Americium-241 phase I: reevaluation for JEFF-3.1.1 and a step forward

Abstract

This article reviews the low energy neutron cross section revision and the capture isomeric ratio evaluation of the ²⁴¹Am neutron data performed for JEFF-3.1.1. It covers the history of the anterior evaluation made for JEF-2.2 and gives the consistent path used for re-evaluating the resolved resonance parameters from differential measurements and “integral” data feedback. This article highlights the procedure pursued to evaluate the ²⁴¹Am capture ISOmeric ratio (ISO _γ) from 0 to 20 MeV in parallel with a valuable estimation of the associated variances. Monte Carlo-type calculations have been made which predict ISO _γ fluctuations over the energy region of the resolved resonances due to the presence of 2 s-wave types exhibiting well separated individual values (estimated to (90 ± 3)% and (76 ± 3)%, respectively, for a 2⁻ and a 3⁻ resonance) and well-resolved γ-multiplicities ( and ). Arguments are developed for using directly pointwise ISO _γ data in reactor codes in the form of resonant partial capture cross sections, possibly from extended multi-level Breit–Wigner resonance parameterization, allowing systematic ISO _γ Doppler broadening for a better comparison between experimental, differential, and integral measurements. This work corrects the fission widths of the lowest resonances inadequately treated during the JEFF-3.1.1 revision with an attempt of spin assignment supported by the present ISO _γ study. Part of this work was also the preamble for the design of a new differential data program at the IRMM/Geel. This article shows the present status on the ²⁴¹Am evaluated neutron data in terms of low energy cross sections and ISO _γ data and, proposes some directions for the next JEFF-3.2 stage.

Keywords:

• Americium-241
• JEFF-3.1.1
• evaluation
• SAMMY
• cross sections
• isomeric ratio and fluctuations
• thermal energy
• resonance parameters
• integral data
• differential data
• isomeric ratio variances

1. Background and goals

The earliest motivation of this work has to be found in the results of the European Joint Evaluated File JEF-2.2 validation. Several analyses of reactor experiments [1,2,3–5] revealed at that time that there could be an underestimation of the ²⁴¹Am capture cross section () in the thermal and epithermal energy ranges. But this information cannot be treated solely from the feedback on two other key parameters: the ^242m Am absorption cross section () and the ²⁴¹Am capture isomeric ratio 1 (ISO _γ) to the ²⁴²Am. The ²⁴¹Am capture decay path (displayed in Figure 1 ) illustrates this context. A posterior work [6] confirmed that the fuel inventory prediction on ^242m Am (see Table 1 ) was still strongly underestimated with the revision 3.0 of the European Joint Evaluated Fission and Fusion file (JEFF-3.0) for high burn-up values in UO _x and MO _x post irradiated assemblies, respectively, from the Cruas and Dampierre French Pressurized Water Reactor (PWR). Another complementary index is the prediction made on the amount of ²⁴¹Am (see Table 1 as well) which sensibility depends especially on at high burn-up values.

Table 1. Discrepancies [%] observed [6] between calculated (C) and experimental (E) values on the ²⁴¹Am and ^242m Am fuel inventory prediction using JEFF-3.0: (C-E)/E ± δE/E ratios, at lσ. The predicted ratio is calculated directly at the end of the cycle (EoC).

Experiment	Cruas UO x	Dampierrre MO x
Spent fuel index	(80GWd/tHM)	(60GWd/tHM)
^241 Am/^238 U EoC	17.4 ± 6.1	16.5 ± 3.7
^242m Am/ ^238 U	−12.5 ± 6.8	−20.2 ± 3.5

Figure 1. Decay path related to ²⁴¹Am capture; E.C = electron capture, I.T = isomeric transition. The isomeric ratio values to ^242g Am and ^242m Am are indicative and are those measured by Fioni et al. [9].

In addition to these investigations, an accurate knowledge on the ²⁴¹Am neutron cross sections is of great importance in nuclear applications for several reasons.

•	In MO x fuel pins (UO2-PuO2), the composition changes with time due to the β− decay of 241Pu and build up of 241Am. An underestimation of the thermal capture cross section of the 241Am leads to a wrong estimation of the Pu ageing. This fact was revealed in the French MO x critical experiments, MISTRAL 2&3 [7], in which the same MO x fuel rods were loaded at different times, and also in a series of dedicated Japanese experiments, continued over a long period, with a single core configuration [8].
•	The prediction of the minor actinides inventory in spent fuels is strongly linked to the characteristics of the 241Am decay chain.
•	As regards to the radio-toxicity level of the americium, neptunium, and curium isotopes, these materials are the minor actinides to be transmuted in priority. An accurate knowledge on their neutron characteristics is needed for defining and studying by simulation burning systems whose fuels would be enriched in minor actinides. All studies in that area are fully in agreement with the axis 1 of the 1991 December French law which is relative to the various possibilities for reactor waste transmutation.

From the observation that the ²⁴¹Am neutron data were not re-evaluated for JEFF-3.0 2 and that new microscopic measurements had been performed since the official release of JEF-2.2 in 1990, a synthesis on the ²⁴¹Am neutron data was made in 2002 [10]. This synthesis was based on the released experimental data (microscopic differential and integral data), 3 the major evaluated data files, and on the nuclear data trends derived from the experimental validation [4] of the neutronic code APOLLO2 and its associated JEF-2.2 based library. The various comparisons made from the evaluated data files (JENDL-3.3, ENDF-BVI.8, BROND3, and JEFF-3.0) have in particular underlined some large discrepancies on the ²⁴¹Am data between differential cross section and integral measurements. The synthesis also pointed out strong discrepancies on values between the various evaluations and their practical treatment (energy average) in reactor calculations. Additionally, it must be noticed that the JEF-2.2 (neither JEFF-3.0) evaluated library did not contain any tabulated (or partial capture cross sections) and uncertainties.

