Simulation method for measurement of the cross-section of the 14N(n, α)11B reaction using a gridded ionization chamber

Yi-Wei Hu? Hao-Yu Jiang ? Zeng-Qi Cui ? Jie Liu ? Hao-Fan Bai ?Huai-Yong Bai,2 ? Jin-Xiang Chen ? Guo-Hui Zhang

Abstract A simulation method for measurement of the cross-section of the 14N(n, α)11B reaction with gas and solid samples using a gridded ionization chamber (GIC)has been established. Using the simulation, the experimental spectra of both 14N(n,α)11B events and background from other reactions can be predicted,and the experimental scheme can be optimized. According to the simulation results, the optimal experimental parameters,including the pressure of the working gas and the compositions of the working gas and the sample, can be determined. In addition, the simulation results can be used to determine the valid event area and calculate the detection efficiency for valid events. A measurement of the cross-sections of the 14N(n, α)11B reaction at En = 4.25, 4.50, 4.75, 5.00, 5.25,and 5.50 MeV, based on the 4.5-MV Van de Graff accelerator at Peking University (PKU) using a GIC as the detector for the outgoing α particles, has been performed.The good agreement of the spectra from the simulation and experiment demonstrated the universality of this simulation method,which can be used to accurately measure neutroninduced light-charged particle emission reactions.

Keywords Gridded ionization chamber ?Monte Carlo simulation ?Cathode–anode two-dimensional spectrum ?14N(n,α)11B reaction

1 Introduction

Nitrogen, which accounts for 78%of the atmosphere,is the most abundant element in air. Nitrogen is also present in amino acids, proteins, and nucleic acids, which play important roles in the human body. The abundance of14N in natural nitrogen is 99.636% [1]. Nitride fuels, such as uranium plutonium nitride (U–Pu–N) and thorium nitride(Th–N)[2],are among the main fuels of the gas-cooled fast reactor(GFR).Zirconium nitride(Zr–N)is used as an inert matrix in fuel elements [3]. Therefore, research regarding the14N(n, α)11B reaction is important in nuclear engineering applications because neutron-induced He production leads to He accumulation and causes serious radiation damage to the active core. In addition, this study is also important with respect to the detection of charged particles caused by neutrons using a gas detector because of the14N(n, α)11B reaction of nitrogen, which is the main component of the air residue in the working gas and is thus the most important background signal.

Regarding the cross-section of the14N(n, α)11B (Qvalue = - 0.159 MeV) reaction, existing measurement results are abundant. For example, in the 3–14 MeV neutron energy region, five measurements [4–8], including those of14N(n, α0)11B and14N(n, α1)11B, can be found in the EXFOR library [9]. However, the existing results have large uncertainties and significant discrepancies. For example, the cross-section of the14N(n, α0)11B reaction measured by Gabbard et al.at 5.05 MeV[4]is nearly three times of that measured by V. A. Khryachkov et al. at 5.04 MeV [8]. The cross-section of the14N(n, α)11B reaction at 4.10–4.94 MeV has only one result [4], and there are no measurements performed in the energy range of 4.94–5.56 MeV according to the EXFOR library[9].All five experiments were performed using ionization chambers without a detailed simulation. To obtain more precise results, an experiment for measuring the cross-section of the14N(n,α)11B reaction in the MeV region was planned to clarify previous experimental results, for which a simulation method for the14N(n, α)11B reaction should be established first.

We have used a gridded ionization chamber (GIC) to measure the (n, α) reaction of a variety of solid samples[10–14], and reliable results have been obtained. The experimental methods for measuring solid samples with the GIC have been verified,but the methods for measuring gas samples with this GIC are still being explored. The measurement method for the gas sample needs to be established by simulation because simulation of the experimental spectra is one of the main steps of the experiment. Before the experiment, simulation spectra can be used to determine the experimental parameters.For example,simulation can help determine whether it is necessary to choose solid samples or gas samples, and the composition of the working gas can be optimized based on the simulation spectra to ensure that the14N(n, α)11B events will not be affected by the background. During the experiment, the simulation spectra can be used for comparison with the experimental spectra to determine whether the working state of the experimental apparatus was suitable. After the experiment, simulation spectra can be used to determine the detection efficiency [11]. For instance, the valid event area of the14N(n,α)11B events can be determined using the experimental spectra, and its detection efficiency can be obtained from the simulated spectrum. Therefore, it is necessary to establish an accurate simulation method.

