Extension of a nuclear reaction calculation code CCONE toward higher incident energies — multiple preequilibrium emission, and spectrum in laboratory system

Abstract

A nuclear reaction calculation code CCONE, which was developed for nuclear data evaluation for JENDL/AC-2008 and JENDL-4, has been upgraded to improve the prediction accuracy for calculated cross sections at nucleon incident energies higher than 20 MeV. Multiple particle emission, in which nucleons and complex particles up to α-particle are involved, from pre-equilibrium reaction process was implemented based on the sequential-decay calculations for all produced exciton states within the framework of the two-component exciton model. The effect of velocity-change of particle-emitting nuclei on the multiple emission in preequilibrium and compound processes, which was not included in the previous evaluations, was taken into account to obtain spectra in the laboratory system using an average velocity approximation for each composite/compound nucleus. Calculated nucleon emission spectra at nucleon incident energies from 20 to 200 MeV were compared with experimental and evaluated data for the proton- and neutron-induced reactions on ²⁷Al. The present results are in good agreement with experimental data. It was found that their predictions were better than those of JENDL/HE-2007 especially for low emission energies at high incident energies.

Keywords:

• nuclear reaction
• cross section
• energy spectrum
• preequilibrium process
• exciton model
• multi-particle emission
• cluster emission
• nuclear data

1. Introduction

The latest version of Japanese Evaluated Nuclear Data Library, JENDL-4.0 [1], was released in 2010. It included the cross sections for neutron-induced reactions below 20 MeV mainly for nuclear energy applications. At Nuclear Data Center, Japan Atomic Energy Agency(JAEA), it was planned to place emphasis on higher energy data after the release of JENDL-4.0. A special purpose file for high energy nuclear data was released as JENDL High Energy File 2004 (JENDL/HE-2004) for 66 nuclides [2] in 2004. Its updated version JENDL/HE-2007 [3], which included 107 nuclides, was released in 2007. They contained cross sections for neutron- and proton-induced reactions up to 3 GeV. The data were evaluated mainly using the GNASH code [4] below 150–250 MeV. For many nuclides [5–8] in JENDL-4.0, the cross sections up to 20 MeV above resonance regions were evaluated by the CCONE code [9]. The CCONE code uses modern nuclear reaction modelings and parametrizations integrating direct, preequilibrium and compound reactions and also has large flexibility such as unrestricted number of nuclei produced by sequential evaporation of particles from excited nuclei realized by the object-oriented approach with C++ programming language. At incident energies higher than several tens of MeV, it is known that the multiple particle emission by preequilibrium process becomes significant [10–12] not only for emitted-particle energy-spectra, but also for residual nucleus productions. The GNASH code took account of it, but the CCONE code did not. To make the predicting power better for the higher incident energies than 20 MeV, the present work was undertaken to incorporate a function of the multiple preequilibrium particle emission into the CCONE code.

Both CCONE and GNASH use the exciton models, which have been successfully applied to nuclear data evaluation and adopted in many other nuclear reaction modeling codes such as POD [13], TALYS [14], EMPIRE [15] and CoH [16,17]. The GNASH code uses the one-component exciton model and the number of particle emission in the pre-equilibrium process is limited to two. The two-component exciton model [18], which distinguishes between proton and neutron exciton states, was adopted in TALYS with no limitation on the number of preequilibrium particle emission [14,19]. In the original CCONE code, the two-component version [18,19] was adopted with modification so as to conserve the flux of occupation probability in the master equation [9] by limiting one particle emission.

The present work aims to extend the applicability of the CCONE code toward higher incident energy region up to 200 MeV by adding a function of multiple preequilibrium particle emission. The applicable incident energy region is determined by the parametrizations used for the optical and exciton models [19,20]. The code has been improved so that there is no limitation on the number of preequilibrium particle emissions in principle; the number is limited by maximum calculation step, which is defined as an input parameter. Nucleons and complex particles up to α-particle are taken into account in the emitting process.

The particle-emission spectrum is usually given in the center of mass system (CMS) by the theoretical model calculations such as the exciton and statistical models. At high incident energies, an effect of boost of the system becomes important to obtain spectra in the laboratory system (LS) especially for light nuclei. The LS spectra are needed to compare with experimental data and to apply to particle transport calculations. The codes such as GNASH and TALYS give only CMS spectra. The CCONE code also could not calculate LS spectra in the previous work [9]. It does not matter when the code is mainly applied to the evaluations for heavy nuclides where the effect of boost is not significant. However it is not ignorable for light nuclei at high incident energies.