Finally, an updated synthesis on americium nuclear data [11] concluded that new microscopic measurements were not worthwhile to significantly improve the accuracy on that americium isotopes data. As a consequence, a new experimental campaign involving a series of transmission, capture, and (n,2n) measurements was performed in the framework of a CEA-IRMM-FZK-BNC 4 collaboration. It must be noted that similar efforts were encountered over the world as for instance at the LANSCE facility [12], at the CERN n_TOF facility [13], or through the JENDL-4.0 file project [14]. An ultimate feedback (summarized in Table 2 ) obtained in 2004 [15] with the APOLLO2 code for high burnup UO _x and MO _x spent fuels has stressed an urgent need for a better accuracy on the ²⁴¹Am cross section and ISO _γ data. This article traces back the revision of both low energy resonant cross sections and ISO _γ behavior versus energy, which were adopted for JEFF-3.1 and maintained in the last official JEFF-3.1.1 release. 5 This article comes as preamble to the next step which will include the results of the latest experimental, differential, and integral datasets using the modern capabilities of the CONRAD [16] tool.

Table 2. Integral data feedback from study [15] relative to ²⁴¹Am neutron data.

Type of integral data analyzed	Suggested correction on Am [%]
^241Am/^241Pu isotopic ratio	+16 ± 4
^242Cm and ^243Cm build-up	+30 ± 15
Reactivity worth due to plutonium ageing	+12 ± 4
Irradiation of ^241Am as separated isotope	+22 ± 10
Weighted average	+15 ± 3

2. Early feedbacks from JEF-2.2 and JEFF-3.0 processing and validation

2.1. JEF-2.2 file story

In the energy range 0–150 eV, the JEF-2.2 file contains the ²⁴¹Am resolved resonance parameters evaluation of Fröhner et al. [17] performed in 1981 for the KEDAK German evaluated data file project. The evaluation of Fröhner et al. [17] includes 188 positive resonances and one negative level at −0.42 eV in the multi-level Breit–Wigner (MLBW) approximation (in the ENDF-6 format sense) of the R-matrix [18]. Ideally, according to the Gilbert and Cameron level density [19] empirical formula, there should be in the s-wave resonance sample around 43% of spin-parity 2⁻ and 57% of spin-parity 3⁻ in the energy range right above the neutron separation energy in the compound system (²⁴²Am^*). Fröhner et al. [17] assigned all resonances to the same average spin value (2.5) since no confident assignment was possible on the s-wave resonance sample. This evaluated resonance parameter dataset was adopted for JEF-2.2 but in the meantime the value of J was changed arbitrary to the physically possible value of 3.0. 6 This should have required a correction on the resonance neutron width (Γ _n ) values only (keeping the product g _J Γ _n unchanged). Unfortunately, a series of errors during this conversion, likewise generated by a wrong tabulation of the bound level neutron width value in KEDAK, led to cross section curves for JEF-2.2 in disagreement with the original work of Fröhner et al. [17]. In order to compensate the differences, a background cross section was added in the file. This problem was noticed by Konieczny and Rowlands in 1995 [20]. Since no revision on the resolved resonance range (RRR) data was made for JEFF-3.0, this error was re-conducted. Additionally to distorted resonance parameter values, this bug was creating an abnormal dip in the scattering cross section value at very low energy. However, the thermal cross section and resonance integral values were slightly different from the original ones. For quality assurance, we repeated the conversion procedure from the original evaluation of F. Fröhner et al. [17] and we have got this time the correct representative values (printed in column “Regenerated JEF-2.2” of Table 3 for reference) without background cross sections.

Table 3. Thermal capture, fission and scattering cross sections, and capture and fission resonance integral (in barns) reconstructed by NJOY [25] at 293.6 K.

	JEF-2.2	JEF-2.2 regenerated	Fröhner et al. [17]
	615	609.6	610 ± 19
	3.18	3.15	3.15 ± 0.16
	12.08	13.07	12 ± 3
I γ	1446	1442
If	16.05	16.03

2.2. ²⁴¹Am evaluated data files content

At this stage, it is convenient to review briefly the content of the major Evaluated Nuclear Data Files (ENDF) in 2006 (so excluding the recent revisions made in particular for JENDL-4.0 [14] which will be commented in the section 5 of this article; ENDF/B-VII.1 is currently relying on this JENDL-4.0 evaluation in terms of resonance range data) as far as capture and fission resonance integrals (I _γ and I_f ) and associated thermal cross sections ( and ) are concerned. The comparison between JEF-2.2 (regenerated) and other evaluated files is summarized in Tables 4 and 5 . All the evaluated thermal capture cross sections and capture resonance integrals (see definition, later in the text) are in a reasonable agreement (respectively, within % and %) except the Belanova et al.'s [21] evaluation (+35% on ). The disagreement between Belanova et al.'s [21] work and the other evaluations comes from the selection made on the experimental datasets, which relies on integral experiments (Bak et al. [22], Harbour et al. [23], and Gavrilov et al. [24]; see Table 7) for the former and on differential measurements for the others (see Table 6 for instance). The results supplied by the integral experiments are in general systematically much higher than the various differential data and this fact is worth to be debated in the next sections.

Table 4. Synopsis of the major evaluations in 2006. Printed values are in barns.

	JEF-2.2 regenerated	JENDL-3.3	ENDF/B-VII.0	BROND-3	Atlas
Year	This article	2002	2006	1997	2006
	609.6	639.5	619	619	587 ± 12
I γ	1442	1460	1386	1390	1425 ± 100
	3.15	3.14	3.14	3.14	3.20 ± 0.09
If	16.03	14.8	15.8	14.7	14.4 ± 1.0

Table 5. Older evaluated files. Printed values are in barns.