In this study,a simulation method for the cathode–anode two-dimensional spectra of solid and gas samples for the14N(n, α)11B reaction was established. Experiments were performed at PKU using adenine (C5H5N5) as the solid sample and nitrogen (N2) as the gas sample to verify the simulation.Finally,new measurements of the cross-section of the14N(n, α)11B reaction are planned based on the proposed simulation method.

2 Methods

Prediction of the measurement events was conducted using a Monte Carlo simulation based on MATLAB-2019a[15]. In the present simulation, the corresponding double differential cross-section data calculated using the TALYS-1.9 code [16] and the stopping powers calculated with the SRIM-2013 code [17] were used.

2.1 Principle of the simulation

As a fast-charged particle is emitted from the sample and passes through the working gas,it ionizes the working gas and generates electron–ion pairs [18]. The kinetic energy of the charged particle is continuously reduced along the ionization track, and the stopping power of the working gas constantly changes. The stopping power of charged particles in the working gas can be calculated using the SRIM-2013 code [17].

When the ions and electrons drift toward the cathode and anode under the force of the electric field, signals of opposite polarity are induced on the cathode and anode of the Frisch-grid ionization chamber. Because the drift velocity of ions is three orders of magnitude slower than that of electrons, both the cathode and anode signals are primarily dominated by the drift of electrons [18]. The present work only considers the part of the ionization track of charged particles in the sensitive area,with two uniform electric fields between the cathode and grid and between the grid and anode.

where dgis the distance from the grid to the beginning of the ionization track, Egais the energy of the charged particle deposited in the grid-anode area, and σgais the shielding inefficiency of the grid, which can be expressed as [22]:

In the present work, Dcgis 6.1 cm. The theoretically calculated value of σgais 0.0028.

As shown in Fig. 1b,when the ionization track exists in both the cathode-grid area and the anode-grid area at the beginning,the trace is divided into two equivalent traces by the grid. Therefore,the signal amplitudes generated by the electrons in these two areas must be calculated according to Eqs. (1) and (2), and Eqs. (4) and (5), respectively. As a result,the signal amplitude of the cathode Acand anode Aacan be expressed as:

Fig.1 (Color online)Schematic diagram for the drift of electrons in the GIC.a The ionization track exists in the cathode-grid area or the gridanode area. b The ionization track exists in both the cathode-grid area and the grid-anode area

2.2 Simulation process

In the present simulation, light-charged particles with random positions and emission angles, including α-particles, protons, deuterons, and tritons, are generated in the area where the target nuclei exist based on the Monte Carlo method.Taking the14N(n,α)11B reaction as an example,if the nuclear reaction occurs in the working gas, it is necessary for the signal amplitudes of both the cathode and anode of the α-particle and11B to be considered and superimposed. If the nuclear reaction occurs in the solid samples, the influence of11B can be ignored because it is difficult for11B to penetrate the solid sample, but the wall effect [23] of the α-particle and its energy loss in the solid sample need to be considered. If a nuclear reaction occurs on the cathode or anode,11B does not need to be considered because it cannot penetrate the electrode plate. There are many nuclei from different materials in the GIC, and the effects of all charged particles generated by neutron irradiation need to be considered.The simulation process is shown in Fig. 2.

Fig. 2 Flow diagram of simulation process

1. Input parameters:physical quantities,including the En,energy level of the recoil nucleus, Q-value, and particle mass, are input to determine whether the reaction could have taken place.

2. Coordinate sampling: for the target nuclei in the solid sample, the position (x, y, z) of the nuclear reaction is randomly selected in the solid sample (the maximum value of z is the thickness of the solid sample);for the target nuclei in the working gas,the position(x,y,z)of the nuclear reaction in the GIC is randomly selected;for the target nuclei on the electrode plate (cathode or anode), the position (x, y, z) of the nuclear reaction is randomly selected.