In the multiple emitting process for both preequilibrium and compound reactions, the velocities of the residual composite/compound nuclei would be varied by the particle emission, which affects the LS spectra; in this paper “composite nuclei” are used for the nuclei on the preequilibrium process to be distinguished from the ones on the compound reaction. However, it is difficult to calculate the velocities of the composite systems accurately because they depend on the energy and angle of all preceding emitted particles. In JENDL/HE-2004 and JENDL/HE-2007, LS spectra were obtained by assuming that all composite/compound nuclei have the same velocities as that of the first composite system, i.e. velocities of the residual nuclei are not changed by particle emission.

In the present work, LS spectra are calculated by taking account of velocity changes of the composite nuclei caused by particle emission, which are not considered in preequilibrium and compound processes so far. It is achieved by an approximated way using average velocities of composite/compound nuclei, which makes it easy to calculate LS spectra significantly. Because the effect is large for light nuclei, the spectra from the nucleon-induced reactions for ²⁷Al, which is one of the lightest nuclei in the present parametrization (A ≥ 24) [19] having abundant experimental data, are studied.

Since the present work attempted to check the applicability of the modeling, the model parameters were not adjusted. No comparison is made with the calculations by other codes because the calculations show large dependence on parameter sets and modeling selected in the calculations by each code. In addition, it is difficult to compare LS spectra that cannot be calculated by other codes. However, the present results are compared with the data of JENDL/HE-2007 to see improvements in nuclear data evaluation using the upgraded CCONE code.

In this paper, the methods of the multiparticle preequilibrium emission and of calculation of spectra in LS are described in Section 2. Impacts of the present modifications are shown in Section 3 by comparing the data calculated by the present model with experimental data and evaluated data of JENDL/HE-2007 for the nucleon-induced reactions on ²⁷Al. Conclusions are stated in Section 4.

2. Method

2.1. Multi-particle emission exciton model

The two-component exciton model in the CCONE code, which is described in detail in Ref. [9], is extended toward higher incident energies by taking account of multi-particle emission on the preequilibrium process. A schematic view of the multi-particle emission exciton model (MPEM) is shown in Figure 1 , where the proton and neutron components are not distinguished for simplicity. In the figure, a preequilibrium reaction starts from an initial state with one particle and zero hole (1p-0h) for the first ZA composite nucleus, which is indicated by the top box on the left edge. The symbol ZA shows a set of the atomic and mass numbers of the composite nucleus involved in the preequilibrium process. In the single particle emission model (SPEM), only change of the exciton states at the same excitation energy as the initial one is considered. The changes of exciton states are indicated by right arrows in Figure 1, where particle–hole annihilation is ignored. In SPEM, the residual composite nucleus was assumed to form an equilibrium compound state without emitting any particles, once a particle in an exciton state was emitted. On the contrary, in MPEM the residual nucleus, ZA − 1, stays in the preequilibrium process with decreasing the particle number of exciton, which is indicated by the down arrows in Figure 1. The residual composite state has the excitation energy depending on the energy of the emitted particle. Then the composite nuclei would have certain distribution not only on particle–hole numbers of exciton states, but also on excitation energies, which cause the increase in the number of degree of freedom in the exciton model.

Figure 1 Schematic view of multiparticle emission exciton model. Each box shows a potential well having fixed numbers of particles and holes indicated by closed circles above Fermi energy E _f and open ones below it, respectively. Transitions of exciton states are indicated by right and down arrows between the same composite nuclei and the different ones, respectively. The right-up arrows mean particle emission. Details are given in the text

In MPEM, energy spectrum σ _b (ε) of b particle emission for T(a, xb) reaction is given by

where σ _a is the reaction cross section to form the initial exciton state, which is calculated by the optical model with subtracting direct-reaction contributions. The symbols Q(ZA, ξ _i , E) and W _b (ZA, ξ _i , E, ε) are time-integrated occupation probability and b-particle emission rate with an energy ε, respectively, for composite nucleus ZA in the exciton state ξ _i at an excitation energy E. The ξ _i is a set of the particle–hole numbers defined by ξ _i = (p _{π, i} , h _{π, i} , p _{ν, i} , h _{ν, i} ), where p _{π, i} , h _{π, i} , p _{ν, i} and h _{ν, i} are the numbers of proton particles, proton holes, neutron particles and neutron holes for the ith state, respectively.

