#  EXFOR-based simultaneous evaluation for fast neutron-induced fission cross
section of thorium-232

Vidya Devi1 Email<EMAIL_ADDRESS>Naohiko Otuka1 S. Ganesan2 1Nuclear
Data Section1Nuclear Data Section Division of Physical and Chemical Sciences
Division of Physical and Chemical Sciences Department of Nuclear Sciences and
Applications Department of Nuclear Sciences and Applications International
Atomic Energy Agency International Atomic Energy Agency A-1400 Wien A-1400
Wien Austria
2Former Raja Ramanna Fellow Austria
2Former Raja Ramanna Fellow Bhabha Atomic Research Centre Bhabha Atomic
Research Centre Mumbai 400085 Mumbai 400085 India India

###### Abstract

The 232Th neutron-induced fission cross section was evaluated from 500 keV to
200 MeV. The experimental 232Th fission cross sections and their ratios to the
235,238U fission cross sections in the EXFOR library were reviewed and
analysed by the least-squares method. The newly published 232Th/235U fission
cross section ratios from the time-of-flight measurements at the CERN n_TOF
and CSNS Back-n facilities were compiled in EXFOR. Additional simultaneous
evaluation was performed by including the experimental 233,238U and
239,240,241Pu fission cross sections and their ratios. The new evaluation
provides the 232Th fission cross section systematically lower than the JENDL-5
cross section. The reduction is 4% in the plateau region between 2 and 6 MeV
and more significant in the subthreshold fission region. The present
evaluation reduces the 232Th fission cross section averaged over the 252Cf
spontaneous fission neutron spectrum from the JENDL-5 evaluation by 4%, which
is closer to the other general purpose libraries but underestimates Grundl et
al’s measurement by 11%.

thorium-232, fission, simultaneous evaluation, JENDL, EXFOR

##  1 Introduction

Over the past three decades, there has been renewed interest in studying the
thorium fuel cycle as a potential source for new types of nuclear fuel. In
comparison to the uranium fuel cycle, thorium-based nuclear systems are
anticipated to offer a significantly higher level of intrinsic safety. Design
studies employing Th-U fuel have also shown the possibility of developing
nuclear power reactors that are more resistant to nuclear proliferation than
the U-Pu fuel cycle. Additionally, research has been reported on design
systems aimed at achieving the goal of efficiently reducing weapon-grade
plutonium using thorium fuel. Another benefit of using thorium fuel is the
reduced creation of higher actinide wastes. For instance, the Indian approach
uses a closed fuel cycle using several fuels. There are many critical reviews
of thorium as a nuclear fuel with huge potential to create nuclear energy for
centuries with better safety characteristics available in the literature [1,
2, 3].

The Accelerator Driven Subcritical System (ADSS) can help to make use of
thorium in power generation faster [4]. In ADSS or comparable fast reactors,
232Th fission accounts for 3% of the fissions and at least for 8% in a gas
cooled reactor. Indeed, 232Th has an important contribution of 2% to delayed
neutrons in these advanced reactor systems around the fission threshold
($\sim$0.7 MeV) as compared to 0.25% for 233U [5]. Therefore, accurate
neutron-induced fission cross section of the order of 5% is required [6]. The
cross section also plays an important role in estimations of energy
amplification and neutron breeding in thorium blanketed fusion-fission hybrid
reactors which have significantly harder neutron spectra [7].

Three decades ago, there was an increase of interest in enhancing the nuclear
data of the thorium fuel cycle. In the Indian context, there has previously
[8, 9, 10] been a brief discussion of the disparities that currently exist and
the need for new and improved data. As multiple fuel cycles (e.g., U-Pu, Th-U)
with the option of closing the fuel cycle are envisaged, the nuclear data
requirements necessary to develop new systems such as Advanced Heavy Water
Reactor (AHWR) [11, 12] with high burnup are demanding and include the entire
range of actinides and fission products for multiple fuels. The International
Atomic Energy Agency (IAEA) also executed a Coordinated Research Project (CRP)
on “Evaluated Nuclear Data for the Th-U Fuel Cycle” [13].