	JEF-2.2 regenerated	JENDL-3.2	Maslov	BNL	Belanova
Year	This paper	1989	1996	1984	1994
	609.6	600	585	587 ± 12	824 ± 20
I γ	1442	1310	1350	1425 ± 100	–
	3.15	3.02	3.14	3.20 ± 0.09	–
If	16.03	13.86	14.5	14.4 ± 1.0	–

Table 6. Differential thermal cross section as retrieved from the EXFOR experimental nuclear reaction data system. The thermal capture cross section is deduced from the thermal scattering and fission cross section values, respectively, set to 12.5b and 3.14b.

	Measurement category
	Transmission	Transmission	Absorption
Year	1976	1955	1976
First author	Belanova	Adamchuck	Weston
EXFOR number^34	40305	40063	10767
	622	584	579 ± 6

Table 7. Survey on ²⁴¹Am microscopic integral capture measurements and associated thermal values. Data base used as support to JEFF-3.1.1. Table 22 lists the most recent values not included in the JEFF-3.1.1 study but used in this article to address new directions in the next JEFF-3.2 stage.

	Year	First author	EXFOR number^34	[b]	I γ[b]
	2006	Bringer	22941.003	714 ± 23
Recent	2001	Maidana	31518	662 ± 10**	1779 ± 91
experiments	2001	Fioni	22696	696 ± 48^33
	1997	Shinohara	22346	797 ± 31*	1897 ± 93
	1976	Gavrilov	40467	853 ± 52	1800 ± 136
Old	1973	Harbour	10317	832 ± 20	1538 ± 118
experiments	1969	Dovbenko	_	647 ± 104
	1967	Bak	40062	740 ± 60	2400 ± 200
	1955	Pomerance	11885	625 ± 35
Note: *Shinohara's datum quoted below is now superseded by the final value reported in 1997 [EXFOR 22727] [31] giving **Maidana's value was extrapolated assuming Fioni's capture value to metastable; .

Table 22. Updated list of recent ²⁴¹Am microscopic integral capture measurements and derived thermal values. Database used as support to next JEFF-3.2 stage. The value, quoted by Letourneau et al. [59] and extracted from a microscopic integral measurement using the MINI-INCA set-up and the canal V4 of the ILL reactor, must be considered as “preliminary.”

Year	First author	EXFOR number [34]			I γ[b]
2011	Letourneau	Unpublished	677 ± 20	586 ± 5
2008	Jandel	14209	665 ± 33
2007	Nakamura [60]	22998	688 ± 22**
2007	Bringer	22941.014	704 ± 32*
2001	Maidana	31518	662 ± 10		1779 ± 91
2001	Fioni	22696	696 ± 48^33
1997	Shinohara	22727	854 ± 58		1808 ± 146
Note: *The measurement by Bringer et al. #22941.014 supersedes the EXFOR set #22941.003 listed in Table 7. **Nakamura's result was extrapolated assuming Fioni's capture value to metastable;.

Although the ²⁴¹Am ENDF/B-VII.0 nuclear data file [26] was the most recent in 2006, the resonance range (E < 30 keV) has not been revised since 1988. The ²⁴¹Am resolved resonance parameters stored in JENDL-3.3 were re-evaluated by Nakagawa et al. [27] after having noticed that the ²⁴¹Am capture cross section given in JENDL-3.2 was about 20% underestimated in the thermal energy range. It must be noticed that the low value (587 ± 12)b recommended by the National Nuclear Data Center of Brookhaven for the thermal capture cross section has been reconducted in the fifth edition [28] of the “Atlas of Neutron Resonances.”

In terms of thermal fission cross section, Tables 4 and 5 show the general consensus existing in 2006 between the various evaluations on the value of 3.14b although the “Atlas of Neutron Resonances” still recommends a slightly larger value (3.20 ± 0.09)b.

2.3. Integral or differential measurements? Example of accuracy on thermal cross section and resonance integral results

During this work, large efforts were spent to make consistent the existing experimental data, especially in terms of capture resonant integral and thermal capture cross section. Each datum can be classified following its origin. One may distinguish results from

1.	chopper or linear accelerator Time of Flight (ToF),
2.	Van de Graaff accelerator,
3.	intense thermal flux reactor and,
4.	power or mock-up reactor reaction rate measurements.

Existing results from the first and second categories are a priori more robust than the so-called “integral” (microscopic or macroscopic) experiments of categories 3 and 4 because they bring information directly at a precise energy. In addition, first category results are usually normalized on transmission measurements, which are considered as absolute measurements and thus fully trustable.

2.3.1. Capture feedback

First category measurements are shown in Table 6 in terms of thermal capture cross section values for comparison with the absorption cross section measurement by Weston and Todd [29] who estimated an uncertainty less than 1% below 1 eV. The oldest total cross section measurement by Adamchuk et al. [30] does not include any uncertainty. The total cross section released by Belanova et al. [21] is only associated to a statistical uncertainty of 1% but an uncertainty of about 3% (meaning σ _n,γ = (622 ± 19) b) was reported by Fröhner et al. [17]. Even if these first category measurements are qualified as absolute, experience shows that they must be definitively double-checked by comparison with integral data results. At the end of the present whole study, we are inferring a plausible renormalization factor larger than +6% on the largest value (Belanova et al. [21] capture cross section dataset).

The differential thermal capture cross section values are in a reasonable agreement but they remain significantly smaller than integral data (displayed in Table 7 ) which show also a larger spreading ((625 ± 35)b ≤  ≤ (853 ± 52)b). The reasons for such a differential/integral data disagreement has to be found in the fact that ²⁴¹Am has two very strong low energy resonances at 0.31 eV and 0.58 eV. These resonances contribute strongly to the measured yield making integral measurements dependent on their actual reactor spectrum. Thereof, most of thermal capture cross section values reported from integral experiments are effective capture cross sections (noted ). The measured effective thermal cross section can differ substantially from the true value (). A direct comparison between integral thermal cross sections and differential thermal cross sections relies on a careful raw integral data reduction which implies precise knowledge on the epithermal to thermal fluxes ratio, on the Westcott factors [28] characterizing the low energy cross section slopes, and on self-shielding factors in epithermal and thermal ranges.