The Q(ZA, ξ _i , E) is obtained by sum of two terms, i.e.,

where the first term Q ₊(ZA, ξ _{i − 1}, E) indicates a contribution of the particle–hole creations on the same nucleus at the same excitation energy E, and the second term, which is added in MPEM, is due to residual composite nucleus production by emitting a particle x; x would be one of proton, neutron, deuteron, triton, ³He, or α-particle.

The term Q ₊ is obtained by solving the master equation (5) in Ref. [9] for each composite nucleus at the excitation energy E. A vector expression of Q ₍₊₎ (= Q or Q ₊) is given by

with

where and are the minimum hole-numbers for ZA nucleus given by and , respectively; Z _T and N _T are the proton and neutron numbers of the target nucleus, respectively. The symbol η _p indicates a set of the exciton states (), whose total particle-number is p. In the same way as in Ref. [9], Q₊ is given by

where A and B are the transition rate matrices given by Equations (9)– (15) in Ref. [9].

In the second term on the right-hand side in Equation (2), ZA _c , ξ _c and E _c are the ZA number, exciton state and excitation energy, respectively, for the composite nucleus contributing to Q(ZA, ξ _i , E) through emission of an x particle of energy ε _x . The sum and integration are made to satisfy the conditions,

where S(ZA _c , x) is the separation energy of x from nucleus ZA _c .

Equation (2) is calculated sequentially from the initial exciton state ξ₀ = (Z _a , 0, N _a , 0) of the first composite nucleus ZA ₀ = ZA _T + ZA _a in increasing and decreasing orders in ξ _i and ZA, respectively, where ZA _T and ZA _a indicate the ZA numbers for the target and the projectile, respectively. The change of the exciton states given by Equation (7) is calculated up to six steps for each composite and the final residue is fed into the statistical model.

2.2. Spectrum in LS

When multi-particle emission occurs at high incident energies, it is not adequate to define the spectrum in CMS because the individual emitting nuclei have different velocities depending on the preceding particle emission and the resulting spectrum observed in LS might be varied depending on the boost of the CMS especially for light nuclei. In such a case, we should use LS to compare calculated energy spectra with measured ones. Therefore, it is needed to transform spectra in CMS, which is used in the nuclear model calculation, to the ones in LS. However, it is not easy to obtain LS spectra for multiple emitting systems since the velocity and its direction of the composite nucleus vary depending on the energies and angles of all preceding particle emission. Hence, in the present work, the transformation to LS is achieved by an approximated way with average velocities for each composite/compound nucleus. If we assume azimuthal symmetry in particle emission, the average velocities of the composite/compound nuclei have only the z-component where z-axis is taken to the incident direction. Then the use of average velocity V _z makes it quite easy to calculate LS spectra. The present work is done within non-relativistic framework.

The value of V _z depends on the nucleus ZA, excitation energy E and exciton state ξ. Using superscript i by indicating (ZA, ξ _i , E), the symbols are denoted as Vⁱ _z ≡V_z (ZA, ξ _i , E), Qⁱ ₍₊₎≡Q ₍₊₎(ZA, ξ _i , E) and Wⁱ _x ≡W_x (ZA, ξ _i , E, ε _x ). The Vⁱ _z is given by taking an average over all contributions to the state i,

where Q ⁱ , Qⁱ ₊ and W^j _x are the same as those of Equation (2). The term V ^{i − 1} _z Q ^{i − 1} ₊ is the contribution from the variation of the exciton state that does not change the velocity. The V ^j,x _z (ε _x ) indicates the average velocity of residual nucleus ZA resulting from x emission process depending on the kinetic energy ε _x . The value of V ^j,x _z is obtained by adding the change of V _z by particle x emission,

where μ(ε _x ) and V(ε _x ) are the mean cosine of angular distribution of x particle with energy ε _x and the velocity of residual ZA in CMS, respectively. The velocity V(ε _x ) is given by

where ɛ _ZA is the kinetic energy of ZA in CMS, and m _x and m _ZA show the masses of x and ZA, respectively. The mean cosine μ(ε _x ) is obtained by taking an average over emission angle,

