneous fission branching ratio was approximately 40:1. Therefore, at the initial stage, the contribution of ²⁵⁰Cf to the neutron emissivity was approximately 0.1%, which had a small effect on the energy spectrum of ²⁵²Cf. However, the contribution to the neutron emissivity of ²⁵⁰Cf gradually increased with time. This also affected the energy spectrum of ²⁵²Cf.

Fig. 10Full-screen View

Effect of the detector efficiency on the ²⁵²Cf standard spectrum. Both curves have been normalized to a value of 1 at 2 MeV

Fig. 11Full-screen View

²⁵²Cf experimental energy spectrum measured by the EJ309 detector compared with the standard ²⁵²Cf energy spectrum from ISO:8529-1 folded with detection efficiency

Table 3Full-screen View

Decay data of Cf isotopes in the Cf source and daughter nuclides

Isotope	Half life (a)	Decay constant (s-1)	Spontaneous fission probability (%)	Average neutron number of each fission
252Cf	2.645	8.304×10-9	3.092	3.767
251Cf	898	2.445×10-11	0	–
250Cf	13.08	1.679×10-9	0.077	3.52
248Cm	3.48×105	6.311×10-14	8.39	3.16

Show more

4.1.2

Time-of-flight spectrum of CLYC detector without sample

After the data was processed as shown in Fig. 6, the final TOF spectrum was obtained, as shown in Fig. 12. The TOF spectrum simulated by MCNP-4C showed the same trend as the measured spectrum in the 80–187 ns (0.15–0.8 MeV) range.

Fig. 12Full-screen View

TOF spectrum measured by the CLYC detector without sample compared with the simulated spectrum

Similarly, the TOF spectrum was converted from the time domain to the energy domain to yield the final PFNS. In Fig. 13, the ²⁵²Cf standard spectrum from ISO:8529-1 is folded with the efficiency curve of the CLYC detector. The final comparison results showed that the shape of the experimental spectrum matched the peak of the ISO:8529-1 spectrum in the low-energy regions. However, the TOF spectrum in the 1.2–5 MeV range appeared slightly lower than expected. In contrast, those in the range over 5.0 MeV were higher than the standard spectrum, with the peak value moving towards the high-energy region. This is related to the CLYC detector that detects neutrons using nuclear reactions. The neutron recorded by the CLYC detector is mainly caused by the following reactions [37]: (1) ⁶Li(n, t)α (Q-value = 4.783 MeV) thermal neutron reaction;(2) ⁶Li(n, t)α fast neutron reaction; (3) ³⁵Cl(n, p)³⁵S (Q = 0.615 MeV) fast neutron reaction and (4) ³⁵Cl(n, α)³²P (Q = 0.937 MeV)fast neutron reaction. The reaction cross-sections are shown in Fig 14. It can be seen that the ⁶Li(n, t)α reaction is mainly effective when measuring neutrons in the 0.1–1 MeV range, whereas ³⁵Cl(n, p)³⁵S and ³⁵Cl(n, α)³⁵P are significant for neutron energies higher than 1.2 MeV. Moreover, a quenching factor exists in the ³⁵Cl fast neutron reactions [37]. For example, 2.5 MeV neutrons are detected by the ³⁵Cl(n, p)³⁵S reaction (2.5 MeV neutrons have a cross section of 0.19 b), as a single energy peak at 2.5 MeV and the Q-value of the reaction, multiplied by a proton quenching factor equal to 0.9, is 2.8 MeV. As a result, the shift in the peak position at energies greater than 1.4 MeV leads to poor agreement between the experimental and standard spectra in the high-energy region. However, this also proves that CLYC (95%⁶Li) is more suitable for measuring TOF spectra in the low-energy region.

Fig. 13Full-screen View

²⁵²Cf experimental energy spectrum obtained by the CLYC detector compared with the standard ²⁵²Cf energy spectrum from ISO:8529-1 folded with detection efficiency

Fig. 14Full-screen View

Cross sections of the different reactions considered. It is to be noted that the cross section value for this neutron absorption reaction at E_n~0.025eV is approximately 940 b (not shown in the figure) [43]

Verification of the benchmark experiment reliability with the standard sample

The elastic scattering of neutrons and hydrogen (n–p scattering) was considered as the standard cross section. Therefore, a benchmark experiment using polyethylene ($\text{Φ}=12\text{cm}$) was conducted to ensure the reliability of the system.

The measured spectra were compared with the spectra simulated using the MCNP-4C code with ENDF/B-VIII.0, CENDL-3.2, JEFF-3.3, and JENDL-5 libraries, as shown in Figs. 15 and 16. The ratios of the calculation to experiment (C/E) obtained by integrating the neutron peaks are listed in Table 4. The measured neutron leakage spectra were consistent with the simulated results obtained using MCNP-4C. In the 0.8–8 MeV (t = 50–162 ns) range, the calculated results were underestimated by approximately 5%, and the uncertainty was less than 3.94%. In the 0.15–0.8 MeV range (t = 80–187 ns), the calculated results were underestimated by approximately 13%, and the uncertainty was less than 8.46%. Therefore, the experimental results agree well with the simulated results in the range of 0.15–8.0 MeV. This indicates that the experimental system and data processing method used in this study are reliable, which ensures the reliability of conducting other sample data measurements.

Fig. 15Full-screen View

Comparison of the measured and simulated neutron leakage TOF spectra with a polyethylene standard sample in the 0.8–8.0 MeV range. (a)The neutron leakage spectrum simulated by MCNP-4C was compared with those measured with EJ309. (b) C/E variation between the simulated spectra and measured spectrum

Fig. 16Full-screen View

Comparison of the measured and calculated neutron leakage TOF spectra with a polyethylene standard sample in the 0.15–0.8 MeV range. (a) The neutron leakage spectrum simulated by MCNP-4C was compared with those measured with CLYC. (b) C/E variation between the simulated spectra and measured spectrum