Cross-section measurements for the 58,60,61Ni(n, α)55,57,58Fe reactions in the 4.50 – 5.50 MeV neutron energy region

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Haoyu Jiang, Zengqi Cui, Yiwei Hu, Jie Liu, Jinxiang Chen, Guohui Zhang, Yu. M. Gledenov, E. Sansarbayar, G. Khuukhenkhuu, L. Krupa and I. Chuprakov. Cross-section measurements for the 58,60,61Ni(n, α)55,57,58Fe reactions in the 4.50 – 5.50 MeV neutron energy region[J]. Chinese Physics C.
Haoyu Jiang, Zengqi Cui, Yiwei Hu, Jie Liu, Jinxiang Chen, Guohui Zhang, Yu. M. Gledenov, E. Sansarbayar, G. Khuukhenkhuu, L. Krupa and I. Chuprakov. Cross-section measurements for the 58,60,61Ni(n, α)55,57,58Fe reactions in the 4.50 – 5.50 MeV neutron energy region[J]. Chinese Physics C. shu
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Received: 2020-01-01
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Cross-section measurements for the 58,60,61Ni(n, α)55,57,58Fe reactions in the 4.50 – 5.50 MeV neutron energy region

    Corresponding author: Guohui Zhang, guohuizhang@pku.edu.cn
  • 1. State Key Laboratory of Nuclear Physics and Technology, Institute of Heavy Ion Physics, Peking University, Beijing 100871, China
  • 2. Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia
  • 3. Nuclear Research Centre, National University of Mongolia, Ulaanbaatar 210646, Mongolia
  • 4. Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, Dubna 141980, Russia
  • 5. Institute of Experimental and Applied Physics, Czech Technical University in Prague, Horska 3a/22, Prague 2 12800, Czech Republic

Abstract: The cross sections of the 58Ni(n, α)55Fe reaction were measured in the 4.50 MeV ≤ En ≤ 5.50 MeV region (5 energy points), 60Ni(n, α)57Fe and 61Ni(n, α)58Fe reactions were measured at En = 5.0 and 5.50 MeV based on the 4.5 MV Van de Graaff Accelerator of Peking University. A gridded twin ionization chamber (GIC) was used as the detector, and the enriched 58Ni, 60Ni, and 61Ni foil samples were prepared and mounted at the sample changer of the GIC. Three highly enriched 238U3O8 samples inside the GIC were used to determine the relative and absolute neutron flux. The neutron energy spectra were obtained through unfolding the pulse height spectra measured by the EJ-309 liquid scintillator. The interferences from the low-energy neutrons and impurities in the samples have been corrected. The present data of the 60Ni(n, α)57Fe reaction are the first measurement results below 6.0 MeV, and those of the 61Ni(n, α)58Fe reactions are the first measurement results in the MeV region. The present results have been compared with existing measurements, evaluations and TALYS-1.9 calculations.

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    1.   Introduction
    • Nickel is widely used for making stainless steel and other corrosion-resistant alloys which play an important role in the construction of nuclear reactors and accelerators. The abundances of 58Ni, 60Ni and 61Ni in natural nickel are 68.0769%, 26.2231% and 1.1399%, respectively [1]. The research of the (n, α) reactions is important in nuclear engineering applications, because the neutron-induced helium production would lead to the helium accumulation and cause serious radiation damage in the materials. Besides, measurements of these cross sections could enhance our understanding of nuclear structure and nuclear reaction mechanisms. For example, The cross section of the 58Ni(n, α)55Fe reaction would enable one to derive the level structure of the residual nucleus 55Fe [2].

      For the cross sections of the 58Ni(n, α)55Fe (Q = 2.899 MeV) reaction, existing measurement results are abundant because the activation method is available for this reaction. In the 4.50 – 5.50 MeV neutron energy region, six measurements [2-7] could be found in the EXFOR library [8], but discrepancies among these measurements are noticeable. For example, the cross section of the 58Ni(n, α)55Fe reaction measured by Gledenov (1997, 5.00 – 7.00 MeV) [6] is higher by ~ 2 times than that obtained by Goverdovskiy (1992, 5.12 MeV) [4]. Besides, the coefficient of variation among different evaluations, including the ENDF/B-VIII.0 [9], ENDF/B-VII.1 [10], JENDL-4.0u+ [11], JEFF-3.3 [12], ROSFOND-2010 [13] and CENDL-3.1 [14] libraries, is 14.92% in the 4.50 MeV ≤ En ≤ 5.50 MeV region [15].

      For the cross sections of the 60Ni(n, α)57Fe (Q = 1.355 MeV) and 61Ni(n, α)58Fe (Q = 3.580 MeV) reactions, because the residual nuclei (57Fe and 58Fe) of these two reactions are stable, the activation method is unavailable for the measurement. For the cross sections of the 60Ni(n, α)57Fe reactions, there is only one measurement (Khromyleva (2018, 6.00 – 7.15 MeV) [16]) in the EXFOR library [8]. For the 61Ni(n, α)58Fe reaction, there is no data in the whole neutron energy region except for several results around En = 0.0253 eV [8]. In the 5.00 MeV ≤ En ≤ 5.50 MeV region, the coefficients of variation among different evaluations are 36.43% and 46.85% for the 60Ni(n, α)57Fe and 61Ni(n, α)58Fe reactions, respectively [9-14].

      Taking these factors into consideration, accurate measurements of the cross sections of the 58Ni(n, α)55Fe, 60Ni(n, α)57Fe and 61Ni(n, α)58Fe reactions are demanded. In the present work, the cross sections of the 58Ni(n, α)55Fe reaction were measured at En = 4.50, 4.75, 5.00, 5.25 and 5.50 MeV energy points, and 60Ni(n, α)57Fe and 61Ni(n, α)58Fe reactions at En = 5.00 and 5.50 MeV energy points. The present data of the 60Ni(n, α)57Fe reaction are the first measurement results below 6.0 MeV, and those of the 61Ni(n, α)58Fe reactions are the first measurement results in the MeV region. The details of the experiments are illustrated in Sect. 2, the data processing and the results are presented in Sect. 3 and Sect. 4, respectively, and the conclusion is drawn in Sect. 5.

