Simultaneous evaluation of uranium and plutonium fast neutron ﬁssion cross sections up to 200 MeV for JENDL-5 and its updates

. Simultaneous evaluation of 233 , 235 , 238 U and 239 , 240 , 241 Pu ﬁssion cross sections for fast neutrons up to 200 MeV was performed for the JENDL-5 library. Experimental covariances were estimated for each experimental dataset of cross sections or cross section ratios extracted from the EXFOR library, and they were stored in an experimental database dedicated to the new evaluation. The cross sections were expressed by Schmittroth’s roof functions, and the values on deﬁned incident energy grids were adjusted by the least-squares method to reproduce the experimental cross sections and their ratios. The newly evaluated cross sections were validated using the spectrum averaged cross sections measured in the 252 Cf spontaneous ﬁssion neutron standard ﬁeld. The evaluation adopted by the JENDL-5 library was further updated by addition of two datasets and deletion of one dataset.


Introduction
Simultaneous evaluation is an approach to evaluate cross sections (e.g., 239 Pu(n,f) cross section) and their ratios to reference cross sections (e.g., 239 Pu(n.f)/ 235 U(n,f) cross section ratio) simultaneously. Evaluation based on an experimental cross section ratio without its conversion to the corresponding absolute cross section is free from choice of the reference cross section and more suitable for evaluation. Therefore, it would be ideal to perform evaluation based on experimental ratio values and absolute values free from reference cross sections (e.g., cross sections measured with the associated particle method).
Since release of the JENDL-4.0 library [1], a number of experimental datasets were newly published and compiled in the EXFOR library [2]. Many of them from time-of-flight facilities cover a high energy region beyond 20 MeV. In order to include the newly available experimental information, simultaneous evaluation of 233,235,238 U and 239,240,241 Pu fast neutron fission cross sections was done by extending the upper boundary energy of evaluation from 20 MeV to 200 MeV for the JENDL-5 library [3] by construction of a new experimental database and its least-squares analysis with the SOK code [4].
This paper briefly introduces the simultaneous evaluation performed for the JENDL-5 library. The reader is referred to the primary reference of our evaluation [5] for more details about the policy and procedure of the simultaneous evaluation and to the report [6] for technical details of experimental database construction and small deviation of the 235,238 U and 239 Pu cross sections included in the JENDL-5 library from those evaluated by us. ⇤ e-mail: n.otsuka@iaea.org ⇤⇤ e-mail: iwamoto.osamu@jaea.go.jp After completion of the evaluation for the JENDL-5 library, we introduced a few updates to our experimental databases to take into account the experimental datasets newly available in the EXFOR library and also to exclude a questionable dataset. This paper also reports the revision with the experimental database updated after release of the JENDL-5 library.

Experimental database for JENDL-5 evaluation
All cross section and cross section ratio datasets compiled in the EXFOR library from articles published in and later than 1980 ( 235 U) or 1970 (other nuclides) were reviewed, and the datasets compiled with information sufficient for covariance estimation (i.e., uncorrelated and correlated components of uncertainty) were selected excluding those digitized from figure images and measured by nuclear explosion experiments. In order to increase the number of usable datasets, we accepted 10 additional datasets by treating the energy-dependent uncertainty not clearly stated as the total uncertainty as total. A full list of the selected datasets is published in Sect. 2.4 of Ref. [6]. It is critical to avoid use of several datasets originating from the same measurement (e.g., preliminary and final datasets); otherwise the measurement gets extra weighting through the evaluation. One can avoid such double counting by excluding the datasets flagged by spsdd (superseded) in EXFOR entries in general, but this flagging is not systematically done for the absolute cross sections measured by the TUD-KRI collaboration (1975)(1976)(1977)(1978)(1979)(1980)(1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990). As the absolute cross section measurements have importance in our evaluation, we selected the experimental datasets from this collaboration with special care (See Sect. 3 of Ref. [6] for more details). We assigned a correlation property (e.g., uncorrelated, correlated) to each partial uncertainty compiled in EXFOR entries (See Sect. 2.5 of Ref. [6] for assignment in each dataset). A newly developed code SOX (Simple Output of eXfor) read the EXFOR file and correlation property list, and printed the cross sections, their total uncertainties and correlation coe cients in ASCII files for reading by the SOK code. The contents of each EX-FOR file used as an input is identical to the EXFOR entry distributed from data centres at the time of evaluation, and this ensures traceability of our evaluation. Note that we (1) modified original EXFOR entries for 10 experimental datasets for grouping etc. (See Sect. 3.3 of Ref. [5]), and (2) added constant uncertainties not coded in the EXFOR entry at the stage of correlation coe cient calculation for 8 experimental datasets (See Table 4 of Ref. [5]). The experimental database and modified EXFOR entries (ASCII files) are available as supplemental materials of Ref. [5].