where f(ε _x , θ _x ) is the angular distribution of the x emission in CMS. For f(ε _x , θ _x ), a systematics proposed by Kalbach [21] is used in the present work. The systematics gives the angular distribution of inclusive spectrum depending on the separation and kinetic energies of both of projectile and ejectile for preequilibrium spectrum. The components of multiple emission have ambiguities. However, only the first particle emission, for which there is no ambiguity by adopting the systematics, is important in the high emission energy region where anisotropy is large. On adopting the Kalbach systematics after the second particle emission, the projectile energy is set to the same as the first ones and separation energies of projectile and ejectile are calculated from each composite nucleus.

The double differential cross sections (DDXs) of x from the state i in CMS is given by

where Ω _x = (θ _x , φ _x ) and φ _x is the azimuthal angle. Since the symbol ε _x means the relative kinetic energy in the x particle emission channel, which is used in exciton model calculations, the energy and cross section are converted those for x particle in CMS. The x particle energy in CMS is given by

and the corresponding DDX is

Since the kinetic energy and cosine of emitted x in LS are given by

with and μ _x = cos θ _x , the DDX in LS is obtained by

where is the Jacobian of the variable transformation from CMS to LS, which is obtained from Equations (19) and (20).

Finally the total DDX in LS is obtained by integrating Equation (21) over all exciton states, excitation energies and composite nuclei.

The velocity change of compound nucleus affects the DDXs of the statistical model. They are also taken into account in the similar way described above. The initial velocities of the compound nuclei are set to those of the residues in the preequilibrium process.

2.3. Model parameters

The global nucleon optical model potential (OMP) by Koning and Delaroche [20] was used for all calculations in the present work. The parameters for the exciton model were taken from the work of global preequilibrium analysis by Koning and Duijvestijn [19]. The global level density parameters given by Mengoni and Nakajima [22] were used for the statistical model calculations.

The distorted wave Born approximation is used to calculate inelastic scattering cross sections for giant resonance states (monopole, quadrupole, and low and high energy octopole ones) with a global parametrization given by Kalbach [23].

The global OMP was used to calculate shape-elastic scattering cross sections, reaction cross section to create the first composite nucleus, inverse reaction cross section for the exciton model, and transmission coefficients for the statistical model. For the complex particles such as an α-particle, a folding model of OMP [14] was applied.

3. Results and discussion

3.1. Multi-particle emission

The DDXs calculated with MPEM are compared with those of SPEM in Figure 2 for the ²⁷Al(p,xn) reactions at an incident energy of 113 MeV. The thick solid and dashed lines show the results of the total DDXs with MPEM and SPEM, respectively. The dotted lines show the preequilibrium spectra decomposed into the composite nucleus components. The hardest spectrum is from the first composite ²⁸Si and the next one is from the second composite ²⁷Al created by emitting proton from ²⁸Si. These two spectra mainly contribute to the total neutron emission spectra of MPEM. The SPEM spectrum that lacks the preequilibrium spectra from ²⁷Al shows significant under estimation above around 10 MeV. Thin solid and dashed lines indicate the DDX components of evaporation spectra for MPEM and SPEM, respectively. The spectra are decomposed into compound nucleus components. It is seen that the spectra of evaporated neutrons of SPEM become harder and larger than those of MPEM. Especially for the ²⁷Al, the difference between SPEM and MEPM is large. It is clear that SPEM fails to predict the experimental data by Meier et al. [24] not only in the high energy region, where the preequilibrium is important, but also in the low energy region, because the underestimation of the high energy part in the spectrum leads to the overestimation of the excited energies of the residual nuclei, which causes the larger emission possibility of particle emission in statistical process and results in the overestimation of low energy part of the spectrum. On the other hand, the result of MPEM agrees well with the experimental data. In the high energy region around 100 MeV, multiparticle emission from preequilibrium process plays a significant role. It is obvious that MPEM is needed to reproduce experimental data.

