EXFOR-based simultaneous evaluation of neutron-induced uranium and plutonium fission cross sections for JENDL-5

Figures & data

Table 1. Evaluation procedures of ^233,235,238U and ^239,240,241Pu fast neutron fission cross sections in recent general purpose libraries.

Target	CENDL-3.2 (2020)	ENDF/B-VIII.0 (2018)	JEFF-3.3 (2017)	BROND-3.1 (2016)	ENDF/B-VII.1 (2011)	JENDL-4.0 (2010)
^233U	800 keV–:	(=JENDL-4.0)	(=ENDF/B-VII.1)	($\sim$ ROSFOND-2010)	(=ENDF/B-VII.0)	22 works (1969–2001)
(10 keV–)	Available works			40 keV–:	5 works (1980–1988)+GNASH
	80–800 keV:			Maslov
	(=CENDL-3.1)			–40 keV: URR
	10 works (1975–1988).
	–80 keV:
	(=ENDF/B-VII.1)
^235U	(=ENDF/VII.1)	75 keV–:	($\sim$ IAEA-2006)	($\sim$ ROSFOND-2010)	(=ENDF/B-VII.0)	16 works (1980–2007)
(10 keV–)		($\sim$ IAEA-2017)		1 MeV–: ?	25 keV–:
		–75 keV:		25 keV–1 MeV:	IAEA-2006
		IAEA-2017		(=ENDF/B-VI.8)	with denser grid
		with denser grid		Poenitz	–25 keV:
				–25 keV:	($\sim$ ENDF-B/VI.8 $\times$ 0.99)
				($\sim$ ENDF-B/VI.8 $\times$ 1.015)	Poenitz
				Poenitz
^238U	150 keV–:	2 MeV–:	1 MeV–:	1 MeV–:	(=ENDF/B-VII.0)	27 works (1961–2007)
(100 keV–)	(=CENDL-2)	($\sim$ IAEA-2017)	($\sim$ IAEA-2006)	($\sim$ ENDF/B-VII.1)	1 MeV–:
	18 works (1975–1984)	500 keV–2 MeV:	–1 MeV:	149 keV–1 MeV:	($\sim$ IAEA-2006)
	–150 keV:	IAEA-2017	TALYS-1.4	(=ENDF/B-VII.1)	–1 MeV:
	(=JENDL-3.2)	with denser grid		–149 keV: URR	(=ENDF/B-VI.8)
	2 works (1977,1978)	149–500 keV: ?			Poenitz and Fröhner
		–149 keV: URR
^239Pu	(=CENDL-2)	40 keV–:	($\sim$ IAEA-2006)	(=JEFF-3.0)	(=ENDF/B-VII.0)	25 works (1968–2007)
(10 keV–)	30 keV–:	($\sim$ IAEA-2017)		30 keV–: GNASH	30 keV–:
	12 works (1964–1988)	–40 keV:		–30 keV: URR	IAEA-2006
	–30 keV: URR	IAEA-2017			with denser grid?
		with denser grid			–30 keV: URR
^240Pu	(=CENDL-2)	6 MeV–:	TALYS-1.4	43 keV–:	550 keV–:	13 works (1961–2004)
(100 keV–)	30 keV–:	($\sim$ ENDF/B-VII.1)		All available works	Mainly one work (1998)
	11 works (1966–1990)	200 keV–6 MeV:		–43 keV: URR	40–550 keV:
	–40 keV: URR	(=ENDF/BVI.8)			(=JENDL/AC-2008)
		3 work (1976–1983)			13 works (1961–2004)
		–200 keV: ?			–40 keV: URR
^241Pu	(=CENDL-3.1)	(=ENDF/B-VII.1)	(=JENDL-4.0)	42 keV–:	40 keV–:	8 works (1961–1978)
(10 keV–)	30 keV–:			Available works	(=ENDF/B-V)
	21 works (1955–1983)			–42 keV: URR	3 works (1970–1975)
	–30 keV: URR				–40 keV: URR

=: Adoption of a preceding library without any modification. ~ Adoption of a preceding library with modifications. ?: Method/origin of the evaluation unknown.

URR: Unresolved resonance region. Works: Experimental works. IAEA: IAEA Neutron Data Standards. Poenitz/Fröhener: Poenitz/Fröhener’s evaluation. Maslov: Maslov’s statistical model calculation.

