Preamble

The measurement of the energy correlations between two Cf prompt fission neutrons Hang Li, Hong-Jun Zhang Huai-Yong Bai

INTRODUCTION

Neutron coincidence and multiplication measurement tech- niques have been developed as nondestructive assay methods for special nuclear materials and nuclear fuels over the past few decades [ ]. The related physical foundation is that more than one prompt fission neutron may be emitted from a spontaneous or induced fission event, resulting in the de- tection of time-correlated neutron events. In addition to the time correlation, the neutron energies emitted in one fission event are interdependent. On the one hand, the neutron en- ergy distributions depend on the actual number of emitted neutrons [ ]. However, the energies of the neutrons are af- fected by the direction and velocity of the corresponding fis- sion fragments, as most of the prompt fission neutrons are emitted from the fast moving fission fragments. Therefore, the energies of the neutrons emitted from the same fission fragment or different fission fragments moving in opposite directions are connected [ However, owing to the lack of available energy correlation data, the energy correlations of prompt fission neutrons have not been considered in neu- tron coincidence and multiplication measurement techniques, despite their wide application and use in some measurement fields as standard methods [ ]. This may lead to some mea- surement deviations, as the detection efficiency is affected by the neutron energy, particularly for fast neutron coincidence and multiplication measurement techniques.

To date, several codes capable of simulating correlations among emitted neutrons in fission reactions on an event-by- event basis have been developed, such as MCNPX-POLIMI, CGMF, and FREYA [ ]. However, these codes require re- liable experimental data to validate their models [ ]. In 2019, P. F. Schuster et al. measured the prompt fission neu- tron energy correlation of Cf for the first and only time.

In the experiment, the Chi-Nu detector array, consisting of 54 EJ309 liquid scintillation detectors with a diameter of 17.78 This work was financially supported by the National Natural Science Foundation of China (No. 12105257) and the Research and Development Fund (No. JMJJ202401).

Cheng-Guo Pang Xiao-Dong Wang, and Li-Sheng Yang cm and thickness of 5.08 cm, was used to detect the prompt fission neutrons, and a fission chamber with a Cf source, whose fission rate was , was used to measure the moment when the fission event occurred [ ]. Accord- ing to their measurements, the correlations between the aver- age energies of the paired neutrons with emission angles of were negative and positive, respectively. How- ever, as they claimed in their paper, the result was inconclu- sive because the experimental uncertainties were noticeable, resulting in the calculated slopes being within 2 of zero [ To obtain more detailed data on the energy correlations of Cf prompt fission neutrons, we conducted an experimen- tal study. Before the measurement, a Monte Carlo simula- tion was developed to predict the energy correlation and in- struct the measurement, in which the neutron energies were obtained using the measured time-of-flight. In most exist- ing measurements, the fission moment, that is, the start mo- ment of the neutron flight, was tagged by detecting the fis- sion fragment with a fission chamber [ ]. However, this tagging technique may not be suitable for measuring neutron energy correlations. In the fission chamber, the Cf source is typically embedded on a metal foil or plate substrate. Most fission fragments would lose part of their energy before en- tering the sensitive region of the chamber, especially those fragments with large emission angles with respect to the nor- mal metal foil or plate substrate. Therefore, the difference in the detection efficiencies of the fission fragments with differ- ent emission angles was noticeable. This may result in some measurement deviations because the prompt fission neutron energy correlations are associated with the corresponding fis- sion fragment moving direction, as introduced above. For Cf, approximately 11.6 -rays are emitted per spontaneous fission [ ]. Because the time interval between the emission moments of almost all fission -rays with energies exceed- ing 0.3 MeV and their corresponding fission moment is less than 0.5 ns, and the flight speed of -ray is well known, the fission moment can be precisely determined by the detection moment of the fission -ray if the measurement threshold is set above 0.3 MeV [ ]. This indicates that the fission mo- ment can be accurately tagged the fission -rays. Therefore, in the present experiment, the fission moment was tagged with fission -rays detected by scintillation detectors rather Ming Su, Zhong-Hua Xiong, Ji Wen, Fan Gao, Chen-Guang Li 1 Institute of Materials, China Academy of Engineering Physics, Jiangyou 621907, China The energy correlations of prompt fission neutrons have not yet been considered in the related coincidence and multiplication measurement techniques. To measure and verify the energy correlations, an experiment was performed with a total measurement duration of approximately 1200 h. In the experiment, eight CLYC detectors and sixteen EJ309 liquid scintillation detectors were utilized, and the fission moment was tagged with the measured fission -rays. The relative ratios of the energy spectra of the neutrons correlated with different energy neutrons to the Cf fission neutron energy spectra were obtained. The present results may be helpful for studying fission physics and nuclear technology applications.