Several integral measurements (Bak et al. [22], Harbour et al. [23], Gavrilov [24], and Shinohara et al. [31]) used the Cd ratio technique and so, are dependent on the effective cut-off energy (function of the Cd thickness) which none sharp value falls into the range of the two lowest energy ²⁴¹Am resonances. Unfortunately, experimental details on neutron spectra in old integral measurements are in most cases not available and so not reproducible. However, when the actual neutron spectrum is rigorously reproduced, reasonable agreement between differential and integral experiments can be established. A notable example is the Cd ratio measurement from Harbour et al. [23] (see Table 7). The authors detailed the treatment of both the Cd cut-off energy and the neutron spectrum characterizing their experiment. Assuming a 2200 m/s evaluated neutron capture cross section value of 582b (previously recommended in ENDF/B-III) and weighting by the measured neutron flux, the authors have found an effective cross section value of 830b, consistent with their measured value (832 ± 20)b. Sometimes an integral experiment is especially adapted for a direct retrieval of the 2200-m/s capture cross section. That was the objective of Dovbenko et al. [32] who performed their measurement in the thermal column of a reactor, yielding a thermal capture cross section of (647 ± 104)b. This value is comparable with the set of differential data. Similarly, Pomerance et al. (1955) measured the capture cross section relative to gold in a pile oscillator experiment. The resulting value 7 was  = (629 ± 35)b.

Recent integral experiments (also displayed on Table 7) demonstrate that the experimentalists are now aware of the importance of a very accurate determination of the self-shielded neutron flux. Among the most recent integral values released in 2006, three of them, respectively performed by Fioni et al. [9] b; Maidana et al. [33] b; and Bringer et al. b, tend to get closer to the differential results. The authors argue that they have recovered the true thermal cross section. The fourth integral measurement, by Shinohara et al. [31] in 1997, still shows a very large measured cross section value:  = (854 ± 58)b. This high value is consistent with the resonance integral they reported: I _γ = (1808 ± 146)b. Such large values essentially show up for integral measurements based on Cd ratio technique which require a very careful data reduction procedure. Additionally, the equivalent Cd cut-off energy corresponding to an ideal full black filter must be calculated to stick to the strict definition of the “reaction resonance integral” (I_r ) defined as: with E_c equal to 0.5 eV.

In the detailed work of Harbour et al. [23], an equivalent cut-off energy has been calculated and found to be equal to 0.369 eV. Correcting Harbour et al.'s [23] value, I _γ = (1538 ± 118)b, on the basis of the resonance integral calculated between 0.369 eV and 0.5 eV, their value is reduced to I _γ = (1420 ± 109)b. This latter value becomes compatible with the evaluated resonance integrals from JEF-2.2 (regenerated) (1442b) and JENDL-3.3 (1460b).

2.3.2. Fission feedback

Although the ²⁴¹Am fission cross section remains negligible below the threshold 8 (from a neutronic point of view); a re-evaluation work must also deal with a precise thermal fission cross section value. Several measurements are available in the EXFOR [34] library. Starting from Cunningham et al. in 1951 until Yamamoto et al. [35] in 1997, the values are spread between 2.8b up to 3.8b. Table 8 lists the experimental data used for JEFF-3.1.1. The evaluation of Fröhner et al. [17] is essentially based on the spectrum-averaged cross section of Hulet et al.,  = (3.13 ± 0.16)b, and converted to the 2200 m/s value,  = (3.15 ± 0.16)b. For the present work, it has been decided to make confidence in the recent measurement,  = (3.15± 0.097)b, performed by Yamamoto et al. [35] in 1997 after having updated the reference ²³⁵U thermal fission cross section to the ENDF-B/VII standard value; 584.33b rather than 586.2b. This simple correction leads to a slight decrease of their value (down to 3.140b).

Table 8. Integral thermal fission cross sections as published – JEFF-3.1.1 database.

Year	First author	EXFOR number^34	[b]	Comments
1951	Cunningham	13574	3.0 ± 0.2	Heavy water
1951	Hanna	12496	3.0	Thermal
1957	Hulet	12497	3.13 ± 0.15	Thermal
1966	Hyakutake	20274	3.8 ± 0.2	Thermal
1967	Bak	–	3.15 ± 0.10	VVR-M reactor
1975	Gavrilov	40467	2.8 ± 0.25	SM-2 reactor
1975	Zhuralev	40436	3.2 ± 0.15	SM-2 reactor
1997	Yamamoto	22344	3.15 ± 0.097	Heavy water, thermal

One large source of uncertainty shows up immediately in the raw data reduction formula (see Equation (1)) employed by Yamamoto et al. [35].

where C^isotope, N^isotope , and stand, respectively, for the measured fission events, the number of atoms, and the Westcott fission factors corresponding to the isotopes contained in the sample and T_n is the neutron temperature characterizing the Maxwellian distribution of the measured spectrum.

The knowledge on the Westcott fission factor (g_f ) value, which classic Westcott formula is recalled by Equation (2), remains often poor and especially on minor actinides.

, the energy equivalent to a neutron temperature spectrum (T_n ) which characterizes the Maxwellian distribution of the measured spectrum.

The authors took a value of 0.996 9 for the ²⁴¹Am and a neutron temperature of 60°C; although Gryntakis et al. [36] gave 1.0220 for instance. An estimation of this factor at 333.6 K using the classic Westcott formula (Equation (2)) and the JENDL-3.3 library leads to a value of 1.0257 close to the result from Gryntakis et al. [36]. Superseding the original value by that one would decrease significantly Yamamoto et al.'s [35] cross section (from 3.14b down to 3.05b). Nonetheless, the value of (3.14 ± 0.097)b was preserved for JEFF-3.1.1 to remain in accordance with Fröhner et al. [17] recommendation (3.15 ± 0.16)b.