Table 2. Number of experimental datasets of fission cross sections and their ratios for final fitting.

	Numerator
Denominator	^233U	^235U	^238U	^239Pu	^240Pu	^241Pu
unity	12	22	14	19	7	8
^233U	–	–	1	–	–	–
^235U	12	–	28	19	13	4
^239Pu	–	–	–	–	2	–

Table 3. Absolute fission cross sections (in barns) from the TUD-KRI collaboration and adopted in present evaluation. ‘$E_n$’ gives the incident energy in MeV and ‘Lab.’ gives the location of the experiment. The underline indicates presence of several cross sections at the same energy from the same laboratory. The parenthesized value refers to the last digits of the uncertainty value (e.g. 1.240(24) means 1.240 $\pm$ 0.024). The incident energy value may slightly vary depending on the article when the same measurement is published twice or more.

		Target nuclide
$E_n$	Lab.	^233U	^235U	^238U	^239Pu
2.6	TUD		1.240(24) [74]
4.5	ROS		1.094(24) [74]
4.8	ROS			0.562(17) [74]	1.773(33) [74]
5.1	ROS			0.554(13) [74]
8.2	ROS			1.041(33) [74]
8.5	ROS		1.855(44) [74]		2.395(40) [74]
8.5	ROS		1.74(11) [86]
14.7	TUD	2.244(42) [52]	2.096(24) [74]	1.194(22) [94]
18.8	ROS		2.068(50) [74]	1.363(43) [74]	2.473(59) [74]
1.9	KRI	1.93(7) [50]	1.28(3) [75]		2.01(5) [50]
2.5	KRI		1.27(3) [75]
14.0	KRI		2.0840(362) [52]
14.5	KRI		2.1010(365) [52]
14.7	KRI	2.254(45) [52]	2.0960(289) [52]	1.171(23) [52]	2.309(30) [52]
14.7	KRI		2.0755(361) [52]		2.349(45) [52]
14.7	KRI		2.1348(308) [52]
14.7	KRI		2.0714(299) [52]

Table 4. Normalization uncertainties not coded in the EXFOR entries but used in the current evaluation. ‘Unc.’ gives the uncertainty in %.

Target	EXFOR #	Unc.	Source of uncertainty
^233U	13890.004	1.0	Uncertainty due to normalization to the thermal value [200] (0.25% from thermal normalization +0.7% from point-wise uncertainty)^6
^233U	51008.002	1.4	Uncertainty in the thermal reference value [202]^7
^238U	13169.003.2	1.0	Normalization uncertainty (minimum 1%, see 13169.002)
^240Pu	40673.004	0.15	Uncertainty in the target half-life (6357±10 yr)
^241Pu	40673.005	1.4	Uncertainty in the target half-life (14.4±0.2 yr)
^241Pu	51009.002	1.5	Uncertainty in the thermal reference value [202]^8
^233U/^235U	41432.003	0.74	Uncertainty in the fissile nucleus number ratio (taken from a preliminary report of the same experiment [160])
^239Pu/^235U	20569.004	1.0	Uncertainty in the sample mass (0.6% from ^239Pu+0.8% from ^235U)

Figure 1. Fitting of the logarithm of experimental cross section ${\mathrm{\Sigma }}_{\mathrm{e}\mathrm{x}\mathrm{p}}$ to Schmittroth’s roof function $\mathrm{\Delta }$ [161].

Figure 2. Fitting to the LANSCE ²⁴¹Pu(n,f)/²³⁵U(n,f) cross section ratio (EXFOR 14271.006.1) [124] with strong correlation (i.e. all partial uncertainties other than the statistical uncertainty are treated as fully correlated) and weak correlation (i.e. all partial uncertainties other than the normalization uncertainty are treated as uncorrelated). Note that the experimental data points below 1 MeV were discarded in the present evaluation.

Figure 3. Comparison of the LANSCE ²⁴¹Pu(n,f) cross section (EXFOR 14271.005) and ²⁴¹Pu(n,f)/²³⁵U(n,f) cross section ratio (EXFOR 14271.006.1) [124] with other datasets. The cross section ratio from LANSCE is normalized to the ratio at 25.3 meV by Tovesson et al. The absolute cross section is converted from the ratio by using the ENDF/B-VII library by Tovesson et al.