    2.   Details of experiments
    • The experiments were performed based on the 4.5-MV Van de Graaff accelerator at Peking University, China. As shown in Fig. 1, the experimental apparatus consists of three main parts: the neutron source, the gridded twin ionization chamber (GIC) as the charged particle detector (with samples inside) and the scintillator detector for neutron energy spectrum measurement. The symmetric double sections of the GIC were defined as 01 side and 02 side, respectively.

      Figure 1.  Schematic drawing of the experimental apparatus.

    • 2.1.   Neutron source

    • Measurements were performed based on the 4.5-MV Van de Graaff accelerator of Peking University. The quasi mono-energetic neutrons were generated through the 2H(d, n)3He reaction using the energetic deuteron beam from the accelerator to bombard a deuterium gas target 2.0 cm in length and 3.0 atm in pressure. The deuterium gas target was separated from the vacuum tube of the accelerator by a molybdenum foil 5.0 μm in thickness. The energy range of the incident deuteron was set as 2.091 – 2.868 MeV so that the neutrons would be generated with the kinetic energy range of 4.50 – 5.50 MeV and the energy spread (1σ) of 0.14 – 0.19 MeV [17]. The deuteron beam current was ~ 2.0 μA throughout the measurement.

    • 2.2.   Samples

    • A sample changer with five sample positions was set at the common cathode of the GIC, and back-to-back double samples can be placed at each of them as presented in Table 1. The sample changer can be rotated through rotating a knob below the GIC without opening it. The samples used in the present measurements were: a) The back-to-back compound alpha sources at No.1 sample position (234U, 4.775 MeV; 239Pu, 5.155 MeV; 238Pu, 5.499 MeV; 244Cm, 5.805 MeV) was used to calibrate the detection system [18]; b) In order to monitor the neutron flux, three highly enriched (99.999%) 238U3O8 samples were prepared, their nucleus number and unevenness were determined using the α spectrum measured by the GIC and details of the method can be found in Ref. [19]. A 238U3O8 sample 43.0 mm in diameter, 62.1% in unevenness and 600.8 μg/cm2 in average thickness at No.2 sample position was used to determine the absolute neutron flux. The other two 238U3O8 samples were glued on the two fission cathodes of the 01 side and 02 side to determine the relative neutron flux, respectively. Their diameters were 45.0 mm and 43.0 mm, unevennesses were 61.6% and 63.3%, and average thicknesses were 604.6 μg/cm2 and 557.5 μg/cm2, respectively. c) Two 58Ni at No.3 sample position, one 60Ni and one 61Ni samples at No.4 sample position were used for the measurement of the foreground events, the data of which are listed in Table 2. The number of the Ni atoms in the samples was determined by weighing the samples. Each Ni sample was prepared on the tantalum backing 0.1 mm in thickness and 48.0 mm in diameter as shown in Fig. 2; d) The back-to-back tantalum backings 0.1 mm in thickness and 48.0 mm in diameter at No.5 position were used for the measurement of the background events.

      Sample positionSample(01 side)Sample(02 side)Purpose
      No.1α sourceα sourceCalibrating the detection system
      No.2238UTaMeasuring the absolute neutron flux
      No.358Ni#I58Ni#IIMeasuring the foreground of the 58Ni(n, α)55Fe reaction
      No.461Ni60NiMeasuring the foreground of the 60,61Ni(n, α)57,58Fe reactions
      No.5TaTaMeasuring the background of the 58,60,61Ni(n, α)55.57,58Fe reactions

      Table 1.  Sample positions of the sample changer.

      SamplesIsotopic enrichment (%)Thickness(μg/cm2)Diameter(mm)Preparation method
      58Ni#Ia99.84601.346.0Rolling
      58Ni#IIa99.84579.442.0Rolling
      60Nib99.65570.446.0Rolling
      61Nic91.50332.443.5Vacuum evaporation
      a Impurities: 60Ni (0.15%), 61Ni (< 0.01%), 62Ni (0.01%), 64Ni (< 0.01%)
      b Impurities: 58Ni (0.29%), 61Ni (0.03%), 62Ni (0.03%), 64Ni (< 0.008%)
      c Impurities: 58Ni (2.85%), 60Ni (3.8%), 62Ni (1.65%), 64Ni (0.2%)

      Table 2.  Description of the Ni samples.

      Figure 2.  Pictures of the Ni samples.

      The uncertainty of the nucleus number is 1.0% for the 58Ni#I sample and 61Ni sample, and 5.0% for the 58Ni#II sample and 60Ni sample. Although there were two 58Ni samples for measurements, the 58Ni#II sample had fairly big uncertainty of nucleus number because a small section of the 58Ni#II sample was broken during operation. So, the data obtained by the two 58Ni samples would be processed individually, and the cross sections obtained by the 58Ni#II sample were used to check those obtained by the 58Ni#I sample. The correction of the interference from the impurities was detailed in Sect. 3.5.

    • 2.3.   Charged particle detector (GIC)

    • Comparing with previous works of our group [20], a new GIC with symmetric double sections was made and installed, and its structure and the electronics are shown in Fig. 3. The old GIC has been used for ~ 20 years, and it faces several problems, such as the gas leakage of the valve, and the instability of the signal when high voltages were applied to the electrodes. The structure of the new GIC is similar to the old one, but its gas tightness was better, and it has a low-level signal noise for high voltages. Besides, the new GIC has two fission cathodes (each with one 238U sample) to monitor the relative neutron flux, while the old GIC has only one.