Among the 232Th fission cross section in the fast neutron region compiled in
the major general purpose libraries, the JENDL-5 library [14] adopts the
JENDL-4.0 [15] cross section, which was obtained by evaluation of the
experimental cross sections (including 232Th/235U fission cross section ratios
multiplied by the JENDL-3.3 235U fission cross section) above 300 keV by the
least-squares analysis code GMA [16]. The CENDL-3.2 library adopts the
CENDL-3.1 cross section calculated by the UNF code [17] but with revision
between 130 and 900 keV considering the measurement by Fursov et al. [18]. The
ENDF/B-VIII.0 [19] cross section is a revision from the cross section
evaluated by the EMPIRE code [20] for the IAEA Coordinated Research Project
[13], and it is also adopted by the JEFF-3.3 [21] and TENDL-2021 [22]
libraries. The BROND-3.1 [23] cross section is originally from the JENDL-4.0
evaluation but adjusted to conserve the reaction cross section constrained by
the optical model. Among these evaluations, the fission cross section averaged
over the 252Cf spontaneous fission neutron spectrum from JENDL-5 is closest to
the experimental values from the most recent measurements by Grundl et al.
[24] and Dezsö et al. [25], and the JENDL-4.0 evaluation is adopted not only
by the JENDL-5 library but also by the IRDFF-II library [26].

The last measurement considered by the JENDL-4.0 evaluation is the time-of-
flight measurement done by Shcherbakov et al. [27]. About 20 years after the
Shcherbakov et al’s measurement, three new time-of-flight measurement results
covering 1 to 200 MeV were published by the CSNS Back-n [28, 29] and CERN
n_TOF facility [30] collaborations this year (2023). Additionally, two new
measurements done with monoenergetic neutron sources were published in
2021-2022 [31, 32].

The purpose of this article is to reevaluate the 232Th neutron-induced fission
cross section between 500 keV and 200 MeV by including these experimental
datasets newly added in the EXFOR library [33], and to check whether the
evaluation considering these new measurements support the JENDL evaluation or
the cross sections in the other major general purpose libraries.

##  2 Evaluation Method

The present evaluation was conducted using the least-squares analysis code SOK
[34, 35], wherein a prior estimate was updated with individual experimental
datasets. For 232Th, the cross section in JENDL-5 (below 20 MeV) and the cross
section evaluated by Yavshits et al. [36] (above 20 MeV) were adopted as the
prior estimates. For other nuclides, the JENDL-5 cross sections were adopted
as the prior estimate except for the 233U cross section above 20 MeV where the
simultaneous evaluation result submitted to the JENDL-5 development [37] was
used.

We followed the JENDL-5 simultaneous evaluation procedure [38] and the
procedures specific for the current evaluation are briefly outlined below. We
first performed simultaneous evaluation with an experimental database
compiling the 232Th,235,238U fission cross sections including the
232Th/235,238U cross section ratios (“three-nuclide evaluation”). Afterwards,
we repeated evaluation with the experimental database extended to 233U and
239,240,241Pu fission cross sections and their ratios (“seven-nuclide
evaluation”).

All experimental datasets of the 232Th cross section and its ratio to the
235,238U cross section in the EXFOR library were reviewed for selection of the
datasets to be analysed. The newly published 232Th/235U fission cross section
ratios from the time-of-flight measurements at the CERN n_TOF and CSNS Back-n
facilities were compiled in EXFOR during this evaluation, and some EXFOR
entries from older measurements were revised to include the experimental
information in the least-squares analysis as much as possible.