2.4. JEFF-3.1.1 low energy differential measurement database

2.4.1. Total cross section

Among several datasets available, two measurements performed within a couple of years (1975–1976) were used as reference in JEF-2.2. These two transmission measurements performed by Belanova et al. [21] in 1976 and by Derrien and Lucas [37] in 1975 are complementary since best suited, respectively, for the two lowest energy resonances (0.31 and 0.58 eV) and the remaining bunch of resonances. The best energy resolved measurement, by Derrien and Lucas [37], was chosen as present reference for the total cross section (except in terms of energy scale which is based on the most precise measurement; see section 2.4.2.) for this limited revision. The measurement by Adamchuk et al. [30] was only kept for the 1/v thermal slope tuning because of a too thick experimental sample that causes the saturation of the signal over the resonances. Only two total cross section datasets covering the two lowest energy resonances were available for this JEFF-3.1.1 work. The two sets, respectively, performed by Belanova et al. [21] and Slaughter et al. [38] differ significantly in magnitude; Slaughter et al. [38] exhibiting the largest values. No experimental errors are reported for the latter measurement, whereas a maximum statistical-type error of 1% is given for the former. Characteristics of the total cross section differential measurements involved in our JEFF-3.1.1 work are listed in Table 9 . Additional fine data reduction parameters tuned during the work are listed as well. Normalization factors applied are determined on the basis of the present reference thermal cross sections (see section 2.5.2) whereas background information is extracted from rough estimation of a constant term between resonances.

Table 9. Total cross section data from differential measurements – JEFF-3.1.1 database.

First author		Belanova	Derrien	Slaughter	Adamchuck
Year		1976	1975	1961	1955
EXFOR number		40305	20415	12478	40063
Energy range [eV]		0.021–400	0.784–1077	0.26–42	0.0063–82
		637.5	–	–	600
Additional	Normalization [%]	+3.94	Our reference	No	+10.44
data	Background [b]	25	Our reference	48	No evidence
reduction	Energy shift?	Yes	Yes	Yes	No evidence

2.4.2. Absorption and capture cross sections

Two datasets were available below 100 eV for this JEFF-3.1.1 work. The most recent measurement (i.e. a capture) performed in 1985 at the IRMM/Geel by Vanpraet et al. [34] does not cover the energy range of the two lowest energy resonances and the first resonances observed are saturated (and so, was not considered during this work). The absorption measurement by Weston and Todd [29], which covers the energy range from 0.01 eV to 380 keV, exhibits a good energy resolution but also a pretty large background in the valleys between resonances (roughly evaluated to 15b in this work). The authors have estimated below the neutron energy of 200 meV a systematic error smaller than 1% and have announced above 1 eV a much larger systematic error (7%) including a 5% normalization uncertainty. The characteristics of these datasets are summarized in Table 10 .

Table 10. Absorption and capture cross sections from differential measurements – JEFF-3.1.1 database.

First author		Vanpraet	Weston
Year		1985	1976
Exfor number		21978	10767
Energy range [eV]		0.68–150000	0.01–377723
		–	582.
Additional	Normalization [%]	Irrelevant	+11.6
data	Background [b]	Irrelevant	15
reduction	Energy shift?	Irrelevant	Yes

2.4.3. Fission cross section

A large amount of fission data was available for the JEFF-3.1.1 revision and their characteristics are summarized in Table 11 . The average data (not displayed in Table 11) obtained by Yamamoto et al. [35] in 1996 from 0.1 eV to 10 keV based on ToF techniques are not suitable for a resolved resonance parameters evaluation. The data obtained by Dabbs et al. [39] were not released yet in 1983 at the time of the Kedak-4 evaluation by Fröhner et al. [17]. Since the authors argued for a better energy calibration than Derrien and Lucas [37], their fission yield measurement is adopted in the present work as absolute reference in terms of energy scale. The experimental fission cross section dataset obtained by Gerasimov et al. can only be used for thermal adjustment since the observed resonances are either distorted or saturated. The missing uncertainties in Bowman et al. dataset are crudely estimated following the empirical law described in Equation (3).

Table 11. Fission cross section from microscopic measurements – JEFF-3.1.1 database.

First author	Dabbs	Derrien	Gerasimov	Bowman	Leonard
Year	1983	1975	1966	1965	1959
Exfor number	12809	20415	40270	12571	12476
Energy range [eV]	0.019–89000	1–40	0.023–50	0.032–5200	0.031–5250
	3.092	3.13	3.127	3.031	3.487
Uncertainties	stat.+syst.	stat.+background	sparce	no	type?
Additional data reduction
Normalization [%]	1.016	1.003	1.004	1.036	0.9005
Energy shift	our reference	yes	no evidence	yes	yes

with the constant, C, chosen such as the ratio be always defined positive.

2.5. Resolved resonance parameters (RRP) approach

2.5.1. JEFF-3.1.1 adopted procedure

Since the existing ²⁴¹Am differential experimental database in the resolved resonance energy range was pretty poor at the time of the JEFF-3.1.1 work and that a large IRMM-CEA-FZK-BNC measurement campaign was initiated from this ascertainment, it was decided to:

•	limit the JEFF-3.1.1 RRP re-evaluation task to the lowest energy range (thermal domain and first four resonances) which supplies the main contribution to the resonance integrals (I γ or If ),
•	keep confidence in the earlier RRP set fitted by Fröhner et al. [17] in the energy range not revised during the present work. This choice forces to stick to the MLBW-ENDF-6 convention used by Fröhner et al. [17] during his resonance parameter analysis.