Formalism
We set the JENDL-4.0 library (below 20 MeV) and JENDL-4.0/HE [7] ( 235,238 U and 239,240,241 Pu above 20 MeV) or Yavshit's evaluation [8] ( 233 U above 20 MeV) as the prior cross sections, and they were updated by the SOK code by addition of an experimental dataset one-byone. A video showing the update procedure is available as a supplemental material of Ref. [5]. The SOK code expresses the logarithm of the evaluated cross section by a linear combination of Schmittroth's roof functions [9]. The mathematical formulation is given in the primary reference of this evaluation [5]. Figure 1. Circles: Logarithms of experimental cross sections of reaction A, reaction B and their ratios at incident energies 1 to 6. Squares: Logarithms of evaluated cross sections of reactions A at E j 1 , E j , E j+1 and of reaction B at E k 1 , E k and E k+1 . Figure 1 shows logarithms of experimental and evaluated cross sections to explain our formalism schematically. In this example, we suppose that the logarithms of the experimental cross sections are available for reaction A at 1 and 2, for reaction B at 3 and 4, and their ratios at 5 and 6. The evaluated cross sections to be determined by fitting are at incident energies E j 1 , E j and E j+1 for reaction A and at E k 1 , E k and E k+1 for reaction B.
where n, j = j (E n ) is the value of Schmittroth's roof function defined between E j 1 and E j+1 at E n : The original SOK code implementing this formalism was slightly extended to use experimental data in arbitrary units (shape data) for the JENDL-5 evaluation, and it was used for two experimental datasets [10,11], for which we preferred to be free from normalization done by the experimentalists.
The least-squares procedure mentioned above produces not only evaluated cross sections but also correlation coe cients. However, the ENDF-6 format accepts the covariances of the group-wise cross sections. In order to submit the covariances from our evaluation to the JENDL-5 library, we repeated least-squares analysis after replacing Schmittroth's roof function with the rectangular function just to accommodate our covariances in the ENDF-6 format.

Extension of experimental database after JENDL-5 evaluation
After release of the JENDL-5 library, we updated our experimental database for the three datasets listed in Table 1.  Table 1. Three datasets relevant to experimental database update after release of JENDL-5. The first one was for deletion whereas the second and third ones were for addition. "Ver.", "Lab." and "Pts." give the date (N2) of the SUBENT record in EXFOR, EXFOR/CINDA abbreviation of the institute where the experiment was performed, and number of data points, respectively. 8.46 MeV in EXFOR 22304.002 [13]). See Table 18 of Ref. [6] for the history of their updates. Unlike the 1980 data point, the 1979 data point was not reexamined by the collaboration for the absorption correction. Therefore, we discarded the lower cross section in our experimental database even though it is more consistent with our JENDL-5 evaluation.

Results
The evaluated cross sections submitted to the JENDL-5 library are plotted and tabulated in Ref. [6]. Evaluated cross sections in an ASCII file are available as a supplemental material of Ref. [5]. Their 235,238 U and 239 Pu cross sections were adjusted when they are compiled in the JENDL-5 library (within +0.8-0.4% for 235 U, within +2.8% for 238 U and within +0.1-0.0% for 239 Pu). See the JENDL-5 reference paper [3] for more details about the adjustment. Figure 2 shows the 235 U(n,f) evaluated cross sections from the JENDL-5 evaluation (20210404) and its update (20220324) between 5 and 15 MeV. Arlt et al.'s data point (1980) from the TUD-KRI project is excluded in the updated evaluation. We do not see any change in the evaluated cross section due to this exclusion, and the evaluated cross section is still consistent with the excluded data point rather than the other (higher) data point from the TUD-KRI project (Merla et al. [13]).      The systematic increase in the 239 Pu(n,f)/ 235 U(n,f) in this energy region also may have an impact on the spectrum averaged cross section defined in the 252 Cf prompt fission neutron standard field [17]( 252 Cf SACS). The 252 Cf SACS from various evaluations are summarized in Table 2 along with the 252 Cf SACS measured by Grundl and Gilliam [18] and recommended by Mannhart [19]. This table also shows the underestimation of the 252 Cf SACS of 238 U discussed in Ref. [5] still remains.

Summary
The results of the simultaneous evaluation of 233,235,238 U and 239,240,241 Pu fast neutron fission cross sections up to 200 MeV were submitted to the JENDL project and adopted in the JENDL-5 library with minor adjustments for 235,238 U and 239 Pu. After this evaluation, we performed least-squares analysis again after deletion of one dataset and addition of two new datasets. Addition of the 235 U dataset by Duran et al.reduced the cross section by 5.8% at the lower boundary (10 keV) and then up to 1.6% below ⇠30 keV. Addition of the 239 Pu/ 235 U dataset by Snyder et al. introduced slight (up to ⇠0.5%) increase in the ratio in the whole energy range of the evaluation.
Absolute scale of the cross sections from our evaluation strongly relies on the 235 U(n,f) experimental data points. Progress in 235 U(n,f) measurements relative to hydrogen scattering were presented by n_TOF and CSNS in this conference, and we are looking forward to receiving their final results in the EXFOR library for further continuation of our evaluation. Table 2. Spectrum averaged fission cross sections (mb) under the 252 Cf prompt fission neutron standard field.