Figure 4. ²³³U fission prior and posterior cross sections with the experimental cross sections used for evaluation [47–58]. The prior cross section is taken from JENDL-4.0 (below 20 MeV) and Yavshits’ evaluation (above 20 MeV).

Figure 5. ²³³U/²³⁵U fission prior and posterior cross section ratios with the experimental cross section ratios used for evaluation [59–69]. The prior cross section is taken from JENDL-4.0 (below 20 MeV), Yavshits’ evaluation (above 20 MeV, ²³³U) and JENDL-4.0/HE (above 20 MeV, ²³⁵U).

Figure 6. ²³⁵U fission prior and posterior cross sections with the experimental cross sections used for evaluation [52–86]. The prior cross section is taken from JENDL-4.0 (below 20 MeV) and JENDL-4.0/HE (above 20 MeV). In the legends of Amaducci et al.’s datasets, ⁶Li and ¹⁰B denote the cross sections normalized with the ⁶Li(n,t)⁴He and ¹⁰B(n,$\alpha$)⁷Li standard cross sections, respectively.

Figure 7. ²³⁸U fission prior and posterior cross sections with the experimental cross sections used for evaluation [52, 71, 74, 87–96]. The prior cross section is taken from JENDL-4.0 (below 20 MeV) and JENDL-4.0/HE (above 20 MeV).

Figure 8. ²³⁸U/²³³U fission prior and posterior cross section ratios with the experimental cross section ratios used for evaluation [97]. The prior cross section is taken from JENDL-4.0 (below 20 MeV), JENDL-4.0/HE (above 20 MeV, ²³⁸U) and Yavshits’ evaluation (above 20 MeV, ²³³U).

Figure 9. ²³⁸U/²³⁵U fission prior and posterior cross section ratios with the experimental cross section ratios used for evaluation [59, 61, 63, 64, 73, 98–114]. The prior cross section is taken from JENDL-4.0 (below 20 MeV) and JENDL-4.0/HE (above 20 MeV).

Figure 10. ²³⁹Pu fission prior and posterior cross sections with the experimental cross sections used for evaluation [50, 52, 56, 74, 80, 81, 95, 115–123]. The prior cross section is taken from JENDL-4.0 (below 20 MeV) and JENDL-4.0/HE (above 20 MeV).

Figure 11. ²³⁹Pu/²³⁵U fission prior and posterior cross section ratios with the experimental cross section ratios used for evaluation [61, 63, 66, 69, 73, 84, 103, 105, 124–133]. The prior cross section is taken from JENDL-4.0 (below 20 MeV) and JENDL-4.0/HE (above 20 MeV).

Figure 12. ²⁴⁰Pu fission prior and posterior cross sections with the experimental cross sections used for evaluation [80, 134–139]. The prior cross section is taken from JENDL-4.0 (below 20 MeV) and JENDL-4.0/HE (above 20 MeV).

Figure 13. ²⁴⁰Pu/²³⁵U fission prior and posterior cross section ratios with the experimental cross section ratios used for evaluation [125, 128, 138, 140–148]. The prior cross section is taken from JENDL-4.0 (below 20 MeV) and JENDL-4.0/HE (above 20 MeV).

Figure 14. ²⁴⁰Pu/²³⁹Pu fission prior and posterior cross section ratios with the experimental cross section ratios used for evaluation [126, 146]. The prior cross section is taken from JENDL-4.0 (below 20 MeV) and JENDL-4.0/HE (above 20 MeV).

Figure 15. ²⁴¹Pu fission prior and posterior cross sections with the experimental cross sections used for evaluation [121, 123, 135, 136, 139, 149–152]. The prior cross section is taken from JENDL-4.0 (below 20 MeV) and JENDL-4.0/HE (above 20 MeV).

Figure 16. ²⁴¹Pu/²³⁵U fission prior and posterior cross section ratios with the experimental cross section ratios used for evaluation [67, 124, 153]. The prior cross section is taken from JENDL-4.0 (below 20 MeV) and JENDL-4.0/HE (above 20 MeV).

Figure 17. Difference of the newly evaluated cross sections from the JENDL-4.0 cross sections in the JFS-3 70-group structure.

Figure 18. Difference of the newly evaluated cross sections from the IAEA Neutron Data Standards 2017 cross sections in the JFS-3 70-group structure.