      Figure 3.  The structure and the electronics of the GIC: FC, fission cathode; A, anode; G, grid; C, cathode; FIFO, fan in–fan out (CAEN N625); PA, charge sensitive preamplifier (MESYTEC MPR-1); TCU, trigger control unit; SA, signal amplifier (ORTEC 572A); DA, delay amplifier (ORTEC 427A); LG, linear gate (ORTEC 542); SC, single channel analyzer (ORTEC 551); PDA, Signatec PDA14 waveform digitizer; GaGe, GaGe OVE-832-007 high resolution PCIe digitizer.

      The GIC have seven electrodes: a common-cathode, two grids, two anodes and two shields. In the present work, in order to monitor the relative neutron flux, two 238U3O8 samples were glued on each of the shield, respectively. So, the two shields would be used as the fission cathodes of the fission chambers. The distance was 6.1 cm from the cathode to the grid, 1.4 cm from the grid to the anode, 1.0 cm from the anode to the fission cathode, and 15.4 cm from the cathode to the front surface of neutron source. Because there is only one foil for the 60Ni sample and 61Ni sample, the GIC would be rotated by 180° during the experiment so that the forward (0° – 180°) and the backward (90°– 180°) cross sections of the (n, α) reaction could be measured. In order to obtain higher fission counts, only the signal of the fission cathode near the neutron source was used. For the 01 side or 02 side of the GIC, the signals from the cathode and anode were recorded by a PDA14 waveform digitizer, which was triggered by the trigger control unit. The trigger control unit would produce the external trigger, which was generated through the coincidence between the grid and the anode signals. The trigger control unit can effectively improve the anti-noise and anti-background performance of the GIC. The signal from the fission cathode was recorded by a GaGe OVE-832-007 high resolution PCIe digitizer.

      The working gas of the GIC was Xe + 8.5% H2, and the pressure was 0.855 atm so that the α-particles could be stopped before reaching the grids. The high voltages applied on the cathodes and anodes were -1200 V and 600 V (the grids electrodes were grounded) which allowed a complete collection of electrons from the ionization tracks.

      For the GIC, the information of the energy and angular distribution of the detected charged particle can be obtained using the cathode and anode signal amplitudes. If a charged particle emits from the sample on the cathode then stopped by the work gas before it reaches the gird, the cathode signal Vc and the anode signal Va can be represented by [21]:

      ${V_{\rm{c}}} = {G_{\rm{C}}}E\left( {1 - \frac{{\overline X }}{d}\cos \theta } \right)$

      (1)

      and

      ${V_{\rm{a}}} = {G_{\rm{a}}}E\left( {1 - \delta \frac{{\overline X }}{d}\cos \theta } \right) \approx {G_{\rm{a}}}E,$

      (2)

      where Gc and Ga are the ratio constants of the cathode and anode, respectively, which could be determined using the energy calibration; E is the energy of the emitted charged particle; d is the distance between the cathode and the grid; $ \bar{X} $ is the distance from the beginning to the center of gravity of the ionization trace. $ \delta $ is the grid-inefficiency of the GIC, according to the theoretical calculation, the grid-inefficiency is 0.0121 in the present work, which was quite small. So, the influence of the grid-inefficiency was negligible in the present work. The charged particle can be identified through the determination of the valid area in the cathode-anode two-dimensional spectrum, because according to Eqs. (1) and (2), different charged particles with the same energy and emitting angle would induced the anode and cathode signals with different amplitudes due to their different ionization traces.

    • 2.4.   Scintillator detector

    • An EJ-309 liquid scintillator detector was used to obtain the neutron spectrum by unfolding the measured pulse height spectra [22]. The axis of the scintillator detector was along the normal line of the electrodes of the ionization chamber as well as the 0° direction of the deuteron beam line. The distance from the entrance surface of the scintillator detector to the front surface of the neutron source was 2.60 m.

    • 2.5.   Experimental steps

    • For each neutron energy point, measurements were performed with the sample at the sample position of No.1, No.2, No.3, No.4 and No.5 in turn, then the GIC was rotated by 180°, after that measurements were performed with the sample at the sample position of No.5, No.4, No.3, No.2 and No.1 in turn. The total neutron beam duration was ~ 70 h.

      During the experiment, the fission counts obtained from the 238U3O8 sample glued on the fission cathode near the neutron source was used to monitor the relative neutron flux, and the ratio of the fission counts during the foreground measurement to that during the background measurement was approximately 1:1 – 2:1. The scintillator detector would run for ~ 15.0 min every hour to obtain the neutron spectrum.

    3.   Data processing
    • Firstly, the compound α sources were used to energy calibration and determine the valid area of α events. Secondly, the fission counts from the 238U3O8 samples were calculated in order to determine the absolute and relative neutron flux. Thirdly, the net α events from the 58Ni(n, α)55Fe, 60Ni(n, α)57Fe and 61Ni(n, α)58Fe reactions were obtained in the valid area after the subtraction of background and the detection efficiency of α events were calculated. Fourthly, the α and fission events induced by the low-energy neutrons was corrected. Fifthly, the α events from the impurity isotopes were corrected. Finally, the cross sections of the 58Ni(n, α)55Fe, 60Ni(n, α)57Fe and 61Ni(n, α)58Fe reactions were obtained, and the spread of neutron energy was unfolded into the specific energy using the iterative method.

    • 3.1.   Calibration of the detection system using the compound α sources

    • The energy response of the detection system was calibrated using the compound α sources. The energy of each channel could be calibrated using the four α energy groups as shown in Fig. 4. According to Eqs. (1) and (2), for the α particles, if let the emitting angles equal 0° and 90°, respectively, the 0° curve and 90° line can be drawn in the cathode-anode two-dimensional spectrum as shown in the Fig. 4, by which the valid area of α events can be determined. Taking the fluctuation of energy resolution into consideration, the valid area is a little lager than the region between the 0° curve and 90° line as the two red dashed curves shown in Fig. 4.