Keywords

Energy correlations, Prompt fission neutrons, Energy spectrum, Fission -rays

than fission fragments detected by a fission chamber.

The present manuscript presents the experimental study of the energy correlations between neutrons emitted at 90 to each other. In the measurement, the prompt fission neutrons were measured using 16 small EJ309 liquid scintilla- tion detectors (5.08 cm in diameter and 5.08 cm in thickness) because of their superior PSD performance, and the fission -rays were detected with eight CLYC detectors (2.54 cm in diameter and 2.54 cm in thickness) [ ]. The measured neu- tron energy spectra, correlated with different energy neutrons, were presented ranging from 1 to 5 MeV for the first time and compared with those obtained using the Monte Carlo simula- tion.

MONTE CARLO SIMULATION Because most prompt fission neutrons are evaporated from fully accelerated fission fragments, their energy and direction in the laboratory system are significantly affected by the en- ergy and direction of the associated fission fragments. There- fore, the yields and energies of the fission fragments, as well as the number of neutrons evaporated from specific fission fragments, are required to predict the energy correlation. A flowchart of the developed Monte Carlo simulation is shown in Fig. . The fission events were simulated one by one, and the procedure was generally divided into three stages: first, the generation of the two fission fragments; second, the gen- eration of the prompt fission neutrons; and finally, the statis- tics of the neutrons.

Generation of the two fission fragments The mass of the light fission fragment was randomly sampled with a probability proportional to the yields shown in Fig. ]. The mass of the paired heavy fission fragment is 252 . Then, the total kinetic energy its corresponding uncertainty were determined using the total kinetic energy distribution and the corresponding uncer- tainty distribution as functions of the light fragment mass, as shown in Fig. . The specific total kinetic energy of the sam- ssion fragment speci ,where randomly sampled from the normal dis -tribution with a standard deviation of . The kinetic of the light fission fragment determined as:

= M H E T M L + M H

The kinetic energy of the heavy fission fragment . Finally, the direction of the light fission frag- in the laboratory system was sampled from an isotrop- ic distribution, and the direction of the heavy fission fragme- nt was opposite to that of the light fragment.

Generation of the prompt fission neutrons The evaporation of the neutrons was simulated via a cas- cade process for the light fission fragments, followed by the heavy fission fragments.

The number of neutrons emitted

from fission fragments with different masses and the corre- sponding uncertainties are shown in Fig. ]. Because is known, can be calculated. The number of neutrons evaporated from the sampled light fission fragment ,where was randomly sampled from the normal distrib- ution with a standard deviation of . In almost all cases, was a non-integer. Thus, was decomposed into an int- eger part (the largest integer smaller than ) and a deci- mal part (where ). Then, a random numb- in [0, 1] was sampled and compared with smaller than , the actual number of neutrons emitted from the light fission fragment was ; otherwise qualed According to the standard nuclear evaporation theory, the fission neutron energy spectrum in the center-of-mass sys- tem of the fission fragment can be described as [

Φ( E ) ∝ E λ exp( − E/T eff ) = E λ exp( − 1 . 09 E/T ) (2)

where is the cascade neutron emission coefficient and denotes the temperature of the fission fragment, as shown in ]. According to the energy distribution calculated using Eq. ( ),the energy of a neutron in the center-of-mass system was sampled.

The direction of the neutron was sampled from an isotropic distribution. Thereafter, the en- ergy and direction of the neutron in the laboratory system, together with those of the light fission fragments, were calc- ulated under the constraints of energy and momentum conse- rvation. light ssion fragmente quals , where represents the number of neutrons evaporated from the light fission fragment until this point. Finally, the energy and direction of the neutron were stored in a queue.

Neutrons were evaporated one by one using the same proc- until neutrons have been evaporated from the light fis- fragment. After the generation of neutrons evaporated the light fission fragment, the neutrons evaporated from heavy fission fragment processed similar mann- Statistics of the neutrons After the generation of prompt fission neutrons, they were tracked to obtain their energy correlations.

