Measurement of neutron energy spectra of 9Be(d,n)10B reaction with a thick beryllium target

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Shuang-Jiao Zhang, Zhi-Jie Hu, Zhi-Ming Hu, Chao Han, Xiao-Hou Bai, Chang-Qi Liu, Chang Huang, Qin Xie, Dong-Ying Huo, Kang Wu, Yang-Bo Nie, Yan-Yan Ding, Kai Zhang, Yu Zhang, Zhi-Yong Deng, Rui Guo, Zheng Wei and Ze-En Yao. Measurement of neutron energy spectra of 9Be(d,n)10B reaction with a thick beryllium target[J]. Chinese Physics C.
Shuang-Jiao Zhang, Zhi-Jie Hu, Zhi-Ming Hu, Chao Han, Xiao-Hou Bai, Chang-Qi Liu, Chang Huang, Qin Xie, Dong-Ying Huo, Kang Wu, Yang-Bo Nie, Yan-Yan Ding, Kai Zhang, Yu Zhang, Zhi-Yong Deng, Rui Guo, Zheng Wei and Ze-En Yao. Measurement of neutron energy spectra of 9Be(d,n)10B reaction with a thick beryllium target[J]. Chinese Physics C. shu
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Measurement of neutron energy spectra of 9Be(d,n)10B reaction with a thick beryllium target

    Corresponding author: Zheng Wei, weizheng@lzu.edu.cn
    Corresponding author: Ze-En Yao, zeyao@lzu.edu.cn
  • 1. School of Nuclear Science and Technology, Lanzhou University, Lanzhou 730000, China
  • 2. Engineering Research Center for Neutron Application Technology, Ministry of Education, Lanzhou University, Lanzhou 730000, China
  • 3. Key Laboratory of Nuclear Data, China Institute of Atomic Energy, Beijing 102413, China
  • 4. Nuclear Power Institute of China, Chengdu 610000, China

Abstract: The new measurements of the neutron energy spectra of the 9Be(d,n)10B reaction with a thick beryllium target are carried out by the fast neutron time-of-flight (TOF) spectrometer for the neutron emission angles $\theta=0^\circ$ and $45^\circ$, and the incident deuteron energies are 250 keV and 300 keV, respectively. The neutron contributions from the 9Be(d,n)10B reaction are distributed relatively independently for the ground state of 10B, 1st, 2nd, and 3rd excited state of 10B. The branching ratio of the 9Be(d,n)10B reaction for different excited states of 10B are obtained for the neutron emission angles $\theta=0^\circ$ and $45^\circ$, and the incident deuteron energies are 250 keV and 300 keV, respectively. The branching ratio of the 9Be(d,n)10B reaction for the 3rd excited state is decreasing with increasing of the incident deuteron energy, and the branching ratio for the ground state and 2nd excited state are rising with increasing of the neutron emission angles.

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    I.   INTRODUCTION
    • As is well known to all, accelerator neutron source is widely used in the field of neutron physics and neutron applications technology owing to its high neutron yields, good controllability, small floor space, and nonproliferation capability [1-9]. Popularly, in exothermic nuclear reactions, deuterium ions bombard deuterons and tritons to produce fusion neutrons from the 2H(d,n)3He (D-D) reaction and 3H(d,n)4He (D-T) reaction, and deuterium ions bombard beryllium to produce neutrons from the 9Be(d,n)10B (D-Be) reaction at low energy $ {D}^{+} $ ions with $\sim {10}^{2} $ keV.

      Compared with the deuterium-adsorption target or tritium-adsorption target, the metal beryllium has the stable chemical proterties and high hardness. Pure metal beryllium target is easy to obtain, which can be easily processed into a variety of shapes. Beryllium has a high melting point (1280°C) and better thermal conduction, which allows the metal beryllium target to withstand the high intensity $ {D}^{+} $ ions beam. Most importantly, the cross section of the 2H(d,n)3He (D-D) reaction is roughly equivalent to the 9Be(d,n)10B (D-Be) reaction at low energy $ {D}^{+} $ ions with $ \sim {10}^{2} $ keV. As a result, the accelerator-based 9Be(d,n)10B reaction neutron source can provide high intensity and continuous-spectrum neutron fields at low energy deuterium ions.