3. Select emission angle:the light-charged particles(p,d,t,and α)with randomly selected φCM(azimuth angle in the center of mass system with the neutron incident direction as the z-axis) are generated every 2° of θCM(polar angle in the center of mass system with the neutron incident direction as the z-axis) between 0°and 180° in the center of mass system. Then, the emission angles and kinetic energies of the lightcharged particles and recoil nucleus are transferred to the laboratory system.

4. Calculate signal amplitude: the signal amplitudes of the cathode and anode are determined by the energy deposition of charged particles along the ionization track in the sensitive area of the GIC according to Eqs.(7)and(8),respectively.The stopping powers and ranges are calculated using the SRIM-2013 code [17].

5. Energy resolution correction:The calculated Acand Aaneed to be corrected according to the energy resolution of the GIC; two numbers are randomly selected from the normal distribution N(1,σ)(σ is determined by the experimental results of compound alpha sources),after which Acand Aaare, respectively, multiplied by these numbers.

6. Count results: after the calculation of each particle released from the nuclear reaction is completed, the weight wtotwill be accumulated to the corresponding position of the signal amplitude on the cathode–anode two-dimensional spectrum. The weight wtotcan be expressed as:

where wσis the corresponding double differential cross-section of the reaction with the generated emission angle calculated using the TALYS-1.9 code [16],wφis the relative flux of neutrons at the generated position of the reaction, and wnis the total number of target nuclei.For the reaction in the solid sample,if the θCMof the charged particle is less than 90°, wtotwill accumulate in the forward direction; otherwise, it will accumulate in the backward direction.For the reaction in the working gas or electrode plate, if the reaction is generated at the front side of the cathode, wtotwill accumulate in the forward direction; otherwise, it will accumulate in the backward direction.

7. Repeat steps: the above steps are repeated for wmctimes for each reaction, as listed in Sect. 2.4.

2.3 Experimental setup

The experimental spectra of the14N(n, α)11B reaction with solid and gas samples at En= 4.25, 4.50, 4.75, 5.00,5.25, and 5.50 MeV were measured based on the 4.5 MV Van de Graaff Accelerator of Peking University for verification of the simulation. As shown in Fig. 3, the experimental apparatus consisted of three main parts:the neutron source, the GIC as the charged particle detector (with the sample inside), and the scintillator detector.

Monoenergetic neutrons were produced by a deuterium gas target through the2H(d,n)3He reaction.The deuterium gas target was a cylinder with a length of 2.0 cm,radius of 0.5 cm, and deuterium gas pressure of 3.0 atm.

The detector was a twin-gridded ionization chamber with a common cathode,the details of which can be found in Ref.[13].The distance from the cathode to the grid was 6.1 cm, that from the grid to the anode was 1.4 cm, that from the anode to the shield electrode was 1.0 cm,and that from the cathode to the forefront of the neutron source was 15.4 cm; the electrode plate side length was 15.6 cm.

A sample changer with five sample positions was set at the common cathode of the GIC,and back-to-back samples were placed at each of them, as shown in Fig. 4. Five sample positions were used in the experiment:(1)back-toback compound alpha sources were used for calibration of the data acquisition system (DAQ) of the GIC; (2) a238U sample was employed to determine the absolute neutron flux;(3)back-to-back compound C5H5N5#3,#4samples with a thickness of 200 μg/cm2were used for the14N(n, α)11B reaction measurement; (4) back-to-back compound C5H5N5#10,#30samples were used as spares; and (5) a Ta backing with a thickness of 0.1 mm was utilized to measure the background events.

Fig. 3 Schematic drawing of the experimental apparatus

Fig. 4 Samples in the sample changer

In addition,a238U sample was set at the shield electrode of the 01 side to monitor the relative neutron flux of each run. When the charged particles of the solid sample exit forward (0°–90°), they enter the two sides. When the charged particles of the solid sample exit backward (90°–180°), they enter the 01 side.