The selection of the experimental datasets for evaluation adhered to the
following criteria:

  * •

including a data point between 500 keV and 200 MeV

  * •

reported from 1970 to the present

  * •

both statistical and systematic uncertainties available

The cutoff year (1970) was chosen to be consistent with the 233,235,238U and
239,240,241Pu fission cross section experimental database developed for the
JENDL-5 simultaneous evaluation [37] and used in the present evaluation. The
least-squares solution of the 232Th cross section near the lower (500 keV) and
upper (200 MeV) energy boundaries may be affected by the experimental data
points not only inside but also outside the energy range, and we included the
experimental data points in 300–500 keV and 200–250 MeV in the present
evaluation as long as the experimental dataset also has a data point between
500 keV and 200 MeV. On the other hand, we excluded the following datasets
from the present evaluation:

  * •

measurement relative to a reference fission cross section but the ratio is not
available in EXFOR [39, 40, 41]

  * •

measurement with neutrons from nuclear explosions [42]

  * •

numerical data not available from the authors in a tabulated form [43, 44]

After the selection, no 232Th cross section dataset was left for our
evaluation, and we used 232Th/235,238U cross section ratio in EXFOR without
any modification except for the 232Th/238U dataset published by Gledenov et
al. [32]. Gledenov et al. obtained two datasets by exchanging the position of
the 232Th and 238U (“backward” and ”forward” measurements), and their results
are compiled in EXFOR 32873.002.1 and 32873.003.1. However, these measurements
used the same Th and U samples and this fact makes correlation between the two
datasets. In order to take into account this correlation in the present
evaluation, we created an ad hoc EXFOR dataset (51011.002) from the two
datasets and included it in our experimental database instead of EXFOR
32873.002.1 and 003.1. Table 1 summarizes the experimental 232Th/235,238U
datasets used in the current evaluation.

Table 1:  232Th/235,238U fission cross section ratios included in the
experimental database for the present evaluation. “Ver.”, “Lab.” and “Pts.”
give the date (N2) of the SUBENT record in EXFOR, EXFOR/CINDA abbreviation
[56] of the institute where the experiment was performed, and number of data
points, respectively.

EXFOR $\\#$ | Ver. | First author | Year | Lab. | Pts. | Energy range (eV) | Ref.
---|---|---|---|---|---|---|---
232Th/235U |  |  |  |  |  |  |  |
32889.002.1 | 20230609 | Z.Ren | 2023 | 3CPRIHP | 86 | 1.0E+06 | 2.1E+08 | [29]
23654.002.1 | 20230502 | D.Tarrío | 2023 | 2ZZZCER | 181 | 1.0E+06 | 2.5E+08 | [30]
32887.002.1 | 20230401 | Y.Chen | 2023 | 3CPRIHP | 109 | 1.0E+06 | 2.4E+08 | [28]
23756.002.1a | 20221007 | V.Michalopoulou | 2021 | 2GRCATH | 2 | 2.0E+06 | 2.5E+06 | [31]
41455.006 | 20220914 | O.Shcherbakov | 2002 | 4RUSLIN | 166 | 5.8E+05 | 2.0E+08 | [27]
41111.002 | 20221011 | B.Fursov | 1991 | 4RUSFEI | 66 | 3.5E+05 | 7.4E+06 | [18]
13134.003.1 | 20170724 | J.W.Meadows | 1988 | 1USAANL | 1 | 1.5E+07 | 1.5E+07 | [57]
22282.002.1 | 20130924 | F.Manabe | 1988 | 2JPNTOH | 4 | 1.3E+07 | 1.5E+07 | [58]
22014.002 | 20210315 | K.Kanda | 1986 | 2JPNTOH | 17 | 1.5E+06 | 6.8E+06 | [59]
40885.002 | 20221017 | A.A.Goverdovskii | 1986 | 4RUSFEI | 1 | 1.6E+07 | 1.6E+07 | [60]
40888.002 | 20221017 | A.A.Goverdovskii | 1986 | 4RUSFEI | 33 | 4.9E+06 | 1.0E+07 | [61]
30813.011 | 20190722 | I.Garlea | 1984 | 3RUMBUC | 1 | 1.5E+07 | 1.5E+07 | [62]
10843.003.1b | 20221018 | J.W.Meadows | 1983 | 1USAANL | 69 | 1.3E+06 | 9.9E+06 | [50]
10658.002 | 20221020 | J.W.Behrens | 1982 | 1USALRL | 144 | 7.1E+05 | 3.3E+07 | [49]
20844.002 | 20221024 | C.Nordborg | 1978 | 2SWDUPP | 23 | 4.6E+06 | 8.8E+06 | [63]
232Th/238U |  |  |  |  |  |  |  |
23756.002.2c | 20221007 | V.Michalopoulou | 2021 | 2GRCATH | 2 | 2.0E+06 | 2.5E+06 | [31]
23756.003.1 | 20221007 | V.Michalopoulou | 2021 | 2GRCATH | 10 | 3.0E+06 | 1.8E+07 | [31]
51011.002d | 20221111 | Yu.M.Gledenov | 2022 | 3CPRBJG | 24 | 4.2E+06 | 1.2E+07 | [32]