As shown in , 36 surface detectors (with a radius of 5 cm) were po- sitioned on a circle (with a radius of 60 cm), and a Cf sour- was located at the center of the circle. The angle between adjacent surface detector normals was 10 . The fission vents, stored in the queue with the energy and directional information of the emitted neutrons, were tracked individu- ally. If a neutron reached any of the detectors, it was coun- ted as a single event. As shown in Fig. , the simulated ener- gy spectrum of the single events agrees well with the prompt fission neutron energy spectrum recommended by IAEA with the relative deviation smaller than ter all the neutrons were tracked, if multiple neutrons emitte in the same fission event reach the detectors, each two neutr- were paired as a group. In this process, the neutron reac- hing the detector with a smaller serial number was designat-e as the first one. In the present work, the correlation events to 180 with the interval of 30 (the angle between the two neutron directions) were counted.

Cf prompt fission neutron en- ergy spectrum to that recommended by IAEA [

As presented in Fig. , the distributions of the correlated events at 90 and 180 are noticeably different from each other.

The neutron energies corresponding to the highest counts at 90 and 180 are 2.6 MeV and 3.0 MeV, respec- tively. To present the energy correlation more clearly, the counts at each angle were normalized in two steps, as shown in Fig. . First, the total counts in each column with neutron energies ranging from 1–5 MeV were normalized. Second, the count distributions in each column were normalized to the simulated Cf prompt fission neutron energy spectrum. As shows, the neutron energy correlations vary with angle.

The second neutron energy trends toward lower values for the correlated events at near 90 , whereas it trends toward higher values for the correlated events at near 0 or 180 . These trends increased with the first neutron energy. Because the crosstalk effect in the measurement is non-negligible for the correlated events at angles smaller than 75 ], the energy correlations at 90 and 180 are measured in the present work as representative cases. and 180

In the measurement, a triple coincident measurement is re- quired, resulting in a very low detection efficiency. Accord- ing to the test, the time resolution of the measurement was approximately 1.5 ns. Therefore, the length-of-flight of neu- trons was set to 62.5 cm to balance both neutron detection ef- ficiency and energy resolution measured using the TOF (time- of-flight) technique.

EXPERIMENTS Experimental setup

The experimental setup is illustrated in Fig. source with a fission rate of approximately used for the experiment. The source was sealed in a stainless steel capsule ( 2 mm in diameter and 5 mm in height) and suspended vertically at a height of 1.5 m above the floor using a fine nylon thread to minimize neutron scattering effects on the detection by the EJ309 liquid scintillation detectors. All detectors were mounted on aluminum supports. Every four EJ309 liquid scintillation detectors were combined into an ar- angle between the normals of the adjacent arrays was

(a), 30 (b), 60 (c), 90 (d), 120 (e), 150 (f) and 180 fixed at 90 . The distance from the Cf source to the front face of the eight CLYC detectors was 6 0.1 cm, and that to the front face of the sixteen EJ309 liquid scintillation detec- tors was 60 0.1 cm. Since the thickness of the EJ309 liquid scintillation detector is 5.08 cm, the uncertainty of the neutron flight path length is 2.15 cm calculated as:

σ L =

where is the thickness of the EJ309 liquid scintillation de- tector, and represents the uncertainty in the distance from Cf source to the front faces of the EJ309 liquid scintil- lation detectors.

The detector signals were acquired using two CAEN VX1730B digitizers. Each digitizer has 16 input channels with a sampling frequency of 500 MS/s. One digitizer was connected to the eight CLYC detectors, and the other was connected to the sixteen EJ309 liquid scintillation detectors.

Both digitizers were operated in list mode with the time- stamp ( ), long and short gate integrated charges ( ) of every event being saved for off-line analysis. The pulse height (PH) and pulse shape discrimination (PSD) pa- rameter can be calculated as [

PH = C A Q L (4)

PSD = C P

where are calibration factors. Calibration of the detectors Before the measurement, the 8 CLYC detectors and the 16 EJ309 liquid scintillation detectors were calibrated with Co (1.33 and 1.17 MeV) and Na (1.28 and 0.55 MeV) sources as shown in Fig. . The signal gains were al- most equivalent for the eight CLYC detectors by adjusting their working high voltages. Similar adjustments to the work- ing high voltage were also applied to the sixteen EJ309 liq- uid scintillation detectors.