      Figure 4.  The measured cathode-anode two-dimensional spectrum of the compound α sources in the forward direction.

    • 3.2.   Statistics of the fission counts

    • The total fission counts from the 238U3O8 sample were used to determine the absolute neutron flux. A typical anode spectrum of the fission fragments is shown in Fig. 5 as an example.

      Figure 5.  The anode spectrum of the fission fragments for the absolute neutron flux measurement at En = 5.50 MeV.

      The detection efficiency (εf) of the fission fragments for the absolute neutron flux measurement is (75.55 – 84.93)% in the present work. The Monte Carlo simulation was used for threshold and self-absorption corrections. The simulation code was written using the Matlab-2019a [23]. The stopping power of the fission fragments in the samples was calculated by SRIM-2013 [24], the mass distribution of the fission fragments was calculated by the GEF code [25] and the angular distributions of fission fragments was obtained from Ref. [26]. Details of the simulation can be found in Ref. [19]. The black curve in Fig. 5 shows the simulation result for the fission fragments, which agrees well with the measurement spectrum. The shape of the simulation spectrum was nearly invariable for different neutron energy points, because the variation of En was negligible compared with the total kinetic energy (TKE) of 238U fission fragments (~ 170 MeV). The change of εf in the present results was due to the different thresholds. The threshold position was adjusted at different energy points to obtain higher fission counts while avoiding the background. The total fission counts could be determined by the fission counts within the thresholds (Nf) divided by εf.

      As described in Sect. 2.5, the absolute neutron flux was measured as an individual experimental step, while the relative neutron flux was continuously measured for different experimental steps. The relative neutron flux can be obtained using the relative fission counts within the thresholds from the 238U3O8 sample glued on the fission cathode for different experimental steps. For the two fission cathodes, the thresholds were fixed, so the detection efficiency of the fission fragments can be regarded as invariant which can be eliminated when calculating the relative counts.

    • 3.3.   Statistics of the net α events

    • The cathode-anode two-dimensional spectra of the 58Ni(n, α)55Fe, 60Ni(n, α)57Fe and 61Ni(n, α)58Fe reactions were analyzed. Fig. 6(a) shows the two-dimensional spectrum for the measurement of the 58Ni(n, α)55Fe reaction in the forward direction (from the 58Ni#I sample) after subtraction background events at En = 5.50 MeV. The background counts were normalized using the fission counts from the 238U3O8 sample glued on the fission cathode. The effective α events could be selected in the valid area described in Sect. 3.1. Then, the two-dimensional spectrum was projected to the anode channel as Fig. 6(b) shows, in which the thresholds were set in order to separate the effective α events from the background which cannot be subtracted. The counts of net α events within the thresholds (${N_\alpha }$) can be determined by

      Figure 6.  (a) The cathode-anode two-dimensional spectrum after subtracting background events and (b) the anode projection spectrum of the foreground, background and net events for the measurement of the 58Ni(n, α)55Fe reaction in the forward direction (from the 58Ni#I sample) at En = 5.50 MeV.

      ${N_\alpha }{\rm{ = }}N_\alpha ^{{\rm{fore}}}{\rm{ - }}{C^{{\rm{f\_b}}}}N_\alpha ^{{\rm{back}}},$

      (3)

      where $N_\alpha ^{{\rm{fore}}}$ and $N_\alpha ^{{\rm{back}}}$ are the total counts within the thresholds of the foreground and background measurements, respectively. ${C^{{\rm{f\_b}}}}$ is the background normalization coefficient, which is the ratio of the fission counts from the 238U3O8 sample glued on the fission cathode during the foreground measurement to that during the background measurement. The detection efficiency of the α particles were determined from the simulation results of the anode spectrum. The detection efficiency was related to the neutron energy and the threshold, and the details will be described in Sect. 3.4.

    • 3.4.   Correction of the events induced by the low-energy neutrons

    • Through the unfolding of the pulse height spectra measured by an EJ-309 liquid scintillator detector, the neutron spectrum at each energy point was obtained [22]. The neutron energy spectrum at En = 5.5 MeV is shown in Fig. 7 as an example (neutrons with the energy below 1 MeV were ignored because they hardly affect the results). The energy of neutrons has been divided into two parts: the main neutron region around the peak at En = 5.50 MeV, and the low-energy neutron region. The variation of the spectrum resulting from the difference between the positions of the scintillator detector and the GIC has been corrected using the Monte Carlo method [27]. In the present work, the low-energy neutrons account for (9.29 – 16.50)% of the total neutrons, and the α events and fission events induced by those should be corrected. $k_\alpha ^{{\rm{low}}}$ and $k_f^{{\rm{low}}}$ are defined as the proportion of the α events and fission events within the thresholds induced by low-energy neutrons, respectively, and they would be calculated as follows.

      Figure 7.  Neutron spectrum at En = 5.50 MeV (neutrons with the energy under 1 MeV were ignored).

      The angular and energy distribution of the α events from the (n, α) reaction would be changed at different neutron energy points, which lead to the change of the detection efficiency, so the anode spectra induced by the neutrons with different energies should be simulated.