aEXFOR # is 51012.002 in our experimental database.
btreated as shape ratio.
cEXFOR # is 51012.003 in our experimental database.
dad hoc EXFOR entry prepared from 32873.002.1 and 003.1.

For the target nuclides other than 232Th, the energy range included in fitting
is the same as the JENDL-5 simultaneous evaluation, namely from 10 keV
(fissile) or 100 keV (non-fissile) to 200 MeV. The experimental database
developed for the JENDL-5 simultaneous evaluation [37] was adopted for these
nuclides with exclusion of one 235U dataset (see the reason outlined in [45])
and inclusion of a few additional datasets as summarized in Table 2.

Belloni et al. [46] determined the 238U cross sections (EXFOR 23653.004.1 and
23653.004.2), which are by-products of their measurements of the 240,242Pu
cross sections relative to n-p scattering and to 238U fission. We merged these
two datasets into an ad hoc EXFOR dataset 51014.002 to include in our
experimental database the correlation between the two datasets originated from
the use of the same neutron flux. Note that they do not report the 240Pu/238U
ratio from their measurement, and we did not use their 240Pu cross section
derived from the measured ratio multiplied by the 238U cross section in IAEA
Neutron Data Standard [47] following our data selection criteria.

Table 2:  Update of the experimental database for 233,235,238U and 239,240,241Pu fission cross sections and their ratios from the database used for JENDL-5 simultaneous evaluation [37]. EXFOR 31833.002 was deleted whereas the other ones were added. See the caption of Table 1 for “Ver.”, “Lab.” and “Pts.”.  Reaction | EXFOR $\\#$ | Ver. | First author | Year | Lab. | Pts. | Energy range (eV) | Ref.
---|---|---|---|---|---|---|---|---
233U/235U | 23654.003.1 | 20230502 | D.Tarrío | 2023 | 2ZZZCER | 110 | 1.0E+04 | 2.3E+08 | [30]
235U | 31833.002 | 20201103 | R.Arlt | 1980 | 2GERZFK | 1 | 8.2E+06 | 8.2E+06 | [64]
235U | 23294.004 | 20211216 | I.Duran | 2019 | 2ZZZCER | 8 | 7.5E+03 | 2.7E+04 | [65]
238U | 51014.002 | 20221222 | F.Belloni | 2022 | 2GERPTB | 4 | 2.5E+06 | 1.5E+07 | [46]
238U/235U | 32886.003.1 | 20230206 | Z.Ren | 2023 | 3CPRIHP | 135 | 5.1E+05 | 1.8E+08 | [66]
239Pu/235U | 14721.002 | 20211220 | L.Snyder | 2021 | 1USALAS | 119 | 1.1E+05 | 9.7E+07 | [67]
240Pu | 23653.002.1 | 20221126 | F.Belloni | 2022 | 2GERPTB | 2 | 2.5E+06 | 1.5E+07 | [46]

The SOX code [37] was utilized to convert all numerical values from the EXFOR
library into the SOK input files. In order to construct the energy-energy
correlation coefficients, it was assumed during processing by SOX that the
uncertainty arising from counting statistics is uncorrelated while the other
uncertainties are fully correlated within the same dataset. We assumed any two
datasets in our experimental database are independent of each other.