In the calibration of the eight CLYC detectors, both the photo peaks and Compton edges were used, and in that of the sixteen EJ309 liquid scintilla- tion detectors, only the Compton edges were utilized. The method for determining the Compton edges was described in Ref. [ ]. The corresponding Compton electron energy

E e = 2 E 2 γ m 0 C 2 + 2 E γ (6)

where denotes the -ray energy and represents the electron rest mass energy (0.511 MeV). sources for a CLYC detector (a) and a EJ309 liquid scin- tillation detector (b).

In Fig. (a), the Compton edge corresponding to the Compton electron energy of 1.12 MeV was obscured because it overlapped with the tail of the 1.17 MeV Photo peak. The position of the Compton edge corresponding to the Comp- ton electron energy of 0.38 MeV could not be determined accurately because it was significantly affected by the mea- surement threshold. Consequently, these two Compton edges were not used in the calibration of the eight CLYC detectors.

Measurement

The experiment was conducted for a total measurement du- ration of approximately 1200 h. Because two VX1730B dig- itizers were used to acquire the detector signals in the experi- ment, they must be operated in a time-synchronized mode to obtain the accurate TOF data. To achieve this, the two dig- itizers shared the internal clock of the one connected to the eight CLYC detectors, and the synchronization settings were configured via the data acquisition software COMPASS, as described in the COMPASS User Manual [ 28 ]. According to our synchronization test with a pulse generator DT5810, the synchronization accuracy was better than 0.1 ns. Although this synchronization accuracy contributes to the experimen- tal time resolution, its influence can be ignored because it is much smaller than the experimental time resolution of 1.5 ns.

RESULTS AND DISCUSSIONS Data analysis With the experimental data, the PH-PSD two dimensional spectra of the eight CLYC detectors and the sixteen EJ309 liquid scintillation detectors were obtained, as illustrated in . By applying optimal discrimination thresholds, event types ( -rays or neutrons) can be identified.

In the present measurement, the measurement thresholds of the CLYC detectors were approximately 250 channels (0.3 MeV for -ray), and those of the EJ309 liquid scintillation detectors were approximately 50 channels (0.5 MeV for pro- tons). Although the low measurement threshold for the EJ309 liquid scintillation detector could lead to the misidentifica-

CLYC detector (a) and an EJ309 liquid scintillation detector (b). tion of event types using PSD for low pulse height events, the probability of classifying a -ray event as a neutron event was low because of the significant TOF difference between and neutron events, as shown in Fig. (Color online) The TOF distribution for the “neutron events” decided by PSD.

To suppress the interference of accidental coincidences, triple time correlation coincidence was adopted in the data analysis; that is, a neutron event was required to correlate with at least -rays detected by either the CLYC or EJ309 liquid scin- tillation detectors. The start moment of TOF

T 0 =

where denotes the time-stamp, and the subscript repre- sents the serial number of the corresponding detected -rays.

The coincident time window was 200 to 200 ns. The aver- age count in the time window from 200 to 50 ns was taken as the accidental coincident background. The net single neutron events can be derived by subtracting from the TOF distribution shown in Fig. . Theoretically, proportional to the detection efficiency and neutron flux

S net ,i = ϕ i ε i (8)

where the subscript represents the serial number of the di- vided TOF bin.

The neutron coincident events at 90 and 180 are shown in Fig. . Triple time correlation coincidence was employed in the data analysis, that is, two neutrons and at least one ray were required to define one coincident event. There are five types of interferential events. The first is the -ray event shown in the purple box. These events do not noticeably af- fect the measurement of the neutron event shown in the white box because the TOF difference between -rays and neutrons is significant. The second one, shown in the green box, indi- cates that the first neutron is an accidental coincident neutron.

The related interference can be deducted using the counts of each column in the white box to subtract the average counts of each column in the corresponding region with TOF ranging 150 to 50 ns for the first neutron. The third, shown in the red box, is that the second neutron is an accidental coin- cident neutron, and the related interference can be subtracted using a data analysis approach similar to that for the second.