      The 9Be(d,n)10B reaction is relatively complex. For low-energy deuterium ions, 9Be(d,n)10B is an exothermic reaction with $ Q $ = +4.36MeV, but there are four well-known excitation states of 10B [10,11]. With energy increasing of deuterium ions, several many-body reactions, 9Be(d,2n)9B ($ Q $ = -4.1 MeV), 9Be(d,np)9B ($ Q $ = −2.2 MeV), 9Be(d,2np)8B ($ Q $ = -3.8 MeV), etc., will markedly enhance the neutron yields and extend the neutron energy spectrum. However, the measured results of the neutron energy spectrum, angular distribution, and integrated yields for the 9Be(d,xn) reaction are scarce, and these studies were mainly focused on the deuterium ion energies from a few MeV to tens MeV [10-36]. Only, Coombe et al. measured the neutron energy spectra from the 9Be(d,n)10B reaction for 80 keV deuterium ions at $ 0^\circ $ and $ 45^\circ $ [37] and Zou et al. measured the angular distribution and neutron yields from the 9Be(d,n)10B reaction for 200 keV and 500 keV deuterium ions [38].

      The 9Be(d,n)10B reaction is a typical direct reaction, and the angular distribution of 9Be(d,n)10B neutron source presents a forward trend. Neutrons from direct reaction mechanisms are still visible at larger angles, but the relative intensity and the position of the maxima decrease with the angle. Consequently, it is more beneficial to select the forwards angles for studying branching ratio of the 9Be(d,n)10B reaction.

      In this work, new measurements of the neutron energy spectra of the 9Be(d,n)10B reaction with a thick beryllium target are carried out for the neutron emission angles $ \theta = 0^\circ $ and $ 45^\circ $, and the incident deuteron energies are 250 keV and 300 keV, respectively. This work would provide basic information for the accelerator-based D-Be neutron source used in the field of neutron physics and neutron application technology.

    II.   EXPERIMENT

      A.   Experimental arrangement

    • The measurements of the neutron energy spectra of the 9Be(d,n)10B reaction with a thick beryllium target for low energy deuterium ions are carried out using the fast neutron time-of-flight (TOF) spectrometer and the Cockcroft-Walton accelerator at China Institute of Atomic Energy (CIAE). The experimental arrangement is shown in Fig. 1. The Cockcroft-Walton accelerator provides $ {D}^{+} $ ions of 250 keV and 300 keV with a frequency of 1.5 MHz and a pulse width of 2.5 ns. The target used in this experiment is a pure metal beryllium sample with diameter of 22.0 mm and thickness of 1.0 mm at $ 0^\circ $ direction with respect to the deuteron beam.

      Figure 1.  The experimental arrangement for measuring the neutron energy spectra of the 9Be(d,n)10B reaction.

      The fast neutron TOF spectrometer is employed at $ 0^\circ $ and $ 45^\circ $ to measure the neutron energy spectra from the 9Be(d,n)10B reaction. The spectrometer consists of a BC501A liquid scintillator with diameter of 5.08 cm and thickness of 2.54 cm, and a HAMAMATSU R329-02 photomultiplier tube. The flight length of the emitted neutrons between the metal beryllium target and the front surface of detector is 3.0 m. In this experiment, the threshold of the BC501A liquid scintillator detector is 0.191 MeV. A silicon surface barrier detector (SSD) is placed at $ 135^\circ $ direction with respect to the deuteron beam to monitor the neutron yields by counting the associated proton from the D(d,n)3He reaction owing to deuterium ions bombard self-injecting deuterons in the target, because the D(d,n)3He reaction is along with the D(d,p)T reaction. The SSD is positioned 90 cm from the Be sample target.

      What’s more, the deuteron beam would self-inject into the beam-limiting diaphragm, and deuterium ions bombard self-injected deuterons in the beam-limiting diaphragm to produce neutrons by the D(d,n)3He reaction. These neutrons would respond in the BC501A liquid scintillator detector. In order to determine the position of the D(d,n)3He neutron peaks in the neutron TOF spectra and neutron energy spectra, the neutron flight distances from the beam-limiting diaphragm to the BC501A liquid scintillator detector are shown in Fig. 1. $ L1 $ is the neutron flight distance at $ 0^\circ $, which is 3.230 m. $ L2 $ is the flight distance at $ 45^\circ $, which is 3.134 m.