##  3 Result and Discussion

We performed fitting to a total of 8695 (3268) experimental data points by
adjusting 597 (261) evaluated cross sections as fitting parameters, and
obtained the least-squares solutions with the reduced chi-square of 4.05
(4.49) for the seven (three)-nuclide evaluation.111The evaluated cross
sections in an ASCII file are available as a Supplemental Material of this
article. The seven-nuclide evaluation shows better consistency between the
fitting result and experimental data points.

###  3.1 Point-wise cross sections

The newly evaluated 232Th cross section and its ratio to the 235U and 238U
cross sections are presented in Figs. 1 to 5. The experimental data points
used in the current evaluation are represented by symbols in these figures
except for Fig. 5, where none of the plotted experimental data points are used
in the present evaluation and they are shown just for comparison with the
result of the present evaluation. The band accompanying the newly evaluated
cross section or its ratio in the figures represents the external uncertainty,
which is the internal uncertainty in the least-squares solution multiplied by
the square root of the reduced chi-square from the seven-nuclide
evaluation.222A reduced chi-square value greater than 1 indicates that the
uncertainty resulting from the least-squares fitting (internal uncertainty) is
less than that anticipated from the actual discrepancy of the experimental
datasets (external uncertainty). See also Sect. 4.4 of Ref. [48].

Figure 1 displays the 232Th/235U cross section ratio below 1 MeV. The ratio is
the same for both the current seven- and three-nuclide evaluations. Only three
experimental datasets are available in this energy range. Among them, Fursov
et al. [18] and Behrens et al. [49] are close to the present evaluation while
Shcherbakov et al. [27] do not agree with these two datasets within their
respective error bars below 0.85 MeV. Considering low counting statics of
232Th fission, Fursov et al. [18] changed the fission fragment detection
device at 0.85 MeV from an ionization chamber to a track (mica) detector and
it could give a more reasonable estimation of the actual ratio than
Shcherbakov et al. In presence of Shcherbakov et al’s high ratio, the ratio
from the present evaluation becomes slightly higher than Fursov et al’s ratio
below 0.7 MeV. Between 0.85 and 1 MeV, all three experimental datasets come
closer and show better consistency with the JENDL-5 and present evaluations.

Figure 1:  232Th/235U fission cross section ratios below 1 MeV from the
present evaluations along with the experimental ratios [27, 18, 49] used in
the present evaluation.

Figure 2 displays the 232Th/235U cross section ratio above 1 MeV. The ratio
initially obtained from the seven-nuclide evaluation was systematically higher
than JENDL-5 and obviously did not represent the experimental information. We
found out that this problem is solved by treating Meadows’ ratio [50] as the
shape ratio (i.e., treat its overall normalization factor as an additional
fitting parameter). This treatment gives more reasonable fitting with
0.922$\pm$0.010 (external uncertainty) as the normalization factor to be
multiplied to the original Meadows’ ratio. We also attempted fitting excluding
Meadows’ ratio and confirmed that the result is very similar to the fitting
with Meadows’ ratio as a shape ratio. This figure shows that the present ratio
is systematically lower than the JENDL-5 ratio from 2 to 6 MeV and 7 to 15
MeV. In the plateau between 2 and 6 MeV, JENDL-5 follows the systematically
high ratio measured by Fursov et al. [18] while the present fitting does not
support it. The inset of Fig. 2 shows that the 232Th/235U ratio in the high
energy region derived from the 235U cross section in JENDL-5 and 232Th cross
section evaluated by Yavshits et al. is too high while the present evaluation
provides a ratio consistent with the experimental datasets. In the high energy
region, the two ratios from CSNS Back-n [28] and CERN n_TOF [30] published
this year (2023) are consistent with the ratio published by Shcherbakov et
al’s ratio. Some data points from the CERN n_TOF measurement are lower than
but still consistent with others within the error bars. The present seven- and
three-nuclide evaluations provide almost the same ratio above 1 MeV.