Figure 19. Californium-252 spontaneous fission neutron spectrum averaged cross sections relative to those measured by Grundl and Gilliam [175] for the present evaluation, JENDL-4.0, ENDF/B-VIII.0, ENDF/B-VII.1, JEFF-3.3 and CENDL-3.2 evaluations as well as Mannhart’s recommendation [177]. Note that ENDF/B-VIII.0 adopts JENDL-4.0 for ²³³U, and JEFF-3.3 adopts JENDL-4.0 for ²⁴¹Pu.

Table 5. Californium-252 spontaneous fission neutron spectrum averaged cross sections (mb).

	^233U	^235U	^238U	^239Pu	^240Pu	^241Pu
Present	1900	1223	316	1808	1340	1606
Grundl [175]	1893 $\pm$ 48	1216 $\pm$ 19	326 $\pm$ 6.5	1824 $\pm$ 35	1337 $\pm$ 32	1616 $\pm$ 80
Mannhart [177]		1210 $\pm$ 15	325.7 $\pm$ 5.3	1812 $\pm$ 25

Figure 20. Comparison of the ²³⁸U(n,f) cross sections from the present evaluation with the evaluated cross sections in ENDF/B-VIII.0 and ENDF/B-VII.1 as well as absolute cross sections in the EXFOR library compiled from the articles published no earlier than 1970. The solid circles show the data points from a recent (2017) absolute measurement at NPL [87].

Figure 21. Ratios to the $\mathrm{\Sigma }\mathrm{\Sigma }$ neutron spectrum averaged cross sections measured by Gârlea et al. [179] for those derived from the cross sections of our present evaluation as well as JENDL-4.0, ENDF/B-VIII.0, ENDF/B-VII.1, JEFF-3.3 and CENDL-3.2 evaluations. Note that ENDF/B-VIII.0 adopts JENDL-4.0 for ²³³U and JEFF-3.3 adopts JENDL-4.0 for ²⁴¹Pu.

Table 6. $\mathrm{\Sigma }\mathrm{\Sigma }$ neutron spectrum averaged cross sections (mb).

	^233U	^235U	^238U	^239Pu	^241Pu
Present	2290	1493	82.36	1753	1972
Gârlea [179]	2325 $\pm$ 93	1512 $\pm$ 53	83.46 $\pm$ 3.3	1780 $\pm$ 62	2026 $\pm$ 81

Figure 22. C/E values of the LANL small-sized fast system criticalities calculated by MVP Version 3 with the cross sections in JENDL-4.0 and those updated with the present evaluation. The standard deviation in the calculated criticality is within the size of the symbol. Courtesy of Yasunobu Nagaya (JAEA).

Figure 23. The ²³⁸U/²³⁵U and ²³⁹Pu/²³⁵U cross section ratios from measurements by Paradela et al. [100], Tovesson et al. [59, 124], Shcherbakov et al. [61], Lisowski et al. [73] and Staples et al. [125] (symbol) as well as the prior (JENDL-4.0 and JENDL-4.0/HE) cross sections (solid line) relative to the ratios from the present evaluation. The EXFOR 23269.003 and 23269.004 datasets by Paradela et al. are from two configurations of the same sample and compiled together in our experimental database as a single dataset (EXFOR 51005.002).

Figure 24. External uncertainties in the fitting parameters in the roof function and rectangular function expressions. The uncertainty in the parameter in the rectangular function expression is equal to the uncertainty in the group-wise cross section. The horizontal dashed line indicates best achievable precision for each nuclide. The additional histogram (thin solid line) between 50 keV and 160 keV of the ²³⁵U panel shows the uncertainty in the cross section measured by Amaducci et al. [70].

Figure 25. Uncertainties from the present evaluation (rectangular function expression) and IAEA Neutron Data Standards 2017 evaluation (group-wise cross section). (a) External uncertainties from the present evaluation and uncertainties including the unrecognized systematic uncertainties (USU) from the IAEA-2017 evaluation. (b) Internal uncertainties from the present evaluation and uncertainties excluding USU from the IAEA-2017 evaluation.

Figure 26. Correlation coefficients of the fitting parameters from the present evaluation in the rectangular function expressions. The numbers on the ticks along the axes on the upper and right sides give the exponentials of the incident energies in eV by power to base 10 (e.g. 6 for ${10}^6$ eV).

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