The fourth one shown in the black frame is that the -ray is an accidental coincident -ray. The corresponding interfer- ence can be deducted using the following two steps. In the first step, the region with TOF ranging from 150 to 50 ns for the first neutron was scanned along the diagonal line us- ing a scanning box identical to the white box shown in Fig.

During the scanning process, the average count of every bin in the scanning box was calculated. In the second step, the cor- responding interference was deducted using the counts in the white box to subtract the average counts of the corresponding bins in the scanning box. The fifth is the events induced by crosstalk, that is, the neutron detected by the second detector is the same one that is scattered and detected by the first de- tector. Although the accurate subtraction of this interference is difficult, it can be significantly mitigated by restricting the TOF to the range of 19–46 ns. This conclusion was drawn based on the Monte Carlo simulation performed by JMCT, as shown in Fig. (a) and After the subtraction of the interference events mentioned above, the net neutron coincident events can be obtained.

To obtain the relative deviation between the neutron energy spectrum of Cf prompt fission neutrons and that of the neu- trons correlated with different energy neutrons, three calcula- tion steps were executed. First, the net neutron coincident events were compared with the net single neutron events

(a) and to obtain the relative ratio

R i,j = D i,j S net ,j

where the subscripts separately denote the TOF bin serials of the first and second detected neutrons, and the subscript also represents the TOF bin serial of the net single events for . It should be mentioned that the influ- ence of the detection efficiencies for different energy neutrons is canceled out in this step. Second, the relative ratios normalized over the TOF region ranging from 19 to 46 ns as follows:

NR N or _ R i,j = i,j �

where is the bin number in the TOF region, ranging from 19 to 46 ns. Third, the neutron TOF was converted into neu- tron energy as shown in Fig. and Tables 1 and 2 using

E n =

where is the neutron flight length, is the speed of light in vacuum, denotes the neutron mass. In the present mea- surement, the influence of relativity can be neglected because the velocity of the detected neutron is much smaller than that of light in vacuum. The calculation of can be simplified

E n = 5228 . 16 L 2

where the units of and TOF are m and ns, respectively.

The measurement uncertainties (1.5 at 90 at 180 ) include those of . The uncertainties of at 90 ; 1.6 ) comprise statistical uncertainties (1.5 at 90 at 180 ) and the uncertainties from the sub- traction of accidental coincidences involving the first neutron at 90 and 180 ), the second neutron ( and 180 ) and the -ray ( at 90 and 180 ). The (a) and 180 (b) to the Cf prompt fission neutron energy spectrum. uncertainties of at 90 ; 0.2 at 180 ) consist of statistical uncertainties (0.2 at 90 ; 0.2 at 180 ) and uncertainties from the subtraction of accidental coincident backgrounds ( at 90 and 180 ). The uncertainty of is contributed by the experimental time resolution of 1.5 ns ) and the uncertainty of the neutron flight path length of 2.15 cm (6.9 Discussions As shown in Figs. and Tables 1 and 2, the re- sults indicate that the influence of a neutron on the energy of the correlated neutron is more pronounced in the high en- ergy region, and the related effect at 180 appears to be more noticeable than that at 90 . In addition to the difference in effect magnitude, the correlated neutron energy shows oppo- site trends between the correlated events at 90 and those at . The energy of the neutron that correlates with a neutron with relatively high energy tends toward a lower value at 90 while it tends toward a higher value at 180 . With the mea- sured relative ratios, the related neutron energy spectra can be derived by multiplying the relative ratios by the Cf prompt fission spectrum recommended by IAEA [ When compared with the measurement results obtained by Schuster et al. [ ] and the simulation results introduced pre- viously, the present results show the same tendency, i.e., the energy correlation between the coincident neutrons at is positive, while the energy correlation between the coin- cident neutrons at is negative. This further enhances the credibility of the measurement results. In addition, the fact that the measurements and simulations show the same energy correlation tendency indicates that the dominant rea- son for this tendency may be the impact of the velocities and directions of fission fragments on the neutron energy. introduced previously, most neutrons are emitted from fast- moving fission fragments, which means that the moving di- rection angle between the high-energy neutron and its cor- responding fission fragment tends to be small, whereas the