Figure 2:  232Th/235U fission cross section ratios above 1 MeV from the
present evaluations along with the experimental ratios [29, 30, 28, 31, 27,
18, 57, 58, 59, 60, 61, 62, 50, 49, 63] used in the present evaluation.
“J.W.Meadows absolute” stands for the seven-nuclide evaluation including
Meadows’ ratio as the absolute ratio.

Figure 3 shows the experimental 232Th/235U cross section ratio relative to the
newly evaluated 232Th/235U cross section ratio for recent time-of-flight
measurements. Additionally, the JENDL-5 232Th/235U cross section ratio
relative to the newly evaluated 232Th/235U cross section ratio is shown by
smooth curve. This figure shows the JENDL-5 evaluation follows the ratio
measured by Fursov et al. very well. The JENDL-5 evaluation also considers the
ratio measured by Shcherbakov et al., Goverdovskii et al. and Behrens et al.,
and it is not clear why the JENDL-5 evaluation is influenced by the ratio
measured by Fursov et al. It is obvious from this figure that the newly
evaluated 232Th/235U ratio is more consistent with the majority of the time-
of-flight measurements published before and after JENDL-5 evaluation. Among
the three datasets published in 2023, only Ren et al. [29] determined the
overall normalization experimentally. Tarrío et al. [30] normalized their
shape ratio to an absolute ratio at 2.5 - 5 MeV from a previous n_TOF
measurement, and Chen et al. [28] normalized their shape ratio to
0.364$\pm$0.007 b at 14.13 MeV.

Figure 3:  232Th/235U fission cross section ratios from time-of-flight
measurements [29, 30, 28, 27, 18, 61, 49] relative to the ratio from present
evaluation above 2 MeV. The smooth curve shows the JENDL-5 232Th/235U cross
section ratio relative to the newly evaluated 232Th/235U cross section ratio.

Figure 4 shows the 232Th/238U ratio. There are three new experimental datasets
measured with monoenergetic neutron sources published in 2021-2022 [32, 31].
The ratio from the present evaluation is systematically lower than the JENDL-5
ratio between 2 and 15 MeV and more consistent with but still systematically
higher than the newly measured ratios. In order to understand this deviation,
we performed additional fitting for the three-nuclide evaluation excluding the
238U/235U experimental ratios, and we found this exclusion improves the
agreement with the evaluated and measured 232Th/238U ratios a lot as shown in
Fig. 4. This fact reminds us that the scale of the 238U cross section from the
JENDL-5 simultaneous evaluation including the 238U/235U experimental ratios is
about 3.5% lower than the scale expected from the 252Cf fission neutron
spectrum averaged cross section measured by Grundl et al. [24] and recommended
by Mannhart [51].

Figure 4:  232Th/238U fission cross section ratios from the present
evaluations along with the experimental ratios [31, 32] used in the present
evaluation. “3 nuclides w/o 238U/235U” stands for the three-nuclide evaluation
excluding the experimental 238U/235U ratios.

Figure 5 shows that the 232Th cross section from the current evaluation along
with the three datasets [40, 39, 42] that were published later than 1970 but
do not fulfill the conditions mentioned in Sect. 2 and excluded from the
present evaluation. Muir et al. [42] determined the cross section by using the
measured 232Th/239Pu ratio with the 239Pu cross section evaluated by Davey
[52]. Muir et al.’s cross section below 1 MeV is systematically higher than
the cross section from the current evaluation. The two datasets of the cross
section measured by Blons et al. [39, 40] show good agreement with the cross
section from the present evaluation except for the energy region near the
upper boundary of their measurement.

Figure 5:  232Th fission cross sections from the present evaluations along
with the experimental cross sections [39, 40, 42] that were excluded from the
present evaluation.