Figure 2 Comparison of the results of multi- and single-particle emission models. Double-differential cross sections (DDXs) for the ²⁷Al(p,xn) reaction at 113 MeV. Solid lines show the DDXs calculated allowing multiparticle emission in the exciton model. The dotted lines show preequilibrium component by the exciton model from various composite nucleus. Dashed lines are the results obtained by restricting the number of emitted particle to one in the exciton model. Thin solid and dashed lines are evaporation spectra from statistical model calculations for MPEM and SPEM, respectively. Thick lines are the total DDXs. Thin lines were separated contributions from composite and compound nuclei. Nuclide-names are shown with and without the parentheses for evaporation and preequilibrium spectra, respectively

3.2. Effect of CMS boost

The effects of the boost of the composite nucleus are shown in Figure 3 . The LS DDXs of ²⁷Al(p,xn) for 113 MeV protons at 7.5, 30 and 60°. laboratory angles were calculated in three different conditions. The solid lines are the results by the present method described in Section 2. The dashed and dotted lines are the DDXs calculated using V _z = V _z0 and V _z = 0, respectively. The symbol V _z0 stands for the velocity of the first composite. At 7.5°, the effect of the boost is the largest. At the high energy end, the DDX of the present method coincides with that of V _z = V _z0, which indicates the theoretically expected maximum energy, while the results of V _z = 0 obviously underestimate the high energy edge. On the other hand, in the low energy region between 1 and 10 MeV, the result of V _z = V _z0 fails to predict the measured spectra and that of V _z = 0 shows rather small value. By contrast, the present result located between them agrees well with the experimental data. For larger angles, the differences of the three methods become smaller as shown in Figure 3.

Figure 3 Comparison of DDX with different velocities of composite nuclei for the ²⁷Al(p,xn) reaction at 113 MeV. The solid lines show the result with the present method. The dashed lines show the results with the assumption that the velocity is equal to the initial compound nucleus. The dotted lines are the results assuming that the velocities of composite nuclei are zero. The DDXs are multiplied by factors shown in the figure for visualization

The present method gives better agreement with experimental data in predicting LS spectra than the other approximations using V _z = V _z0 and V _z = 0, especially for the low energy region where the evaporation spectra from the statistical model is a dominant component. It is important to estimate the velocities of compound nuclei that are produced through the preequilibrium process. Thus the consistent calculation of average velocities for both of preequilibrium and statistical processes is needed. It is concluded that the present average velocity method is adequate to calculate the LS spectra.

Note that underestimation of all calculations at 7 and 30°on high energy sides might be due to lack of direct reaction contributions such as quasi-elastic scattering, isobaric analog and Gamov-Teller resonances [25], which are not considered in the present work.

3.3. Comparison with experimental and evaluated data

Figures 4 and 5 show the DDXs for the ²⁷Al(p,xp) reactions for 61.7 and 200 MeV protons, respectively. The present results are compared with the experimental data and the evaluated data of JENDL/HE-2007. In comparison with the experimental data by Bertrand and Peelle [26], the present results slightly underestimate those of 11 and 160°and overestimates those between 16 and 110°. The evaluated data of JENDL/HE-2007 show similar tendency to the present results. For the DDX at 160°, the JENDL/HE-2007 evaluation is in better agreement with the experimental data of Bertrand and Peelle than the present work. However, the present result for ²⁷Al(n,p) reaction at similar energy 62.7 MeV, which will be shown below, agrees well with the experimental data at a backward angle 177°, where JENDL/HE-2007 overestimates them. It is difficult to explain the reason why this inconsistency is seen. Further investigations are needed on this point. On the other hand, the present calculations well reproduce the data at 200 MeV as shown in Figure 5, although the JENDL evaluation deviates from the measurements. Note that the elastic scattering peak of JENDL at 20°seems to be overestimated in comparison with the experimental data, while the present result gives good agreement.

Figure 4 DDX for the ²⁷Al(p,xp) reaction at 61.7 MeV. The symbols indicate the experimental data by Bertrand and Peelle [26]. The solid and dashed lines show the present results and evaluated data of JENDL/HE-2007 [3], respectively. The DDXs are multiplied by factors shown in the figure for visualization

Figure 5 DDX for the ²⁷Al(p,xp) reaction at 200 MeV. The solid squares and open circles indicate the experimental data of Förtsch et al. [27] and Avan et al. [28], respectively. The solid and dashed lines show the present results and evaluated data of JENDL/HE-2007 [3], respectively. The DDXs are multiplied by factors shown in the figure for visualization

