Analyses of JAEA/FNS iron in-situ experiment with latest nuclear data libraries

. We found ENDF/B-VIII.0 caused the following problems through our analyses of the iron in-situ experiment at JAEA/FNS; 1) the neutron flux of 1 - 10 keV is overestimated more in the shallower region of the iron assembly, 2) the reaction rate of 115 In (n,n’) 115m In is underestimated more in the deeper region, 3) the neutron flux above 10 MeV is underestimated more in the deeper region. The reasons for these problems were investigated in detail and it was specified that the inelastic scattering data of 56 Fe in ENDF/B-VIII.0 mainly caused the first and second problems and that the cross section of the (n,2n) reaction and the angular distribution data of the elastic scattering of 56 Fe in ENDF/B-VIII.0 caused the third problem.


Introduction
For the JENDL-5 [1] development we analyzed the iron in-situ experiment [2] at the DT neutron source facility FNS (Fusion Neutronics Source) in JAEA (Japan Atomic Energy Agency) with the two-dimensional Sn code DORT [3] and the latest nuclear data libraries in 2020: JENDL-4.0 [4], ENDF/B-VIII.0 [5] and JEFF-3.3 [6]. As a result, the calculation results with JENDL-4.0 and JEFF-3.3 agreed with the measured data well, while the result with ENDF/B-VIII.0 reproduced the measured data worse than those with JENDL-4.0 and JEFF-3.3.
Here we investigate the reasons of this ENDF/B-VIII.0 issue. Figure 1 shows an experimental configuration of the iron in-situ experiment at JAEA/FNS. The cylindrical iron assembly of 1000 mm in diameter and 950 mm in height was irradiated with the DT neutron source. Neutron spectra over almost the whole energy with an NE213 detector, proton recoil counters, and the slowing down time method and reaction rates of the reactions in Table 1 were measured along the centerline inside the iron assembly. The details of the measurement are described in Ref. 2.

Calculation Method
The two-dimensional Sn code DORT was used because of short calculation time, no statistical error and similar results to those with the Monte Carlo code MCNP [7]. The latest nuclear data libraries in 2020, JENDL-4.0, ENDF/B-VIII.0 and JEFF-3.3, were selected for the analysis of the iron experiment. ENDF/B-VII.1 [8] was additionally used because the calculation result with ENDF/B-VII.1 agreed the measured data better than that with ENDF/B-VIII.0 as described in the next section. MATXS files [9] (neutron: 199 groups) of these nuclear data libraries were produced with the NJOY2016 code [9]. Multigroup libraries for the iron experiment with the self-shielding correction were generated from the MATXS files with the TRANSX code [10].
The P5-S16 approximation was adopted in the calculation. The R and Z intervals of the iron assembly were both 20 mm except for near the boundary of the iron assembly and air, where the intervals were 5 or 10 mm. Before the DORT calculation a first collision source was calculated with the GRTUNCL code [3]. For detail comparison of the measured and calculated neutron spectra, the ratios of the calculated neutron fluxes to the measured ones (C/E) in specific energy regions from the neutron spectra are plotted in        Fig. 6. Most of the calculated neutron fluxes agree with the measured ones within 20%. However, the calculated neutron fluxes above 10 MeV with ENDF/B-VIII.0, JEFF-3.3 and ENDF/B-VII.1 underestimate the measured one at the deeper region and that from 1 to 10 keV with ENDF/B-VIII.0 overestimates the measured one at the shallower region. Figure 7 shows the C/Es of the reaction rates. The C/Es of the 93 Nb(n,2n) 92m Nb and 27 Al(n,a) 24 Na reaction rates are similar with those of the neutron flux above 10 MeV. The C/Es of the 197 Au(n,g) 198 Au reaction rate are similar with those of the neutron flux from 10 to 100 eV. However the C/Es of the 115 In(n,n') 115m In reaction rate have a different trend; only the calculated reaction rate with ENDF/B-VIII.0 underestimates the measured one more at the deeper region, while the other calculation results agree with the measurement well.

Problems of ENDF/B-VIII.0
The following problems of ENDF/B-VIII.0 are found from the calculation results shown in Section 4.
Problem 1: The neutron flux of 1 -10 keV is overestimated more at the shallower region. Problem 2: The reaction rate of 115 In(n,n') 115m In sensitive to neutrons above 0.3 MeV is underestimated more at the deeper region. Problem 3: The neutron flux above 10 MeV is underestimated more at the deeper region. Note that Problem 3 is also true of JEFF-3.3 and ENDF/B-VII.1. We investigate the reasons of these problems in detail.