      In the experiment, all events from the detector were recorded by a list mode by event basis with a CAMAC data acquisition system. For each event, there are three parameters, Pulse Height (PH), Pulse Shape Discrimination (PSD), and Time-Of-Flight (TOF). The PH and PSD are used for the detection threshold determination and n-$ \gamma $ discrimination, respectively, in the offline analysis.

    • B.   TOF spectra

    • As shown in Fig. 1, the BC501A liquid scintillator detector is used as the primary detector in the experiment to measure the neutron spectra. Although BC501A liquid scintillator detector is sensitive to both neutron and gamma, the output pulse shape of neutron and gamma in liquid scintillator detector are different. the neutron and gamma signals can be distinguished by the output pulse shape. In this work, a 4-channel pulse shape discriminator is used to distinguish the neutron and gamma signals by the zero-crossing time method for all measured TOF spectra to reject the gamma response. The neutron -only TOF spectra can be obtained by filtering the mixed TOF spectra of neutron and gamma by chosen the neutron signal in the two-dimensional distributions of the zero-crossing time versus pulse height of the BC501A liquid scintillator detector in the offline analysis.

      Fig. 2 shows the measured TOF spectra of the 9Be(d,n)10B reaction with deuteron energies of 250 keV and 300 keV at neutron emission angles of $ 0^\circ $ and $ 45^\circ $, respectively. Among, the time-zero ($ Ch_{0} $) in the experimentally measured neutron time-of-flight spectrum can be determined as $ \ Ch_{0} = P+L /(c\times W) $, where $ P $ is the gamma peak position in the measured neutron time-of-flight spectrum. $ L $ is the neutron flight distance. $ W $ is the channel width of time-to-amplitude converters (TAC), and $ c $ is the flight speed of gamma-rays. In this work, $ P $ can be determined by comparing the neutron-only TOF spectrum and the mixed TOF spectrum of neutron and gamma, $ L $ = 3.0 m, $ W $ = 0.23 ns, and $ c $ is the speed of light.

      Figure 2.  The measured TOF spectra of the 9Be(d,n)10B reaction with deuteron energies of 250 keV and 300 keV at neutron emission angles of 0° and 45°, repectively. The channel width is 0.23 ns. The red solid curves denote the mixed TOF spectra of neutron and gamma. the black solid curves denote the neutron-only TOF spectra. Arrows are the calculated results. The red arrow represents neutrons from the D(d,n)3He reaction for the metal beryllium target. The violet arrow represents neutrons from the D(d,n)3He reaction for the beam-limiting diaphragm. The navy arrow represents gamma-rays. The orange arrow represents the time-zero of flight time. The black arrows are neutrons from the 9Be(d,n)10B reaction, and right to left represent the ground state of 10B (Q = 4.36MeV), 1st (Q = 3.64MeV), 2nd (Q = 2.62MeV), 3rd (Q = 2.21MeV), and 4th excited state of 10B (Q = 0.78MeV), respectively.

      As shown in Fig. 2, the gamma responses can be well excluded in the measured neutron TOF spectra of the 9Be(d,n)10B reaction. One can see that there are six neutron energy peaks in the 1800-2500 channel range, corresponding to neutrons from the 9Be(d,n)10B reaction for different excited states of 10B, neutrons from the D(d,n)3He reaction for the beam-limiting diaphragm and the metal beryllium target. The peak positions in the experimentally measured flight time spectra are all in good agreement with the calculated results. The relationship between the neutron energy and the neutron flight time can be discribed by the following formula:

      $ T_{n} = \frac{72.306\times L}{\sqrt{E_{n}}} $

      (1)

      where $ E_{n} $ is the neutron energy, $ T_{n} $ is the neutron flight time, and $ L $ is the neutron flight distance.

    III.   RESULTS AND DISCUSSION
    • The measured TOF spectra are converted into the neutron energy spectra based on the neutron flight distance, the channel width of time-to-amplitude converters (TAC), and the gamma peak position, and typical results are shown in Fig. 3. The neutron energy spectra are all modified by the neutron detection efficiency of the BC501A liquid scintillator detector calculated by the NEFF code [39].