Since the subthreshold fission cross section is pretty small in the ²⁴²Am^* compound system and no fission clusters show up, our low energy RRP re-evaluation procedure was divided in two quasi-independent steps: the first step has involved the determination of the neutron and capture resonance widths via a quasi-simultaneous analysis (sequential procedure) of differential total and absorption cross section data within the limits imposed by the feedback on the integral data validation and, a second step was dedicated to a fit on the fission widths from differential fission cross section experimental data. The second step was not included in JEFF-3.1 nor in the subsequent JEFF-3.1.1 file and explains why both files contain fission widths (tabulated in record 2-151 which corresponds to the resonance parameters section of the evaluated data file) not consistent with the revised set of neutron widths. The present article aims to correct these erroneous fission widths. It also proposes a dedicated resonance spin assignment over the whole set of resolved resonances. This assignment was achieved using the CALENDF code [40] which is based on a statistical Wigner spacing distribution law (corrected for spacing correlations) coupled with a Gilbert and Cameron level density function. However, this prior statistical information was amended, as far as the low energy resonances (bound levels and four real resonances) are concerned, with the feedback coming from our isomeric ratio analysis (see section 3.2.). It explains why the JEFF-3.1.1 file contains two bound levels, one of each s-wave possible spin groups (2⁻) and (3⁻) since no additional information was inferred at that time. The present set of low energy resonances is constrained only by one bound level of spin 2⁻.

The SAMMY computer code [41] was used to recalculate the cross sections in the thermal range and in the low energy domain covering the first four resonances. The calculated cross sections are fitted to the experimental data by solving Bayes equations for values of the variable parameters. The analysis of the set of experimental data provides the physical parameters pertaining to the formalism (i.e. the resonance channel widths) and the fine-tuned experimental parameters listed in Tables 9 –11 (additional background and normalization corrections, effective sample temperature (295.5 K on a free gas model basis with a ²⁴¹AmO₂ sample Debye temperature of 121 K and an experimental average temperature of 293 K), energy scale shift, etc.). The SAMMY fit requires a set of valuable prior RRP which was established from Fröhner et al.'s [17] parameters after the above spin assignment. Table 12 gives the original KEDAK-4 values (resonance energies and 2g_j Γ _n products) and the newly associated spins. Since the present RRP revision remains limited and because of the poor degree of consistency noted between the set of differential data, it has been decided to preserve the nuclear radius a_c and the “effective” radius R′ [18] values tabulated in JEF-2.2. The a_c calculation sticks to the ENDF-6 convention [42] a_c  = (1.23A ^1/3 + 0.80) = 8.43 fm and is used to calculate centrifugal penetrabilities P_c and level shift factors S_c , whereas R′ is substituted to the radius in the hard-sphere phase φ_c formulation involved in the collision matrix which describes the ²⁴²Am^* compound system in interaction. In addition, the SAMMY fits are performed such as the observed cross section peaks occur at the formal resonance energies E _λ corresponding to a zero level shift (so-called Δ_λγ factor). The resonance energies are free to vary during the fit in order to compensate the energy scale shifts observed among the various datasets. The ultimate resonance energies are fitted on our reference energy scale dataset (i.e. Dabbs et al. [39]).

Table 12. (²⁴¹Am+n) resonance parameter sets, prior and posterior to the present two-steps analysis. Present spin assignment (1 = 0 assumed throughout) is given.

	Prior values (Kedak-4)				Posterior values (present two-steps analysis)
Eλ [eV]	gJ	2gj Γ n [eV]	Γγ [meV]	Γ f [meV]		J ^π	gJ	2gj Γ n [eV]	Γγ [meV]	Γ f [meV]
−0.423	0.5	5.79100E-04	46.0	0.188	−0.421	2^–	5/12	5.99200E-04	45.13	0.205
0.308	0.5	5.80000E-05	46.9	0.390	0.305	2^–	5/12	7.14000E-05	43.53	0.264
0.577	0.5	9.70000E-05	47.0	0.290	0.575	3^–	7/12	1.10600E-04	40.67	0.093
1.273	0.5	3.40000E-04	47.2	0.390	1.269	2^–	5/12	3.38500E-04	48.44	0.383
1.927	0.5	1.13000E-04	44.3	0.075	1.929	3^–	7/12	1.21400E-04	48.82	0.081

The SAMMY code is designed to fit simultaneously differential data and microscopic integral quantities such as Maxwellian average at thermal energy (see Equation (4)). Unfortunately, the SAMMY energy bounds (E ₁ and E ₂) are imposed to 10⁻⁵ eV and 3 eV, respectively, which do not allow much fitting flexibility. At final, the procedure favored has relied on simultaneous differential data fits (including constrained thermal cross sections values) with subsequent APOLLO2 calculations (requesting an update of the APOLLO2 data testing library with the newly fitted ²⁴¹Am resonance parameters set). This hand-made trial-error procedure was repeated several times to get a reasonable agreement among differential data and integral Post Irradiated Experiments (P.I.E.) trends such as the increase on the epithermal capture resonance integral value reaches the desired target (+15% ± 3%(1σ)) within the energy range [0.1–2.2 eV]. This value is extracted from an exhaustive data validation study [15] which involves the average of four independent integral observables weighted by their relative uncertainties (δE/E)². Table 2 lists these observables. The energy domain implied in the recommendation [0.1–1.5 eV] has been slightly enlarged for the purpose of the present work.

where E ₁ = 10⁻⁵, E ₂ = 3eV, and E ₀ = 0.0253eV.

2.5.2. Differential database and thermal cross section selection

From the arguments developed in section 2.3, the following constraints were applied to the thermal values:

•	was assigned to 647b; value which was a reasonable compromise between microscopic integral and differential values available at the time of the JEFF-3.1.1 evaluation.
•	was set to the recent measurement by Yamamoto et al. [35] performed in 1997 although it has been demonstrated in section 2.3.2, that there is some room left by the assumptions made during the raw data reduction process. The value of 3.14b seems to be satisfactory in regards to Table 8 and presents the advantage to be in accordance with the recommendation made by Fröhner et al. [17].
•	was left as free parameter in the re-evaluation procedure within the limits (12 ± 3)b fixed by Fröhner et al. [17].