Figure 6 illustrates the change in the 232Th cross sections in the new
evaluations from the JENDL-5 evaluation in the SAND-II 725 energy group
structure. The figure shows that the cross sections from the three- and seven-
nuclide evaluations are very similar and they are systematically lower than
the JENDL-5 cross section except for a few groups. The reduction from the
JENDL-5 cross section is about 4% in the plateau region between 2 and 6 MeV.
This partly resolves the discrepancy between the JENDL-5 and n_TOF cross
section (7%) discussed in Ref. [30]. Below 1 MeV, the deviations from the
JENDL-5 evaluation become more significant as it is also seen in Fig. 1.

Figure 6:  Difference in 232Th fission cross sections between evaluations.

The present evaluation is simultaneous evaluation and the least-squares
fitting provides not only the 232Th cross section but also the 233,235,238U
and 239,240,241Pu (235,238U) cross sections in the seven-nuclide (three-
nuclide) evaluation. Among these cross sections, the 235U cross section
adopted in the JENDL-5 library has been validated by various integral
benchmark tests (e.g., [53]) and the cross section from the present evaluation
should be very close to the JENDL-5 cross section. Figure 7 compares the 235U
cross section from the present evaluation with the prior cross section taken
from the JENDL-5 library. The figure reveals that the seven-nuclide evaluation
does not introduce significant changes from the JENDL-5 235U cross section
below 100 MeV. Conversely, the three-nuclide evaluation systematically reduces
the prior estimate (i.e., JENDL-5 cross section) between 0.2 and 2 MeV. The
unphysical structure of the cross section between 0.1 and 0.2 MeV from the
three-nuclide evaluation is resolved in the seven-nuclide evaluation. Based on
these findings, we conclude that the seven-nuclide evaluation provides a more
reasonable assessment of the 232Th cross section though the two evaluations do
not show much difference as seen in Fig. 6.

Figure 7:  235U fission cross sections from the present evaluations along with
the experimental cross sections [65, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77,
78, 79, 80, 81, 82, 83, 84, 85, 86] used in the present evaluation.

###  3.2 Validation by 252Cf spontaneous fission neutron spectrum averaged
cross section

The 252Cf spontaneous fission neutron field over the energy range from 0.1 to
20 MeV is recognized as the standard neutron field by the IRDFF-II library.
The JENDL-5 simultaneous evaluation [38] utilized the spectrum averaged cross
section (SACS) measured in this neutron field for validation of the evaluated
235,238U and 239Pu cross sections by comparison with those recommended by
Mannhart [51]. He does not provide a recommended value for the 232Th cross
section but quotes in the same document [51] the SACS measured by Grundl et
al. [24] (89.4$\pm$2.7 mb, the latest experimental 252Cf SACS of the 232Th
cross section in EXFOR) for comparison with the SACS derived from the 232Th
cross sections in two dosimetry libraries (IRDF-90.2 [54] and JENDL/D-99
[55]). To validate the newly evaluated 232Th cross sections cross sections, we
converted the evaluated point-wise cross sections into group-wise cross
sections within the SAND-II 725 energy group structure, and averaged over the
252Cf spontaneous fission neutron spectrum in the same group structure
compiled in the IRDFF-II library following the procedure described in Ref.
[38]. The SACS of the present results was obtained by joining the newly
evaluated cross section above 500 keV to the cross section in the JENDL-5
library below 500 keV.

Figure 8 shows the ratios to the SACS measured by Grundl et al. for the
present evaluation, JENDL-5, CENDL-3.2, JEFF-3.3, ENDF/B-VIII.0 and BROND-3.1
evaluations. Note that the JEFF-3.3 library adopts the ENDF/B-VIII.0 232Th
cross section. The figure shows that the SACS from all evaluations are
inconsistent with the SACS measured by Grundl et al. despite the fact that all
SACS from these evaluations other than BROND-3.1 evaluation fall within the
error bar of the second most recent experimental SACS measured by Dezsö et al.
[25]. The present update from JENDL-5 increases the discrepancy from the
measurement by Grundl et al. from 7% to 11%.