      For the simulation, the relative intensity of the neutrons at different energy bin was obtained from the measured neutron spectrum, the stopping power of α particles in the samples was calculated using SRIM-2013 [24], the angular and energy distributions of α particles were calculated using TALYS-1.9 [28], and the cross section was obtained from the ENDF/B-VIII.0 library as the initial condition [9]. Because the counts of the simulated spectrum may be systematically higher or lower than the measured ones, the simulated spectrum was multiplied by a factor to fit the measurements, which means only the variation trend of the cross section obtained from the ENDF/B-VIII.0 library was used in the present results. The detection efficiencies of α events (εα) were obtained from the simulated spectrum. According to the simulation, εα is 86.73 – 92.64% for the 58Ni(n, α)55Fe reaction in the 4.50 MeV ≤ En ≤ 5.50 MeV region, 69.47 – 87.00% for the 60Ni(n, α)57Fe reaction and 84.11 – 91.48% for the 61Ni(n, α)58Fe reaction in the 5.00 MeV ≤ En ≤ 5.50 MeV region.

      Because the cross sections were not measured for the low neutron energy in the present work, it is necessary to use the evaluation cross sections to calculate the final results. In order to estimate the uncertainty of the evaluation cross sections, other evaluation library, such as the ENDF/B-VII.1 library, was used and the final result has been recalculated again. Then the difference between the new result and the old result was regarded as the uncertainty.

      As an example, Fig. 8 shows the α events of the 58Ni(n, α)55Fe reaction (in the forward direction at En = 5.50 MeV) induced by total neutrons, main neutrons, low-energy neutrons and the neutrons with the specific energy of 5.50 MeV as “Simulation (total neutrons)”, “Simulation (main neutrons)”, “Simulation (low-energy neutrons)”, and “Simulation ([5.50 MeV] neutrons)”, respectively. Using the simulated spectra of “Simulation (low-energy neutrons)” and “Simulation (total neutrons)”, the proportion of α events within the thresholds induced by the low-energy neutrons ($k_\alpha ^{{\rm{low}}}$) could be determined. The values of $k_\alpha ^{{\rm{low}}}$ are (2.93 – 5.25)%, (0.22 – 1.35)% and (2.96 – 4.44)% for the 58Ni(n, α)55Fe, 60Ni(n, α)57Fe and 61Ni(n, α)58Fe reactions, respectively.

      Figure 8.  The measured and simulated anode projection spectrum for the measurement of the 58Ni(n, α)55Fe reaction in the forward direction (from the 58Ni#I sample) at En = 5.50 MeV. The simulated α events were induced by the neutrons in different energy regions.

      As described in Sect. 3.2, the detection efficiency of the fission events could be regarded as invariant with the change of neutron energy when the thresholds were fixed, then it can be eliminated when calculated the proportion of fission events induced by the neutrons with different energies. So, the proportion of the fission events within the thresholds induced by the low-energy neutrons ($k_f^{{\rm{low}}}$) could be determined using the standard cross section of the 238U(n, f) reaction [29] and the measured neutron spectrum. According to calculation, $k_f^{{\rm{low}}}$ is (9.41 – 16.32)% at different neutron energy points.

      The correction coefficient of the events induced by low-energy neutrons (ρlow) was introduced by

      ${\rho ^{_{{\rm{low}}}}}{\rm{ = }}\dfrac{{{\rm{1 - }}k_\alpha ^{{\rm{low}}}}}{{{\rm{1 - }}k_f^{{\rm{low}}}}}.$

      (4)

      The values of ${\rho ^{_{{\rm{low}}}}}$ are 1.064 – 1.132, 1.125 – 1.164 and 1.090 – 1.127 for the 58Ni(n, α)55Fe, 60Ni(n, α)57Fe or 61Ni(n, α)58Fe reactions, respectively. The values of ${\rho ^{_{{\rm{low}}}}}$ are bigger than 1, because the low-energy neutrons would lead to a stronger influence on fission events than that on α events.

    • 3.5.   Correction the α events from the impurity isotopes

    • As shown in Table 2, in addition to the main isotopes in the samples there are some impurity isotopes, including 58Ni, 60Ni, 61Ni, 62Ni and 64Ni isotopes. The α events from 62Ni and 64Ni impurity isotopes can hardly affect the results because the cross sections of the (n, a) reactions of these two isotopes were smaller than those of other isotopes by two order of magnitude [15]. So, only the influences from the 58Ni, 60Ni and 61Ni isotopes were taken into consideration.

      For the measurement of the 58Ni(n, α)55Fe reaction, the interference from the impurities was negligible because the cross sections of the (n, α) reactions of the 60Ni and 61Ni impurity isotopes were fairly small comparing with the 58Ni(n, α)55Fe reaction, and the purity of the 58Ni sample was very high (99.84%). For the measurements of the 60Ni(n, α)57Fe and 61Ni(n, α)58Fe reactions, the interference from the impurities in the samples was non-negligible, because the cross sections of the two reactions were approximately (70 – 90)% lower than that of the 58Ni(n, α)55Fe reaction, and 58Ni was the main impurity isotope in the 60Ni and 61Ni samples.

      In order to correct the interference of the impurity isotopes, the anode spectrum contributed by different isotopic compositions was simulated according to their proportions presented in Table 1. A typical example is shown in Fig. 9. The conditions for simulation were the same as that described in Sect. 3.3 but the cross sections of the (n, α) from the impurity isotopes were obtained from the present results: for the measurement of the 58Ni(n, α)55Fe reaction, the interference from the impurities was negligible, so the cross sections of the 58Ni(n, α)55Fe reaction can be obtained without the correction of the impurity isotopes; then for the measurement of the 60Ni(n, α)57Fe reaction, the interference was mainly from the 58Ni(n, α)55Fe reaction, whose cross sections have been already obtained; lastly for the measurement of the 61Ni(n, α)58Fe reaction, the interference was mainly from the 58Ni(n, α)55Fe and 60Ni(n, α)57Fe reactions, whose cross sections have also been already obtained.

      Figure 9.  The measured and simulated anode projection spectrum for the measurement of the 61Ni(n, α)55Fe reaction in the forward direction at En = 5.50 MeV. The simulated α events were from all isotopes in the 61Ni sample, including 61Ni isotope, 58Ni and 60Ni impurity isotopes.