to the Cf prompt fission neutron energy spectrum. (MeV) (MeV) to the Cf prompt fission neutron energy spectrum. (MeV) (MeV) moving direction angle between the low-energy neutron and its corresponding fission fragment tends to be large. For the correlated neutrons at 90 , if the energy of the first neutron is relatively high, the energy of the second neutron tends to be low. This is because the relatively high energy of the first neutron indicates a small moving direction angle between this neutron and its corresponding fission fragment with a high probability. Therefore, regardless of whether these two neu- trons are emitted from the same fission fragment or two dif- ferent fragments, considering the opposite directions of the two fission fragments, the moving direction angle between the second neutron and its corresponding fission fragment is

to the Cf prompt fission neutron energy spectrum. (MeV) (MeV) to the Cf prompt fission neutron energy spectrum. (MeV) (MeV) relatively large with a high likelihood. This results in a rel- atively low energy of the second neutron. Similarly, for cor- related neutrons at 180 , a relatively high energy of the first neutron tends to result in low energy of the second neutron if they are emitted from the same fission fragment, but in high energy if they are emitted from different ones. As the proba- bility of detecting neutrons from the same fission fragment is noticeably smaller than that from different fission fragments, the total tendency shows that a high-energy neutron is more likely to be correlated with another high-energy neutron. For example, if each fission fragment emits two neutrons and the detection efficiencies of these neutrons are even, the probabil-

ity of detecting neutrons from the same fission fragment is ap- proximately half that from different fission fragments. Addi- tionally, it should be noted that the energy correlation should also be contributed by some other factors besides the impact of the velocities and directions of fission fragments, such as the energy competition relationship among the neutrons emit- ted from the same fragment, as pointed out in Ref. [

CONCLUSIONS

The relative ratios of the energy spectra of the neutrons correlated with different energy neutrons to the Cf prompt M.C. Miller, R.C. Byrd, N. Ensslin et al., Design of a fast neu- trons coincidence counter. Appl. Radiat. Isot. (10-12), 1549– 1555 (1997).

C. Lee, S. Yoon, S.K. Ahn et al., Fast neutron coincidence counter using scintillators for safeguards verification of the TRU/RE waste. J. Radioanal. Nucl. Chem. (12), 5283-5288 (2023).

M. J. Joyce, K. A. A. Gamage, M. D. Aspinall et al., Real-time, fast neutron coincidence assay of plutonium with a 4-channel multiplexed analyzer and organic scintilla- tors. IEEE Trans. Nucl. Sci. (3), 1340–1348 (2014). 10.1109/TNS.2014.2313574 W.X. Xie, J.S. Li, J.Y. Zhu, Uranium mass and neutron mul- tiplication factor estimates from time-correlation coincidence counts. Nucl. Instrum. Methods Phys. Res. A , 182–187 (2015).

Q.H. Zhang, J.Q. Yang, X.S. Li et al., High order fast neu- tron multiplicity measurement equations based on liquid scin- tillation detector. Appl. Radiat. Isot. , 45–51 (2019).

I. Pazsit, N.G. Sjostrand, V. Fhager et al., On the signifi- cance of the energy correlations of spallation neutrons on the neutron fluctuations in accelerator-driven subcritical systems.

Nucl. Instrum. Methods Phys. Res. A , 256–265 (2000).

Z. Elter and I. Pazsit, Energy correlation of prompt fission neu- trons. EPJ Web Conf. , 05003 (2016). conf/201611105003 W.H. Geist, L.A. Carrillo, L.A. Carrillo et al., Evaluation of a fast neutron coincidence counter for the measurements of ura- nium samples. Nucl. Instrum. Methods Phys. Res. A , 590– 599 (2001).

S.A. Pozzi, S.D. Clarke, W.J. Walsh et al., MCNPX- PoliMi for nuclear nonproliferation applications. Nucl. In- strum. Methods Phys. Res., Sect. A , 119 (2012).

Talou, Kawano Stetcu, Prompt fission neutrons and gamma rays in a Monte Carlo Hauser- Feshbach formalism. Phys. Procedia , 39–46 (2013).

P. Talou, I. Stetcu and T. Kawano, Modeling the emis- sion of prompt fission rays for fundamental physics and applications. Phys. Procedia , 83–88 (2014).

fission spectrum were measured for the first time in the re- gion ranging from 0.96 to 5.7 MeV. The measurement results indicated that the energies of the neutrons emitted from one fission reaction were correlated. The largest deviation be- tween the measured energy spectra of the neutrons correlated with 5.7 MeV neutrons and the fission neutron energy spec- tra is close to 20 % . Furthermore, according to the measured and simulated energy correlation trends, the deviation is ex- pected to be more significant in the higher neutron energy region. This indicates that neutron energy correlations should be considered in the coincidence and multiplication measure- ment techniques to obtain more reliable measurement results, particularly for fast neutron coincidence and multiplication measurement techniques.