In addition to the solid samples with a thickness of 200 μg/cm2,the N content in the working gas at 0.20 mbar was used as a gas sample to make the number of events from the solid samples and the gas sample similar for observation. Air at a pressure of 0.25 mbar in the GIC can be used as the gas sample for the14N(n, α)11B reaction because its N content is 78%. The working gas of the GIC was Kr + 2.70% CO2+ 0.05% air, and the pressure within the GIC was 0.5 bar. The high voltages applied to the cathodes and anodes were - 1000 and 500 V(the gridelectrodes were grounded), which allowed the complete collection of electrons from the tracks.

An EJ-309 liquid scintillator detector, which was located 274.0 cm away from the forefront of the neutron source on the axis of the neutron source, was used to obtain the neutron spectrum by unfolding the measured pulse height spectra;details regarding the detector can be found in Ref.[24].

2.4 Simulation parameters and simulated reactions

The parameters used in the simulation were consistent with those used in the experiment. In addition, the mass thickness of the water vapor absorbed by the electrode plate was approximately 50 μg/cm2, which was estimated based on the proton-event peak in the anode spectrum measured in the experiment. Therefore, the reactions considered in the present simulation were the1H(n, el)1H,14N(n, α)11B, and14N(n, p)14C reactions from the C5H5N5samples; the78,80,82,83,84Kr(n, α)75,77,79,80,81Se,14N(n,α)11B,14N(n, p)14C, and16,17O(n, α)13,14C reactions in the working gas; and the1H(n, el)1H and16,17O(n, α)13,14C reactions on the cathode and anode. Other reactions, such as13C(n, α)10Be,18O(n, α)15C, and181Ta(n, p)181Hf, were not considered because of their small cross-sections, small numbers of nuclei, or both.

3 Results

Simulations of measurements at En= 4.25, 4.50, 4.75,5.00,5.25,and 5.50 MeV were completed.The preliminary results of the measurement and those of the simulation at En= 4.50 MeV are compared in Fig. 5 as an example.Figures 5a, c, e, and g show the simulation results, which are the forward and backward cathode–anode two-dimensional spectra and the forward and backward anode spectra.The corresponding experimental results are shown in Fig. 5b, d, f, and h.

Comparing the experimental results with the simulation results, good agreement is shown by the high similarity of the cathode–anode two-dimensional spectrum and the anode spectrum. The present simulation results of the14N(n, α0)11B events from solid samples in Fig. 5a, c are compared with the experimental results shown in Fig. 5b,d. Even if the interference of16,17O(n, α)13,14C events of the gas sample could be eliminated after background subtraction,both simulation and experiments showed that only part of the14N(n,α0)11B events in the forward direction do not experience interference with the background. Another part of the14N(n, α0)11B events, which are under 84 channels of the anode, are primarily interfered with by14N(n, α1)11B,14N(n, p)14C, and1H(n, el)1H events. This part of the14N(n, α0)11B events lost most of the energy in the solid samples.Because of the mixture of14N(n,α1)11B events and the14N(n,α0)11B events and the interference of the forward1H(n,el)1H events from C5H5N5samples,it is impossible to obtain14N(n, α1)11B events in the forward direction through background subtraction. Because the number of1H(n, el)1H events from the electrode plates is several orders of magnitude higher than that of the14N(n,α)11B events, none of the experimental results of14N(n,α)11B events in the backward direction shown in Fig. 5h with the blue line are as clear as the present simulation results, which are shown in Fig. 5g, because of the poor statistics.The present simulation found that the background interference in the area of the14N(n, α)11B events of the solid sample is very high, so it is necessary to use gas samples for14N(n, α)11B experiments. This suggests the necessity of the simulation.