      Figure 3.  The measured neutron energy spectra of the 9Be(d,n)10B reaction with deuteron energies of 250 keV and 300 keV at neutron emission angles of 0° and 45°, repectively. Arrows are the results of the calculations. Red arrow represents neutrons from the D(d,n)3He reaction for the metal beryllium target. Violet arrow represents neutrons from the D(d,n)3He reaction at the beam-limiting diaphragm. The black arrows are neutrons from the 9Be(d,n)10B reaction with 10B in different excited states.

      As for the 9Be(d,n)10B reaction, emitted neutrons are different energies because 10B would be in different excited states [15,20]. The excited states of 10B would be 0, 0.72, 1.74, 2.15, 3.58, 5.17 MeV,corresponding to $ Q $-energies of 4.36, 3.64, 2.62, 2.21, 0.78, -0.81 MeV, respectively. Emitted neutron energies in different excited states of 10B can be calculated by the $ Q $-equation [40]

      $ \begin{aligned}[b] E_{n} = &\frac{m_{d}\times m_{n}}{(m_{n}+m_{B})^2}\times E_{d}\\&\times\left[cos\theta_{L} \pm \sqrt{cos^2\theta_{L}+\frac{m_{n}+m_{B}}{m_{d}\cdot m_{n} }\left(m_{B}-m_{d}+\frac{Q}{E_{d}}\cdot m_{B}\right)}\right]^2 \end{aligned} $

      (2)

      where $ E_{d} $ is the incident deuteron energy, $ m_{d} $, $ m_{n} $, $ m_{B} $ denote the mass of deuteron, neutron, and boron, respectively. $ Q $ is the $ Q $-energy of the 9Be(d,n)10B reaction, and $ \theta_{L} $ is the emitted neutron angle in the laboratory system.

      The measured neutron energy spectra of the 9Be(d,n)10B reaction with deuteron energies of 250 keV and 300 keV at neutron emission angles of $ 0^\circ $ and $ 45^\circ $ are shown in Fig. 3. One can see that typical six neutron energy peaks, corresponding to neutrons from the D(d,n)3He reaction for the beam-limiting diaphragm, neutrons from the 9Be(d,n)10B reaction for the ground state of 10B ($ Q $ = 4.36 MeV), neutrons from the 9Be(d,n)10B reaction for the 1st excited state of 10B ($ Q $ = 3.64 MeV), neutrons from the D(d,n)3He reaction for the metal beryllium target, neutrons from the 9Be(d,n)10B reaction for the 2nd excited state of 10B ($ Q $ = 2.62 MeV), and neutrons from the 9Be(d,n)10B reaction for the 3rd excited state of 10B ($ Q $ = 2.21 MeV) [peak positions from right to left]. The neutron energy peak, corresponding to neutrons from the 9Be(d,n)10B reaction for the 4th excited state of 10B ($ Q $ = 0.78MeV), has very high counts due to the modification of the small neutron detection efficiency at 1.1MeV. Because of the large uncertainty in the efficiency of neutron detection at 1.1MeV, this neutron energy peak is not analyzed. In order to verify the accuracy of the measured neutron energy spectra of the 9Be(d,n)10B reaction, the neutron energies of the 9Be(d,n)10B reaction and the D(d,n)3He reaction were calculated using the Q-equation, and the results are shown by the arrows in Fig. 3. The calculated neutron energies and the neutron peak position energies in the measured neutron energy spectra of the 9Be(d,n)10B reaction are compared in Table 1. The relative deviation ($ RD $) between the calculated neutron energy and the neutron peak position energy can be used to verify the accuracy of the measured neutron energy specctra of the 9Be(d,n)10B reaction and can be calculated using the following equation:

      $E_{d}$/Angle states $E_{cal}$ (MeV) $E_{exp}$ (MeV) $RD$ (%)
      250 keV/0° DD 6.58 6.7 1.82
      0.00 4.42 4.5 1.81
      0.72 3.74 3.8 1.60
      DD 3.15 3.1 1.59
      1.74 2.78
      2.15 2.39 2.4 0.42

      250 keV/45° DD 6.52 6.5 0.31
      0.00 4.33 4.4 1.62
      0.72 3.66 3.7 1.09
      DD 2.95 3.0 1.69
      1.74 2.71 2.7 0.37
      2.15 2.33 2.3 1.29

      300 keV/0° DD 6.21 6.2 0.16
      0.00 4.48 4.5 0.45
      0.72 3.80 3.8 0.00
      DD 3.23 3.3 2.17
      1.74 2.84 2.9 2.11
      2.15 2.45 2.4 2.04