J. Randrup and R. Vogt, Calculation of fission observables through event-by-event simulation. Phys. Rev. C (2), 024601 (2009).

R. Vogt and J. Randrup, Event-by-event study of neutron ob- servables in spontaneous and thermal fission. Phys. Rev. C (4), 044621 (2011).

P. F. Schuster, M. J. Marcath, S. Marin et al., High resolution measurement of tagged two-neutron energy and angle corre- lations in Cf(sf). Phys. Rev. C , 014605 (2019). 10.1103/PhysRevC.100.014605 P. Talou, R. Vogt, J. Randrup et al., Correlated Prompt Fission Data in Transport Simulations. Eur. Phys. J. A , 9 (2018).

M. J. Marcath, R. C. Haight, R. Vogt et al., Measured and simu- lated Cf(sf) prompt neutron-photon competition. Phys. Rev. , 044622 (2018).

M.X. Kang, J.Z. Zhang, H.Y. Wu et al., Commissioning of the fast neutron detector array at China Institute of Atomic En- ergy. Nucl. Sci. Tech. , 86 (2025).

T. He, P. Zheng, and J. Xiao, Measurement of the prompt neu- tron spectrum from thermal-neutron-induced fission in U-235 using the recoil proton method. Nucl. Sci. Tech. , 112 (2019).

K. Skarsvag, Time distribution of -rays from spontaneous fission of Cf. Nucl. Phys. A (1), 82-96 (1970). 10.1016/0375-9474(70)90757-8 K. Skarsvag, Time distribution of -rays from spontaneous fis- sion of Cf at short times. Nucl. Phys. A (2), 274-288 (1975).

M. Ellis, C. Tintori, P. Schotanus et al., The effect of detector geometry on EJ-309 pulse shape discrimination performance.

IEEE (2013). C. B. Jorgensen and H. H. Knitter, Simultaneous investigation of fission fragments and neutrons in Cf(sf). Nucl. Phys. A , 307-328 (1988).

IAEA NEUTRON DATA STANDARDS (2017) Y.Q. Zhang, L.Q. Hu, G.Q. Zhong et al., Development of a high-speed digital pulse signal acquisition and processing sys- tem based on MTCA for liquid scintillator neutron detector on EAST. Nucl. Sci. Tech. , 150 (2023).

Y.Y. Liang, Y.D. Liu, P.S. Wang et al., Optical transmittance and pulse shape discrimination of polystyrene/poly(methyl methacrylate)-based plastic scintillators. Nucl. Sci. Tech. 9 (2025).

L. Chang, Y. Liu, L. Du et al., Pulse shape discrimination and energy calibration of EJ301 liquid scintillation detector. Nucl.

Tech. (2), 1-6 (2015). ( in Chinese H.Y. Bai, Z.M. Wang, L.Y. Zhang et al., Calibration of an EJ309 liquid scintillator using an AmBe neutron source. Methods Phys. Res. A , 47-54 (2017).

COMPASS User Manual, CAEN, it/products/compass/ G. Li, B.Y. Zhang, L. Deng et al., Development of Monte Carlo particle transport code JMCT. High Power Laser & Particle Beams (1), 158-162 (2013). (i n Chinese 10.3788/HPLPB20132501.0158 Q. Li, L.J. Wang, J.Y. Tang et al., B-doped MCP de- tector developed for neutron resonance imaging at Back-n white neutron source. Nucl. Sci. Tech. , 142 (2024). 10.1007/s41365-024-01512-3 X.Y. Liu, Y.W. Yang, R. Liu et al., Measurement of the neu- tron total cross section of carbon at the Back-n white neu- tron beam of CSNS. Nucl. Sci. Tech. , 139 (2019). 10.1007/s41365-019-0660-9 Y.T. Wei, C.L. Lan, B. Gao et al., Benchmark experiment sys- tem for Cf spontaneous fission source using tagging. Nucl.

Sci. Tech. , 201 (2025).