      Through the simulated results, the counts of the α events from different isotopes could be determined. The proportion of the α events from the impurity isotope (βimpurity) could be determined using the ratio of the simulated counts within the thresholds from the impurity isotopes to those from all isotopes. βimpurity is ~ 0% for the 58Ni(n, α)55Fe reaction, (0.89 – 1.07)% for the 60Ni(n, α)57Fe reaction, and (11.69 – 12.95)% for the 61Ni(n, α)58Fe reaction.

    • 3.6.   Calculation of the cross sections

    • The forward or backward cross sections (σα) of the (n, α) reactions can be calculated by

      ${\sigma _\alpha }{\rm{ }} = {\sigma _f} \cdot \frac{{{N_{\rm{U}}} \cdot {N_\alpha } \cdot {\varepsilon _f} \cdot {\rho ^{_{{\rm{low}}}}} \cdot ({\rm{1 - }}{\beta ^{{\rm{impurity}}}})}}{{{N_{{\rm{Ni}}}} \cdot {N_f} \cdot {\varepsilon _\alpha } \cdot G \cdot {C^{{\rm{f\_}}fission}}}} \cdot {R^{{\rm{unfolding}}}},$

      (5)

      where σf is the standard cross section of the 238U(n, f) reaction, and the values of σf used in the present results are 0.5592, 0.5579, 0.5483, 0.5517 and 0.5482 b at En = 4.50, 4.75, 5.00, 5.25 and 5.50 MeV, respectively [29]. NU and NNi are the numbers of the 238U and 58, 60,, 61Ni nucleus in the samples, respectively. Nα and Nf are the counts of the net α events and fission events described in Sects. 3.3 and 3.2, respectively. εf and εα are the detection efficiencies for the fission fragments and α particles at the specific neutron energy described in Sect. 3.2 and 3.3, respectively. ρlow is the correction coefficient of the events induced by the low-energy neutrons described in Sect. 3.5. βimpurity is the proportion of the α events from the impurity isotope described in Sect. 3.5. G = 0.9890 – 1.003 is the ratio of the average neutron flux in the area of nickel sample to that of the 238U3O8 sample in the sample changer, and G is obtained by the Monte Carlo method (G is introduced because there is a little difference between the diameters of the two samples). Cf_fission is the ratio of the fission counts from the 238U3O8 sample glued on the fission cathode during the foreground measurement to that during the absolute neutron flux measurement. Runfolding is the unfolding coefficient, which will be explained as follows.

      According to the measured neutron spectrum shown in Fig. 7, in the main neutron region, the width of the neutron peak is non-negligible, and the corresponding uncertainty of En is (2.5 – 4.2)% in the 4.50 MeV ≤ En ≤ 5.50 MeV region. The spread of neutron energy could be unfolded using the iterative method. $k_\alpha ^{{{\bar E}_{\rm{n}}}}$ and $k_f^{{{\bar E}_{\rm{n}}}}$, which are the ratios of the counts of α events and fission events within the thresholds induced by the neutrons with the specific energy ${\bar E_{\rm{n}}}$ to those induced by main neutrons, should be determined for the neutron spectrum unfolding.

      $k_\alpha ^{{{\bar E}_{\rm{n}}}}$ can be determined using the simulation method. As shown in Fig. 8, the α events induced by main neutrons and the neutrons with the specific energy ${\bar E_{\rm{n}}}$ can be determined using the simulated counts of “Simulation (main neutrons)” and “Simulation ([5.50 MeV] neutrons)”. The conditions for simulation were the same as that described in Sect. 3.3 except for the cross section of the (n, α) reaction. The forward or backward cross section of the (n, α) reaction was obtained from the last iteration using Eq. (3). Because in the main neutron region, the neutron energies were very close and the excitation functions of the (n, α) reactions are smooth, the cross section can be obtained from the measured results using the linear interpolation or extrapolation method. $k_f^{{{\bar E}_{\rm{n}}}}$ could be determined using the standard cross section of the 238U(n, f) reactions [29] and the measured neutron spectrum.

      Next, the unfolding coefficient Runfolding was calculated by

      ${R^{{\rm{unfolding}}}}{\rm{ = }}\frac{{k_\alpha ^{{{\bar E}_{\rm{n}}}}}}{{k_f^{{{\bar E}_{\rm{n}}}}}}.$

      (6)

      Then, the new cross section σα would be calculated using Eq. (5). This deconvolution process was iterated until the variation of the cross section was less than 0.1% (usually 10 times). Runfolding was set to be 1 as the initial value. In the present work, the final value of Runfolding is 0.9705 – 1.018 which would slightly correct the origin results by (-2.95 – 1.80)%. The value of Runfolding is mainly affected by the average neutron energy in the main neutron region. If the average neutron energy is smaller than the specific energy ${\bar E_{\rm{n}}}$, Runfolding would be bigger than 1, otherwise smaller than 1. The unfolding method could decrease the uncertainty of En from (2.5 – 4.2)% to (1.4 – 1.5)%, and the final uncertainty of En is contributed by the energy resolution of the scintillator detector.

    4.   Results

      4.1.   Measured results

    • The forward and backward cross sections of the 58Ni(n, α)55Fe, 60Ni(n, α)57Fe and 61Ni(n, α)58Fe reactions can be calculated using Eq. (5). Sources of uncertainty and their magnitudes are presented in Table 3. Total (n, α) cross section could be acquired by adding the forward cross section and backward one together. And forward/backward ratios in the laboratory reference system could be obtained through the division of them. The results are shown in Tables. 46 and Figs. 1012 (results of the 58Ni(n, α)55Fe reaction were obtained from the 58Ni#I sample).