Table 3 summarizes the SACS from the present evaluations, JENDL-5 simultaneous
evaluation (sok20210404) [38] and its update (sok20220324) [45] in parallel
with the measured, evaluated and recommended values. Note that the SACS
derived from the JENDL-5 library is slightly different from the SACS from the
simultaneous evaluation submitted to the JENDL project (sok20210404) due to
adjustments [14, 37]. The SACS from the present evaluation is 4% lower than
the 232Th SACS in JENDL-5, which is consistent with what we observe in Fig. 6.
Table 3 shows that the 233,235,238U and 239,240,241Pu SACS from the present
evaluation is almost unchanged from those derived in the latest SOK
simultaneous fitting [45] except for the 235U SACS from the three-nuclide
evaluation.

Figure 8:  252Cf spontaneous fission neutron spectrum averaged cross sections relative to those measured by Grundl et al. [24] for the present evaluation, evaluated data libraries [14, 87, 21, 23, 19] as well as the one measured by Dezsö [25]. The JEFF-3.3 adopts ENDF/B-VIII evaluation.  Table 3:  Californium-252 spontaneous fission neutron spectrum averaged cross sections (mb).  |  232Th |  233U |  235U |  238U |  239Pu |  240Pu |  241Pu
---|---|---|---|---|---|---|---
Present (7 nuclides) | 81.1 | 1900 | 1220 | 314 | 1812 | 1337 | 1606
Present (3 nuclides) | 81.2 |  | 1209 | 314 |  |  |
sok20220324 [45] |  | 1899 | 1221 | 315 | 1814 | 1339 | 1608
sok20210404 [38] |  | 1900 | 1223 | 316 | 1808 | 1340 | 1606
JENDL-5 [14] | 83.6 | 1901 | 1221 | 321 | 1808 | 1340 | 1606
Dezsö and Csikai[25] | 84.7$\pm$4.9 |  |  | 310.9$\pm$14.0 |  |  |
Grundl and Gilliam [24] | 89.4$\pm$2.7 | 1893$\pm$48 | 1216$\pm$19 | 326$\pm$6.5 | 1824$\pm$35 | 1337$\pm$32 | 1616$\pm$80
Mannhart [51] |  |  | 1210$\pm$15 | 325.7$\pm$5.3 | 1812 $\pm$25 |  |

##  4 Summary

We presented a new evaluation of the 232Th neutron-induced fission cross
section by the least-squares method in the energy range from 500 keV to 200
MeV. The simultaneous evaluation considers not only the 232Th but also the
235,238U fission cross sections to include the experimental 232Th/235U and
232Th/238U fission cross section ratios in the evaluation. We also expanded
the scope of the evaluation from the three nuclides to seven nuclides
including the 233U and 239,240,241Pu fission cross sections and their
corresponding ratios in fitting.

The three- and seven-nuclide evaluations give similar 232Th neutron fission
cross sections, and they are systematically lower than the JENDL-5 cross
sections. The reduction is about 4% in the plateau region between 2 and 6 MeV
and more significant in the subthreshold region. Comparisons with the measured
and evaluated values were done for the 252Cf fission neutron spectra averaged
cross section (SACS) of the 232Th fission cross section. The SACS from the
present evaluation is lower than the SACS measured by Grundl et al. by 11%
while closer than the JENDL-5 SACS to the SACS of the other general purpose
libraries.

## Acknowledgement

We are grateful to Yonghao Chen (Institute of High Energy Physics, China),
Diego Tarrío (Uppsala University, Sweden) and Zhizhou Ren (University of
Science and Technology of China, China) for sharing with us the newly
published 232Th/235U ratio data and Veatriki Michalopoulou (National Technical
University of Athens) and Francesca Belloni (CEA Saclay) for answering to our
questions on their experimental data. EXFOR compilation of the 232Th/235U
ratios measured at the CSNS Back-n and CERN n_TOF facilities were done with
Jimin Wang (China Institute of Atomic Energy) and Emmeric Dupont (CEA Saclay),
respectively. We also would like to thank the members of the International
Network of Nuclear Reaction Data Centres (NRDC) for maintenance and
development of the EXFOR library.

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