      300 keV/45° DD 6.12 6.2 1.31
      0.00 4.39 4.4 0.23
      0.72 3.72 3.7 0.54
      DD 3.01 3.0 0.33
      1.74 2.77
      2.15 2.38 2.4 0.84

      Table 1.  The comparison between the calculated neutron energies and the experimental results for the 9Be(d,n)10B reaction

      $ RD = 100\times\left|\frac{E_{exp}-E_{cal}}{E_{cal}}\right| $

      (3)

      where $ E_{cal} $ is the calculated neutron energy, and $ E_{exp} $ is the neutron peak position energy in the measured neutron energy spectra. As can be seen in the Table 1. The maximum value of the relative deviation is 2.17%, which fully demonstrates the accuracy of the experimentally measured neutron energy spectra of the 9Be(d,n)10B reaction.

      As shown in Fig. 3, obviously, neutrons from the D(d,n)3He reaction for the metal beryllium target seriously influence the neutron energy spectrum distribution of the 9Be(d,n)10B reaction in the experiment. It is necessary to exclude neutrons of the D(d,n)3He reaction for the metal beryllium target from the neutron energy spectrum of the 9Be(d,n)10B reaction. In order to exclude neutrons of the D(d,n)3He reaction on the metal beryllium, in this work, a thick deuterium-adsorption target replaces the metal beryllium target in the original target position. The Cockcroft-Walton accelerator provides $ {D}^{+} $ ions, which bombard the thick deuterium-adsorption target to produce only D-D neutrons. The fast neutron TOF spectrometer is employed to measure the neutron energy spectra from the D(d,n)3He reaction, and the silicon surface barrier detector (SSD) is used to count the associated protons from the D(d,p)T reaction taken place along with the D(d,n)3He reaction, as shown in Fig. 1.

      Fig. 4 shows the measured neutron energy spectrum of the D(d,n)3He reaction with deuteron energy of 300 keV at neutron emission angle of $ 0^\circ $, as an example. One can see that there are two typical neutron peaks in the experimentally measured neutron energy spectrum of the D(d,n)3He reaction. The right peak represents the main peak of D-D neutrons, and neutron energy is 3.23 MeV, which is in good agreement with the calculated result by the $ Q $-equation. The left peak represents neutron’s contribution from D-D neutrons slowing down and scattering.

      Figure 4.  The measured neutron energy spectrum of the D(d,n)3He reaction with deuteron energy of 300 keV at neutron emission angle of 0°. The black arrow denote the calculated neutron energy from the D(d,n)3He reaction.

      Because the D(d,n)3He reaction is accompanying with the D(d,p)T reaction, the silicon surface barrier detector (SSD) can measure the associated protons to monitor the neutron yields of the D(d,n)3He reaction. Either the metal beryllium target (self-injecting deuterons in the target) or the deuterium-adsorption target, associated protons from the D(d,p)T reaction can be served as a normalized standard. In excluding neutrons of the D(d,n)3He reaction for the metal beryllium target from the neutron energy spectrum of the 9Be(d,n)10B reaction, the experimentally measured D(d,n)3He neutron spectrum and 9Be(d,n)10B neutron spectrum need to be normalized corresponding to a single proton counts measured by the silicon surface barrier detector (SSD) at $ 135^\circ $ direction. The normalized 9Be(d,n)10B neutron energy spectrum excluding the effect of D(d,n)3He neutrons can be obtained by subtracting the normalized D(d,n)3He neutron energy spectrum from the normalzied 9Be(d,n)10B neutron energy spectrum, and can be calculated using the following equation:

      $ n_{net} = \frac{N_{Be\_target}}{N(SSD)_{Be\_target}}-\frac{N_{D\_target}}{N(SSD)_{D\_target}} $

      (4)

      where $ n_{net} $ is normalized 9Be(d,n)10B neutron energy spectrum excluding the effect of D(d,n)3He neutrons. $ N_{Be\_target} $ and $ N(SSD)_{Be\_target} $ represent measured the neutron energy spectrum of the 9Be(d,n)10B reaction and the counts of associated protons for the beryllium target. $ N_{D\_target} $ and $ N(SSD)_{D\_target} $ represent measured the neutron energy spectrum of the D(d,n)3He reaction and the counts of associated protons for the deuterium-absorption target. The typical result is shown in Fig. 5. One can see that the D(d,n)3He neutrons peak at 3.23 MeV in the 9Be(d,n)10B neutron spectrum are well excluded, which certified the validity of D(d,n)3He neutrons exclusion method. It needs to be emphasized that, as shown in Fig. 5, the rightmost neutrons peak is corresponding to neutrons from the D(d,n)3He reaction for the beam-limiting diaphragm, which don’t affect the neutron energy spectrum distribution of the 9Be(d,n)10B reaction for different excited states of 10B.