The simulation results of the14N(n, α0)11B events from the gas sample in Fig. 5a,c are shown by the chain lines in Fig. 5e,g.The experimental results show that the energy of the14N(n, α)11B events of the gas sample is higher than those of the solid samples. This is because the11B of the14N(n, α)11B reaction of the solid samples loses all energy in the solid sample.All the emitted charged particles of the14N(n, α)11B reaction of the gas sample were detected by the GIC.As described in Sect. 2.3,the simulation takes this into consideration, so the simulation results shown in Fig. 5a, e agree with the experimental results shown in Fig. 5b, f. Because the neutron source used in the experiment produced neutrons at an angle of 4π, many charged particles were generated at the edge of the sensitive area of the GIC, and the energy of the charged particles was not fully deposited in the sensitive area. Therefore, the lowenergy tail predicted by simulation of the14N(n, α0)11B events from the gas sample events can be observed in the experimental results, as shown in Fig. 5. As shown in Fig. 5a, c, the results of the simulations show that the part of the14N(n,α0)11B event that is above 100 channels is not interfered with by the background,but all the14N(n,α1)11B events will be interfered with by16O(n,α)13C events in the working gas and1H(n,el)1H events on the electrode plates,as verified by experiments in Fig. 5b, d. Therefore, if the water vapor adsorbed on the electrode plate cannot be removed or the working gas still contains16O, the14N(n,α1)11B events from the gas sample cannot be measured.The neutron source needs to be collimated to reduce the low-energy tail of14N(n, α0)11B events from the gas sample.

Fig. 5 (Color online) Results of simulation and experiment for the 14N(n, α)11B reaction measurement at 4.50 MeV. a Cathode–anode two-dimensional spectrum (simulation) in the forward direction.b Cathode–anode two-dimensional spectrum (experiment) in the forward direction. c Cathode–anode two-dimensional spectrum (simulation)in the backward direction.d Cathode–anode two-dimensional spectrum (experiment) in the backward direction. e Anode spectrum of the simulation in the forward direction. f Anode spectrum of the experiment in the forward direction. g Anode spectrum of the simulation in the backward direction. h Anode spectrum of the experiment in the backward direction

The resolution of the two-dimensional spectrum of the experiment for low-energy events was worse than that of the simulation because the low-amplitude signals of the cathode and anode have a poor signal-to-noise ratio.Because the counting rate of the1H(n,el)1H reaction on the electrode plate is too high,protons may be generated in the forward and backward directions at the same time, so the common cathode amplitude will be superimposed,which is the main reason for the difference between simulation and experiment with fewer than 100 channels. Furthermore,with fewer channels, the noise interference grows more severe. Therefore, the threshold of the DAQ was set to 20 channels.

4 Future experimental plan

Based on the established simulation method,a new plan for the measurement of the cross-section of the14N(n,α)11B reaction was designed, and the experimental parameters were optimized according to the simulation results.

4.1 Gas sample

According to the simulation and experiment, the backward events of the14N(n, α0)11B reaction from the solid samples are difficult to count. Therefore, natural nitrogen will be used as a gas sample in the new experiments. The working gas in the new simulation was Kr + 5.00% N2at 0.5 atm,and the thickness of the water vapor on the plate is the same as above.A schematic of the simulation apparatus is shown in Fig. 6.

The simulation results on the 01 side (half of the GIC near the neutron source) were used as an example of predicting the results of the gas sample experiment. The distance from the cathode to the forefront of the neutron source was 15.4 cm from the cathode to the grid is 6.1 cm,that from the grid to the anode is 1.4 cm, and the side length of the square electrode plate was 15.6 cm. The78,80,82,83,84Kr(n, α)75,77,79,80,81Se,14N(n, α)11B, and14N(n,p)14C reactions from the working gas and the1H(n, el)1H and16,17O(n, α)13,14C reactions on the cathode and anode are considered.The preliminary results of the 01 side of the simulation at En= 4.50 MeV are presented in Fig. 7 as an example.

As shown in Fig. 7a,the recoil proton background from the plate occludes14N(n, α1)11B events. The α-particles emitted from14N(n, α0)11B in the backward direction lose energy from the anode,which causes this part of the events to be lost as a result of the cathode signal threshold.Because only a part of the kinetic energy of the charged particles that are generated at the edge of the plate is deposited in the sensitive area,the14N(n,α0)11B events on the edge of the plate will be distributed to the14N(n,α1)11B event area or background area. It is not only difficult to count these events, but it is also difficult to count these nuclei. Therefore, it is necessary for gas sample experiments of14N(n,α)11B to exclude14N(n,α)11B events close to the plate,and installing a collimator is required to reduce the area of the event area in the two-dimensional spectrum for the convenience of counting the number of events.