Table 13 enumerates the various differential data employed during the present thermal and low energy two-steps cross section fits, on the basis of the comments made in section 2.4.

Table 13. Differential database used in the present two-steps analysis.

			Fitting database
			Resonance energies [eV]
Data type	First author	Thermal slope	−0.421	0.305	0.575	1.269	1.929
σ n,t	Adamchuck	Yes	Yes	–	–	–	–
σ n,t	Belanova	Yes	Yes	Yes	Yes	–	Yes
σ n,t	Slaughter	–	–	Yes	Yes	Yes	Yes
σ n,t	Derrien	–	–	–	–	Yes	Yes
σ n,a	Weston	Yes	Yes	Yes	Yes	Yes	Yes
σ n,f	Bowman	Yes	Yes	Yes	Yes	Yes	–
σ n,f	Dabbs	Yes	Yes	Yes	Yes	Yes	Yes
σ n,f	Leonard	Yes	Yes	Yes	Yes	–	–
σ n,f	Derrien	–	–	–	–	Yes	Yes
σ n,f	Gerasimov	Yes	Yes

2.5.3. JEFF-3.1.1 vs. JEF-2.2

2.5.3.1. Total cross section

The total cross sections obtained after the one- (JEFF-3.1.1) and two-step (so-called “present fit” including the fission Resonance Parameter (RP) adjustment and an attempt of spins assignment) processes are easily viewed in Figures 2 – 5 . The two-steps calculation remains logically close to the official JEFF-3.1.1 curve in terms of total cross section. In agreement with our goal, both calculations present a thermal total cross section value significantly enhanced (+6%; 662b) compared to JEF-2.2 (regenerated) (626b) or JEF-2.2 (original) (630b). Because of the integral feedback suggesting to increase the epithermal resonance integral, the differential data of Slaughter et al. [38] were favored in the present work by assigning small uncertainties within the energy range of the two lowest resonances.

Figure 2. Comparison of the one- (JEFF-3.1.1) or two-steps fitted total cross sections with both the major evaluated data files released in 2006 and the relevant differential data sets over the thermal energy range. As several data uncertainty sets had been tested for each experiment during the fits, the original experimental uncertainties, often underestimated, have not been drawn on the figure above or on the next graphics.

Figure 3. Comparison of the one- (JEFF-3.1.1) or two-steps fitted total cross sections with both the major evaluated data files released in 2006 and the relevant differential data sets over the energy range of the two lowest energy resonances. The resonance energy is a free variable parameter which is finally fitted on our reference measurement (Dabbs et al. [39]) in terms of energy scale. The experimental data set of Slaughter et al. [38], here referenced as “cleaned,” was purified from spurious values according to the procedure described within the text.

Figure 4. Comparison of the one- (JEFF-3.1.1) or two-steps fitted total cross sections with both the major evaluated data files released in 2006 and the relevant differential data sets over the third resonance. The resonance energy is a free variable parameter which is finally fitted on our reference measurement in terms of energy scale (Dabbs et al. [39]).

Figure 5. Comparison of the one- (JEFF-3.1.1) or two-steps fitted total cross sections with both the major evaluated data files released in 2006 and the relevant differential data sets in the neighborhood of the fourth resonance. The resonance energy is a free variable parameter which is finally fitted on our reference measurement in terms of energy scale (Dabbs et al. [39]).

From Figure 3, we observe that the JENDL-3.3 total cross section is close to Belanova et al. [21] (corrected) data for the first resonance and in between Slaughter et al. [38] and Belanova et al. [21] for the second one. The JEF-2.2 and ENDF/B-VII.0 curves stick to Belanova et al. [21]. Twelve data points were removed from the experimental data set of Slaughter et al. [38]: the six lowest energy data points likely manifesting a flux cutoff behavior and six other points counted in the valley between resonances which values were still too large after additional background subtraction. This purified experimental dataset is referenced in Figures 3 –5 as “cleaned.”

Above 0.8 eV, the availability of another transmission measurement by Derrien and Lucas [37] supplies another piece of information which seems to discard the large peak magnitude observed again by Slaughter et al. [38] within the third resonance (Figure 4). Belanova et al.'s [21] results relative to this resonance are clearly distorted and were very weakly considered during the fit on this resonance. From these considerations, the resulting one- (JEFF-3.1.1) or present two-steps fitted curves are logically close to Derrien and Lucas [37] data and so, remain consistent with JEF-2.2 within the range of the third resonance.

As far as the fourth resonance is concerned (Figure 5), Derrien and Lucas's [37] data and Slaughter et al.'s [38] data show surprisingly a better agreement whereas Belanova et al.'s [21] data are still significantly lower (around −12% on the peak magnitude). The one- (JEFF-3.1.1) or two-step fitted curves are in between Derrien and Lucas's [37] data and Slaughter et al.'s [38] data points and are consistent with ENDF/B-VII.0 and JENDL-3.3.

2.5.3.2. Capture cross section

The one- (JEFF-3.1.1) and two-step (present fit) capture cross sections are displayed (in terms of absorption cross section) in Figures 6 – 9 and compared to the unique absorption measurement available in 2006 over these resonances and performed by Weston and Todd [29]. On the basis of a thermal absorption cross section value of 650b, Weston and Todd's [29] measurement has to be significantly renormalized (+11.6%). Unfortunately, even with such a renormalization, Weston and Todd's [29] results still do not corroborate P.I.E. trends and so, our SAMMY fit, mainly oriented on Slaughter et al.'s [38] data, do not reproduce the renormalized data of Weston and Todd [29] in the energy range of the four lowest energy resonances.