      Figure 5.  The normalized 9Be(d,n)10B neutron energy spectrum for excluding neutrons of the D(d,n)3He reaction for the metal beryllium target with deuteron energy of 300 keV at neutron emission angle of 0°. The arrows indicate the calculated neutron energy. The red and violet arrows denote the neutrons from the D(d,n)3He reaction on the metal beryllium target and the beam-limiting diaphragm, respectively, and the black arrows are the neutrons from the 9Be(d,n)10B reaction with 10B in different excited states.

      Based on the above-mentioned data analysis method, the measured neutron energy spectra of the 9Be(d,n)10B reaction excluded neutrons of the D(d,n)3He reaction for the metal beryllium target with deuteron energies of 250 keV and 300 keV at neutron emission angles of $ 0^\circ $ and $ 45^\circ $ are shown in Fig. 6. The neutron contributions from the 9Be(d,n)10B reaction are distributed relatively independently for different excited states of 10B (from right to left, the ground state of 10B ($ Q $ = 4.36 MeV), 1st ($ Q $ = 3.64 MeV), 2nd ($ Q $ = 2.62 MeV), and 3rd excited state of 10B ($ Q $ = 2.21 MeV).)

      Figure 6.  The measured neutron energy spectra of the 9Be(d,n)10B reaction for excluding neutrons of the D(d,n)3He reaction for the metal beryllium target with deuteron energies of 250 keV and 300 keV at neutron emission angles of 0° and 45°, respectively. The olive arrow denote the neutrons from the D(d,n)3He reaction on the beam-limiting diaphragm. The black arrows are the neutrons from the 9Be(d,n)10B reaction with 10B in different excited states.

      Neutrons from the D(d,n)3He reaction for the beam-limiting diaphragm can't be excluded, which cause higher background in measured neutron energy spectra of the 9Be(d,n)10B reaction. According to the beam dynamics of the accelerator, with increasing of the incident deuteron energy, neutrons from the D(d,n)3He reaction for the beam-limiting diaphragm are more and more due to the deuterium ions space charge effect influences, particularly, at large neutron emission angle. Obviously, background neutrons in Fig. 6(d) is higher than Fig. 6(a)-6(c).

      By the analysis of the data, the branching ratio of the 9Be(d,n)10B reaction for different excited states of 10B are obtained, as shown in Fig. 6. The branching ratio of the 9Be(d,n)10B reaction for the ground state, 1st, 2nd, and 3rd excited state are 48.21%, 100.00%, 11.99%, and 39.11%, respectively, for deuteron energy of 250 keV at neutron emission angle of $ 0^\circ $. The branching ratio of the 9Be(d,n)10B reaction for the ground state, 1st, 2nd, and 3rd excited state are 58.61%, 100.00%, 12.43%, and 37.71%, respectively, for deuteron energy of 250 keV at neutron emission angle of $ 45^\circ $. The branching ratio of the 9Be(d,n)10B reaction for the ground state, 1st, 2nd, and 3rd excited state are 45.61%, 100.00%, 11.65%, and 32.61%, respectively, for deuteron energy of 300 keV at neutron emission angle of $ 0^\circ $. The branching ratio of the 9Be(d,n)10B reaction for the ground state, 1st, 2nd, and 3rd excited state are 91.85%, 100.00%, 18.31%, and 32.98%, respectively, for deuteron energy of 300 keV at neutron emission angle of $ 45^\circ $. With increasing of the incident deuteron energy, the branching ratio of the 9Be(d,n)10B reaction for the 3rd excited state is decreasing, obviously. With increasing of the neutron emission angles, the branching ratio for the ground state and 2nd excited state are rising.