Fig. 6 Schematic drawing of the simulation

Fig. 7 (Color online) Results of simulation for the 14N(n, α)11B reaction measurement at 4.50 MeV. a Cathode–anode two-dimensional spectrum. b The anode spectrum

4.2 Neutron collimator

The working gas in the simulation was Kr + 5.00% N2of 0.5 at and 1.0 atm.To determine the number of nuclei in the gas sample for measurement, a neutron collimator device is planned to collimate the neutron beam, as shown in Fig. 8.

The distance from the cathode to the neutron source is 66.0 cm, R1is 3.4 cm, R2is 3.5 cm, and h is 4.1 cm. The present simulation only considers the nuclear reaction in the sample volume (the yellow area in Fig. 8), and the78,80,82,83,84Kr(n, α)75,77,79,80,81Se,14N(n, α)11B, and14N(n,p)14C, reactions in the working gas are considered. The preliminary results of the 01 side of the simulation at En-= 4.50 MeV with pressures of 0.5 atm and 1.0 atm are compared in Fig. 9.

The simulation suggested that the collimator can collimate the neutron beam, and the α-events from the gas sample of the14N(n,α)11B reaction are more concentrated.The events from the gas sample14N(n, α)11B reaction will not be lost because of the threshold cut. Figure 9a shows that when the pressure in the GIC is 0.5 atm, some of the14N(n, α0)11B events emitted in the forward direction will lose energy because they are stopped by the cathode and form a tail interfering with the14N(n, α1)11B event area.However, increasing the pressure of the working gas to 1.0 atm can reduce the events of14N(n, α0)11B in the tail;however,the GIC will collect more proton energy,causing the14N(n, α1)11B event to be interfered with by14N(n,p)14C events, as shown in Fig. 9c, d. In summary, the following experiments for the measurement of the crosssection of the14N(n, α)11B reaction use nitrogen as a gas sample, and the collimator needs to be set up as such. The14N(n, α)11B events generated near the plate need to be eliminated, and the working gas is 1.0 atm Kr + 5.00%N2.

Fig. 8 Schematic drawing of the simulation with neutron collimator

Fig. 9 (Color online) Results of simulation for the 14N(n, α)11B reaction measurement at 4.50 MeV. a Cathode–anode two-dimensional spectrum (0.5 atm). b Anode spectrum (0.5 atm). c Cathode–anode two-dimensional spectrum (1.0 atm). d Anode spectrum (1.0 atm)

5 Conclusion

In this study,a method for simulating the cathode–anode two-dimensional spectrum of a GIC for measuring gas and solid samples was established. This method is universal and can be used to predict the experimental spectra of neutron-induced light-charged particle emission reactions(n,lcp)from different nuclei using the GIC.The agreement between simulation and experiment regarding the14N(n,α)11B events and the background indicates that the simulation can be used as a guide for the experiment. The simulation method can also be used to separate the background and14N(n, α)11B events, to determine the valid event area, and to calculate the detection efficiency for valid events. The experiments and simulations will be compared to obtain more accurate results for the14N(n,α)11B reaction in the future.

AcknowledgementsThe authors are grateful to Prof. Y. M. Gledenov and Dr. E. Sansarbayar from JINR, Dubna, for providing and maintaining the twin-gridded ionization chamber. They also thank Prof. G. Khuukhenkhuu from Ulaanbaatar University for installing the solid samples.

Author contributionsAll authors contributed to the study conception and design. The simulation method was performed by Yi-Wei Hu, Hao-Yu Jiang and Huai-Yong Bai. Material preparation, data collection and analysis were performed by Yi-Wei Hu,Hao-Yu Jiang,Zeng-Qi Cui and Jie Liu.The first draft of the manuscript was written by Yi-Wei Hu.The reviewing and editing were performed by Yi-Wei Hu, Hao-Yu Jiang, Zeng-Qi Cui, Jie Liu, Hao-Fan Bai, Huai-Yong Bai, Jin-Xiang Chen and Guo-Hui Zhang and all authors commented on previous versions of the manuscript.All authors read and approved the final manuscript.