The neutron emission spectra for the proton-induced reactions on ²⁷Al are compared with the experimental data and the evaluated data of JENDL/HE-2007 in Figures 6 – 8 . The present results are in good agreement with the experimental data for low emission energy region where neutron evaporation from compound nuclei is dominant for the energy spectra at 90 MeV and the DDXs at 113 MeV, although the JENDL/HE-2007 evaluation overestimates both of the measurements. For the DDXs for 160.3 MeV protons, the present results cannot reproduce the measured data at 0 and 145°, while better agreement is seen for the angles of 45 and 95°. In the present work, the adjustments of the model parameters were not done. Modifications of the exciton model parameters may improve the results. However, both the present work and JENDL/HE-2007 substantially underestimate the measured data at 145°. It might be difficult to achieve agreement within the present framework. The peaks seen at high emission energies at 0°are considered as direct reaction contributions such as isobaric analog and Gamov–Teller resonances [25], which are not taken into account in the present work. It is needed to include such direct reaction models to improve the DDX at the forward angles.

Figure 6 Energy spectra for the ²⁷Al(p,xn) reaction. The solid and open squares show the experimental data of Kalend et al. [29] at 90 MeV and of Svirin et al. [30] at 22.4 MeV, respectively. The solid and dashed lines show the present results and evaluated data of JENDL/HE-2007 [3], respectively. The spectra are multiplied by factors shown in the figure for visualization

Figure 7 DDXs for the ²⁷Al(p,xn) reaction at 113 MeV. The symbols show the experimental data of Meier et al. [24] The solid and dashed lines show the present results and evaluated data of JENDL/HE-2007 [3], respectively. The DDXs are multiplied by factors shown in the figure for visualization

Figure 8 DDXs for the ²⁷Al(p,xn) reaction at 160.3 MeV. The symbols show the experimental data of Scobel et al. [31] The solid and dashed lines show the present results and evaluated data of JENDL/HE-2007 [3], respectively. The DDXs are multiplied by factors shown in the figure for visualization

Proton emission spectra from the neutron-induced reaction on ²⁷Al are compared in Figure 9 . The present results are in good agreement with the experimental data at incident energies of 28.5–62.7 MeV, while JENDL/HE-2007 slightly overestimates the measured data in the low energy region, which are the tails of proton evaporation. The fluctuation located at high energy edge is originated from the discrete excited states taken into account in the calculation. The DDXs at 62.7 MeV are also shown in Figure 10 . The present results agree well with experimental data from forward (2°) to backward (177°) angles.

Figure 9 Proton energy spectra for the ²⁷Al(n,xp) reaction for neutron energy from 28.5 to 62.7 MeV. Symbols show the experimental data of Benck et al. [32] The solid and dashed lines show the present results and evaluated data of JENDL/HE-2007 [3], respectively. The DDXs are multiplied by factors shown in the figure for visualization

Figure 10 DDXs for the ²⁷Al(n,xp) reaction at 62.7 MeV. Symbols show the experimental data of Benck et al. [32] The solid and dashed lines show the present results and evaluated data of JENDL/HE-2007 [3], respectively. The DDXs are multiplied by factors shown in the figure for visualization

4. Concluding remarks

The present work aimed to extend the applicability of the nuclear reaction calculation code CCONE toward higher incident energy region. Achieving that, a function of multiple emission from the preequilibrium exciton model was incorporated into the code. In addition, the effect of velocity-change of composite nuclei was considered for calculating LS spectra. Importance of the multi-particle preequilibrium emission in predicting emission energy spectra was demonstrated by comparing the spectra with and without multiple emission. It was shown that it affects not only preequilibrium spectra, but also evaporation ones. For LS spectrum calculation, the validity of the present method was confirmed by comparing its predictions with the experimental data.

The calculated results were compared with experimental and evaluated data for the nucleon emission spectra for the proton- and neutron-induced reactions on ²⁷Al. The present results show good agreement with experimental data between 20 and 200 MeV. It was found that the present work gives better agreement with experimental data than those of JENDL/HE-2007 especially in low emission energy regions at high incident energies.

The present work focused on the validation of the models of multiple preequilibrium emission and CMS boost. As the next step, it is needed to investigate predictability to other nuclei, especially to heavy ones, including optimization of the parameters.

Acknowledgements

The author is grateful to the members of the Nuclear Data Center in JAEA for the valuable comments on the present work.