      The statistical errors (SE) in the measured neutron energy spectra of the 9Be(d,n)10B reaction for excluding neutrons of the D(d,n)3He reaction on the metal beryllium target can be calculated using 1/$ \sqrt{N} $, where $ N $ is the number of neutrons in each energy range of the neutron energy spectra, and the calculation results are shown in Fig. 6. One can see that the statistical errors (SE) of the neutron energy spectra are very small. The maximum statistical errors of the neutron peaks for 10B in different excited states are 2.49% and 2.31% for deuteron energy of 250 keV at neutron emission angles of $ 0^\circ $ and $ 45^\circ $, and 1.32% and 2.23% for deuteron energy of 300 keV at neutron emission angles of $ 0^\circ $ and $ 45^\circ $, respectively.

      The energy resolution represents the ability of a time-of-flight spectrometer to discriminate neutrons with close energies, which can be expressed as [41]

      $ \frac{\Delta E}{E} = \frac{2\Delta t}{t}+\frac{2\Delta L}{L} $

      (5)

      where $ E $ is the neutron energy. $ \Delta E $ is the full width at half maximum. $ t $ is the neutron flight time. $ L $ is the neutron flight length, $ L $ = 3.0 m. $ \Delta L $ is the uncertainty of the neutron flight distance, which is about 0.2 cm. $ \Delta t $ is the uncertainty of the neutron flight time, which is calculated as

      $ \Delta t = [(\Delta t_{0})^2+(\Delta t_{h})^2+(\Delta t_{w})^2+(\Delta t_{s})^2+(\Delta t_{\Delta E})^2]^\frac{1}{2} $

      (6)

      where $ \Delta t_{0} $ is the time width of the pulse beam, which is about 2.5 ns. $ \Delta t_{h} $ is the time uncertainty in the measurement due to the crystal thickness of the scintillator detector, which can be calculated using $ \Delta t_{h} = 1.837/ \sqrt{E_{n}} $. $ \Delta t_{w} $ is the time uncertainty of the timing and time analyzer, which is about 0.5 ns. $ \Delta t_{s} $ is the uncertainty of the crossing time of the photomultiplier tube. $ \Delta t_{\Delta E} $ is the time uncertainty caused by the neutron energy divergence due to the scattering of primary neutrons in the target chamber. $ \Delta t_{s} $ and $ \Delta t_{\Delta E} $ can be neglected owing to small. Therefore, the uncertainty of neutron flight time $ \Delta t = \sqrt{(6.5\times E_{n}+3.375)/E_{n}} $. The energy resolution as a function of the emitted neutron energy is shown in Fig. 7. One can see that the neutron energy resolution of TOF is lower than 10% at neutron energy below 16 MeV.

      Figure 7.  The neutron energy resolution as a function of the emitted neutron energy in this work.

    IV.   CONCLUSION
    • The neutron energy spectra of the 9Be(d,n)10B reaction with a thick beryllium target are measured by the fast neutron time-of-flight (TOF) spectrometer, the incident deuteron energies are 250 keV and 300 keV, and neutron emission angles are $ 0^\circ $ and $ 45^\circ $, respectively. In this work, the neutrons of the D(d,n)3He reaction for the metal beryllium target are excluded from the neutron energy spectra of the 9Be(d,n)10B reaction. But neutrons from the D(d,n)3He reaction for the beam-limiting diaphragm are still in the neutron energy spectra of the 9Be(d,n)10B reaction, which don’t affect the neutron energy spectra distribution of the 9Be(d,n)10B reaction for different excited states of 10B.

      The neutron contributions from the 9Be(d,n)10B reaction are distributed relatively independently for different excited states of 10B, including the ground state of 10B, 1st, 2nd, and 3rd excited state of 10B. The branching ratio of the 9Be(d,n)10B reaction for different excited states of 10B are obtained for the neutron emission angles $ \theta = 0^\circ $ and $ 45^\circ $, and the incident deuteron energies are 250 keV and 300 keV, respectively. With increasing of the incident deuteron energy, the branching ratio of the 9Be(d,n)10B reaction for the 3rd excited state is decreasing, obviously. With increasing of the neutron emission angles, the branching ratio for the ground state and 2nd excited state are rising. This work would provide basic data for studying the physical mechanism of the 9Be(d,n)10B reaction, as well as provide the neutron energy distributions for low-energy-accelerator-based D-Be neutron source used in the field of neutron physics and neutron applications technology.

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