      SourceMagnitude (%)
      58Ni(n, α)55Fe60Ni(n, α)57Fe61Ni(n, α)58Fe
      NU1.0a, b1.0a, b1.0a, b
      NNi1.0a, b5.0a, b1.0a, b
      σf0.6 – 0.7 a, b0.6 – 0.7 a, b0.6 – 0.7 a, b
      Nα2.9 – 4.4 a, 2.7 – 5.0 b8.0 – 11.6 a, 13.2 – 18.5 b6.4 – 7.0 a, 8.3 – 8.5 b
      Nf1.0 – 1.1 a, b1.0 – 1.1 a, b1.0 – 1.1 a, b
      ρlow1.4 – 1.7 a, 1.0 – 2.1 b1.4 – 1.6 a, 1.5 – 1.6 b1.4 – 1.7 a, 1.5 – 1.7 b
      εf1.9 – 3.1 a, b2.1 – 3.1 a, b2.1 – 3.1 a, b
      εα1.8 – 3.2 a, 2.2 – 3.3 b3.3 – 6.2 a, 6.5 – 7.6 b2.2 – 4.0 a, 2.1 – 3.5 b
      G< 0.5 a, b< 0.5 a, b< 0.5 a, b
      βimpurity––< 0.1 a, b1.8 – 2.0 a, 1.8 – 1.9 b
      Runfolding1.0 – 2.1 a, 1.0 – 2.7 b2.0 – 3.7 a, 1.0 – 4.6 b0.3 – 1.1a, 0.5 – 1.1b
      En(later error after the unfolding process)1.4 – 1.5 a, b1.4 – 1.5 a, b1.4 – 1.5 a, b
      σα5.2 – 6.6 a, 5.3 – 7.6 b, 5.2 – 7.0 c11.6 – 12.8 a, 15.7 – 20.4 b,13.9 – 15.0 c8.6 – 8.7 a, 9.8 – 10.2 b,9.0 – 9.4 c
      a For the forward cross section
      b For the backward cross section
      c For the total cross section (forward cross section + backward cross section)

      Table 3.  Sources of the uncertainty and their magnitudes.

      En(MeV)Cross section (mb)Forward/backward ratio
      MeasurementCalculationMeasurementCalculation
      4.50 ± 0.0725.7 ± 1.324.60.96 ± 0.071.05
      4.75 ± 0.0728.7 ± 2.030.71.03 ± 0.101.05
      5.00 ± 0.0737.2 ± 2.236.81.03 ± 0.091.05
      5.25 ± 0.0844.6 ± 2.742.91.05 ± 0.091.05
      5.50 ± 0.0851.7 ± 3.048.71.04±0.081.04

      Table 4.  Measured 58Ni(n, α)55Fe cross sections and forward/backward ratios in the laboratory reference system (results were obtained from the 58Ni#I sample) compared with TALYS-1.9 calculations using the adjusted input parameters.

      En(MeV)Cross section (mb)Forward/backward ratio
      MeasurementCalculationMeasurementCalculation
      5.00 ± 0.079.40 ± 0.849.361.04 ± 0.131.05
      5.50 ± 0.0811.9 ± 1.112.01.00 ± 0.131.04

      Table 6.  Measured 61Ni(n, α)58Fe cross sections and forward/backward ratios in the laboratory reference system compared with TALYS-1.9 calculations using the adjusted input parameters

      Figure 10.  The present 58Ni(n, α)55Fe cross sections (obtained from the 58Ni#I sample) compared with existing measurements and evaluations and TALYS-1.9 calculations [8, 15, 28, 30].

      Figure 12.  The present 61Ni(n, α)58Fe cross sections compared with existing measurements and evaluations and TALYS-1.9 calculations [8, 15, 28, 30].

      Figure 11.  The present 60Ni(n, α)57Fe cross sections compared with existing measurements, evaluations and TALYS-1.9 calculations [8, 15, 28, 30].

      As described in Sect. 2.2, the present cross sections of the 58Ni(n, α)55Fe reaction were obtained from the 58Ni#I sample, and they were checked using the results obtained from the 58Ni#II sample as Fig. 13 shows. Results obtained from the two samples agreed with each other, by which the reliability of the measurement results has been verified.

      Figure 13.  The present 58Ni(n, α)55Fe cross sections obtained from the 58Ni#I and 58Ni#II samples compared with evaluations and TALYS-1.9 calculations [15, 28, 30].

    • 4.2.   Theoretical calculation using TALYS-1.9

    • TALYS-1.9 [28] was used to calculate the cross sections of the 58Ni(n, α)55Fe, 60Ni(n, α)57Fe and 61Ni(n, α)58Fe reactions. To agree better with the present results, several input parameters including those of the optic, the level density and stripping models were adjusted from the default input values as listed in Table 7 (parameters of the stripping model mainly affect the results for En > 10.0 MeV). The calculated cross sections and forward/backward ratios agree well with the measured results as presented in Tables 46 and Figs. 1012. With the adjusted parameters, the calculated cross sections of other major reaction channels including the (n, tot), (n, el), (n, n’) and (n, p) reactions, and the angular distributions of elastic scattering have been checked. The calculated results of these reactions also agree well with most existing measurements and evaluations, by which the reliability of the adjusted parameters was verified.

      58Ni(n, α)55Fe60Ni(n, α)57Fe
      KeywordParameterKeywordParameter
      rvadjust ap 1.03rvadjust ap 1.14
      rvadjust aa 0.92rvadjust aa 1.091
      rwadjust aa 1.58aadjust b28 60 1.14
      tljadjust aa 0.50 1
      tljadjust aa 1.50 1
      tljadjust aa 3.00 2
      tljadjust aa 2.02 361Ni(n, α)58Fe
      aadjust b26 55 0.90KeywordParameter
      Tadjust b26 55 0.95rvadjust ap 1.12
      cstrip ca 0.80rvadjust aa 1.02
      a Parameters of the optic model [28].
      b Parameters of the level density model [28].
      c Parameters of the striping model [28].