Problems 1 and 2
In order to specify which iron isotope causes Problems 1 and 2, we replaced the iron isotope files one by one from ENDF/B-VIII.0 to ENDF/B-VII.1, which did not cause the problems, and analyzed the experiment. Figure 8 shows the result, where for example 'ENDF/B-VIII.0 (Fe54:b71)' means that 54 Fe is ENDF/B-VII.1 and the other iron isotopes are ENDF/B-VIII.0, and indicates that 56 Fe in ENDF/B-VIII.0 mainly causes Problems 1 and 2. Note that inelastic scattering and (n,2n) reaction produce secondary neutrons from 1 to 10 keV.
Next, we compared each reaction data of 56 Fe in ENDF/B-VIII.0 with that in ENDF/B-VII.1. Then the inelastic scattering and (n,2n) reaction cross sections were different between ENDF/B-VIII.0 and ENDF/B-VII.1 as shown in Fig. 9. These data of 56 Fe in ENDF/B-VIII.0 were replaced with those in ENDF/B-VII.1 separately and the experiment was analyzed with the modified 56 Fe files. Figure 10  The inelastic scattering consists of the discrete inelastic scattering (mt=4 except for mt=91) and continuum inelastic scattering (mt=91). Figure 11 compares the cross sections of the discrete and continuum inelastic scatterings of 56 Fe in ENDF/B-VIII.0 and ENDF/B-VII.1. Both the cross sections in ENDF/B-VIII.0 are larger than those in ENDF/B-VII.1, but the energy regions of the differences are distinct:     below 7 MeV for the discrete inelastic scattering and around 10 MeV for the continuum inelastic scattering. Then we studied effects of the discrete and continuum inelastic scatterings separately by replacing the data of the discrete and continuum inelastic scatterings of 56 Fe in ENDF/B-VIII.0 with those in ENDF/B-VII.1, respectively. The result with the modified 56 Fe files is shown in Fig. 12, where 'inela.', 'disc.' and 'cont.' mean 'inelastic scattering', 'discrete' and 'continuum', respectively. From Fig. 12 it is concluded that Problem 1 is mainly caused by the discrete inelastic scattering data of 56 Fe in ENDF/B-VIII.0 and Problem 2 is caused by both the discrete and continuum inelastic scattering data of 56 Fe in ENDF/B-VIII.0.

Problem 3
The same procedure as that for Problems 1 and 2 was also carried out for Problem 3, but JENDL-4.0, not ENDF/B-VII.1, was used because only JENDL-4.0 did not cause Problem 3 as shown in Fig. 6 (a). Figure 13 shows the results by replacing the iron isotope files one by one from ENDF/B-VIII.0 to JENDL-4.0. It suggests that 56 Fe in ENDF/B-VIII.0 also causes Problem 3 mainly.
Next, we compared each reaction data above  Figure 15 shows the result, where 'j40' and 'scat. ang.' mean 'JENDL-4.0' and 'scattering angular distribution', respectively. It specifies that both the (n,2n) reaction cross section and angular distribution of elastic scattering in 56 Fe of ENDF/B-VIII.0 mainly cause Problem 3. Note that we studied the same issue for ENDF/B-VI in 1998 [11].

Conclusion
We analyzed the iron in-situ experiment at JAEA/FNS for the JENDL-5 development with the latest nuclear data libraries in 2020. The results clearly showed that ENDF/B-VIII.0 caused the following problems.
Problem 1: The neutron flux of 1 -10 keV is overestimated more at the shallower region. Problem 2: The reaction rate of the 115 In(n,n') 115m In reaction is underestimated more at the deeper region. Problem 3: The neutron flux above 10 MeV is underestimated more at the deeper region. Our detail study specified reasons of the problems as follows.
Problem 1: the discrete inelastic scattering data of 56 Fe. Problem 2: the discrete and continuum inelastic scattering data of 56 Fe. Problem 3: the (n,2n) reaction data and angular distribution data of elastic scattering of 56 Fe. We hope that the 56 Fe data in ENDF/B-VIII.0 will be revised in the next ENDF/B based on this study.