      Table 7.  Adjusted input parameters of TALYS-1.9

    • 4.3.   Comparison of the results with existing measurements and evaluations

    • The present cross sections were compared with existing measurement data obtained from the EXFOR library [8] and evaluations obtained from the ENDF/B-VIII.0 [9], ENDF/B-VII.1 [10], JENDL-4.0u+ [11], JEFF-3.3 [12], ROSFOND-2010 [13], CENDL-3.1 [14] and TENDL-2019 [30] libraries:

      1) For the 58Ni(n, α)55Fe reaction, the present cross sections in the 4.50 MeV ≤ En ≤ 5.50 MeV region agree well with the measurement data of Fessler (1999, 5.36 MeV – 19.4 MeV) [7], T. Sanami (1998, 4.51 – 6.51 MeV) [2], S. M. Qaim (1984, 5.36 – 9.49 MeV) [3] and the ENDF/B-VII.1 evaluation [10]. Besides, the excitation function calculated using TALYS-1.9 with the adjusted parameters also accords with the ENDF/B-VII.1 evaluation [10].

      The present cross sections are 21.6% lower than the measurement data of Gledenov (1997, 5.00 – 7.00 MeV) [6] and 79.1% higher than those of Goverdovskiy (1992, 5.12 MeV) [4] in the 4.50 MeV ≤ En ≤ 5.50 MeV region. Comparing with other measurement data in this neutron energy region, the results of Gledenov [6] and Goverdovskiy [4] are the highest and the lowest values, respectively. Uncertainties of their results are larger than 10%, while those of the present results are smaller than 7%. The measurement data of V. V. Ketlerov (1996, 3.55 – 6.83 MeV) [5] suggest that there is a “valley structure” of the excitation function around En = 4.92 MeV. However, the present results as well as all the evaluations do not show this structure [9 - 14, 30].

      2) For the 60Ni(n, α)57Fe reaction, there is only one measurement (Khromyleva (2018, 6.00 – 7.15 MeV) [16] in the MeV region which consistent with our measurement results. The present cross sections agree well with the data from the JEFF-3.3 (= ROSFOND-2010) library [12, 13]. The excitation function calculated using TALYS-1.9 with the adjusted parameters accords with both measurements and the JEFF-3.3 (= ROSFOND-2010) library [12, 13].

      3) For the 61Ni(n, α)58Fe reaction, there is no measurement in the MeV region, and there is fairly big deviation among different evaluations. Comparing with different evaluations, the present results agree better with the ENDF/B-VIII.0 library [9]. The excitation function calculated using TALYS-1.9 with the adjusted parameters is close to the ENDF/B-VIII.0 library for En < 6.0 MeV [9] and the TENDL-2019 library for En > 6.0 MeV [30].

      As Tables. 4, 5 and 6 present, nearly symmetrical distributions for forward and backward directions of the outgoing alpha-particles mean that the compound mechanism predominates for the 58Ni(n, α)55Fe and 61Ni(n, α)58Fe reactions. However, in the case of the 60Ni(n, α)57Fe reaction, the slight non-statistical effect may be available.

      En(MeV)Cross section (mb)Forward/backward ratio
      MeasurementCalculationMeasurementCalculation
      5.00 ± 0.074.22 ± 0.634.031.31 ± 0.311.06
      5.50 ± 0.087.87 ± 1.098.101.32 ± 0.271.05

      Table 5.  Measured 60Ni(n, α)57Fe cross sections and forward/backward ratios in the laboratory reference system compared with TALYS-1.9 calculations using the adjusted input parameters

    • 4.4.   Future plan

    • Above En = 5.50 MeV region, the cross sections of the 58Ni(n, α)55Fe, 60Ni(n, α)57Fe and 61Ni(n, α)58Fe reactions are noticeably growing with the increasing of the neutron energy. The cross sections of the three reactions in the 8.50 MeV ≤ En ≤ 10.50 MeV region are approximately 2 – 10 times larger than those in the 4.50 MeV ≤ En ≤ 5.50 MeV region [9]. However, in the 8.50 MeV ≤ En ≤ 10.50 MeV region, the existing measurement data for the 58Ni(n, α)55Fe reactions are scarce, and there is no measurement for the 60Ni(n, α)57Fe and 61Ni(n, α)58Fe reactions [8]. Also, there are big discrepancies among different evaluations in this neutron energy region [9]. Taking these factors into consideration, measurements of the cross sections of the three reactions are planned in the 8.50 MeV ≤ En ≤ 10.50 MeV region based on the HI-13 tandem accelerator of China Institute of Atomic Energy (CIAE).

    5.   Conclusions
    • In the present work, the cross sections of the 58Ni(n, α)55Fe, 60Ni(n, α)57Fe and 61Ni(n, α)58Fe reactions have been measured in the 4.50 – 5.50 MeV neutron energy region based on the 4.5-MV Van de Graaff accelerator, GIC detector, enriched nickel isotopic foil samples, 238U3O8 samples and EJ-309 liquid scintillator detector. The present data of the 58Ni(n, α)55Fe reaction are consistent with the data of most existing measurements and the ENDF/B-VII.1 evaluation [8, 10]. The present data of the 60Ni(n, α)57Fe reaction are the first measurement results below 6.0 MeV, and those of the 61Ni(n, α)58Fe reactions are the first measurement results in the MeV region. The calculated results using TALYS-1.9 with the adjusted parameters agree well with the present data. Considering the discrepancies among existing measurements and evaluations, the present results would be significant to clarify the deviations.

      The authors are indebted to the operation crew of the 4.5-MV Van de Graaff accelerator of Peking University. Dr. Qiwen Fan from China Institute of Atomic Energy is appreciated for preparing the 58Ni, 60Ni and 61Ni samples.

Reference (30)

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