Figure 6. Comparison of the one- (JEFF-3.1.1) or two-steps fitted absorption cross sections with both the major evaluated data files released in 2006 and Weston and Todd [29] data over the thermal energy range.

Figure 7. Comparison of the one- (JEFF-3.1.1) or two-steps fitted absorption cross sections with both the major evaluated data files released in 2006 and Weston and Todd [29] data over the two lowest resonances energy domain. The resonance energy is a free variable parameter which is finally fitted on our reference measurement in terms of energy scale (Dabbs et al. [39]).

Figure 8. Comparison of the one- (JEFF-3.1.1) or two-steps fitted absorption cross sections with both the major evaluated data files released in 2006 and Weston and Todd [29] data in the neighborhood of the third resonance. The resonance energy is a free variable parameter which is finally fitted on our reference measurement in terms of energy scale (Dabbs et al. [39]).

Figure 9. Comparison of the one- (JEFF-3.1.1) or two-steps fitted absorption cross sections with both the major evaluated data files released in 2006 and Weston et al. data in the neighborhood of the fourth resonance. The resonance energy is a free variable parameter which is finally fitted on our reference measurement in terms of energy scale (Dabbs and Todd [29]).

The agreement between the one- (JEFF-3.1.1) or present two-step fitted absorption cross sections and Weston and Todd's [29] data over the third resonance energy domain (see Figure 8) is much better because our fit is no more driven by Slaughter et al. [38] but also by the transmission measurement of Derrien and Lucas [37]. The one- or two-step fitted cross sections are slightly higher than the curves reconstructed from the JENDL-3.3 and ENDF/B-VII.0 libraries and lead to a largest integral value over the third resonance. No significant RP tuning was needed relatively to the JEF-2.2 evaluation for this resonance.

As far as the fourth resonance is concerned (see Figure 9), JEFF-3.1.1, JEF-2.2, JENDL-3.3, and the ENDF/B-VII.0 libraries as well as the present two-steps calculation are in agreement and are smaller in magnitude than Weston and Todd's [29] renormalized data. Since all theses evaluated curves are also smaller than the transmission measurement by Derrien and Lucas [37], we can say that in the “current” knowledge there is some room for increasing the integral value over this resonance.

2.5.3.3. Fission cross section

The actual difference between the JEFF-3.1.1 RRP set and the present work (two steps SAMMY fit) shows up essentially in this paragraph because no fission cross section fit had been performed according to JEFF-3.1.1. Subsequently, JEFF-3.1.1 contains fission widths (tabulated in file 2-151 in ENDF-6 format [42]) which are not consistent with the associated neutron and capture widths as far as the four lowest energy resonances are concerned. The present work aims to correct this anomaly.

As summarized in Table 11, five differential fission datasets were found relevant for fitting the cross section in the thermal range. The listed thermal fission cross sections are either those directly published (e.g.; Derrien and Lucas measurement [37] which is calibrated on a value of 3.13b at 0.0253 eV) or were retrieved by interpolation/extrapolation upon standard energy dependency law (). Resulting thermal values are spread over the range [3.03 – 3.49] b to be compared to the variance weighted thermal cross section obtained from the uncorrected integral database (covered by Table 8) and equal to (3.16 ± 0.05)b. From these considerations, the value of 3.14b seemed to be a reasonable choice and remains consistent with Fröhner et al. [17] and Derrien and Lucas [37] recommendations and the recent integral measurement by Yamamoto et al. [35]

Figure 10 shows the various differential fission cross section datasets, renormalized to a thermal value of 3.14b, relatively to the major evaluated files released in 2006. Unfortunately, each dataset exhibits a different thermal fission cross section slope as it is well shown on Figure 11 . Since there is no evidence on the choice of the right slope, the thermal fit is mainly constrained by the thermal fission cross section target. The present two-steps fitted curve is consistent with the JENDL-3.3 curve and eventually confirms the slope addressed in the fission cross section measurement by Bowman et al.

Figure 10. Comparison of the one- (JEFF-3.1.1) or two-steps fitted fission cross sections with both the major evaluated data files released in 2006 and the relevant differential data sets over the thermal energy range.

Figure 11. Comparison of the one- (JEFF-3.1.1) or two-steps fitted fission cross sections with both the major evaluated data files released in 2006 and the relevant differential data sets (with a linear regression representation) over the thermal energy range.

Among the differential datasets listed in Table 11 and covering the range of the four lowest energy resonances, Gerasimov et al. data exhibit saturated or deformed resonances, Derrien and Lucas's [37] measurement counts from 0.8 eV, Leonard et al.'s and Bowman et al.'s results manifest alterations signs, respectively, above the second and the third resonance. Only Dabbs et al.'s [39] data supply relevant resonance parameter information over the whole range of the four resonances. Table 11 recalls the experimental features and the additional data reduction treatment needed during this work to get a consistency among fission cross section datasets.

The fission cross section resulting from the present two-steps fit is now in agreement with Dabbs et al. [39] data within the two lowest resonances ( Figure 12 ) and with both Dabbs et al. [39] and Derrien and Lucas [37] within the region of the third and the fourth resonances ( Figures 13 and 14 ) and so, is in adequacy with JENDL-3.3. It corrects the erroneous “one-step fit” fission width parameters released as JEFF-3.1.1 of which reconstructed fission cross section curve was quite too high at least for the first two resonances because of large neutron width parameter enhancement for the purpose of the JEFF3.1.1 task. It can be seen that it was also the case for the JEF-2.2 reconstructed fission cross section over the energy region of the second resonance (similarly to Fröhner et al.'s [17] calculation). Table 12 displays the new resonance parameters, extracted from the present two-steps fit, which supersede those given in the JEFF-3.1.1 file. This present fit confirms the abnormally large value of the fission cross section over the second resonance showing up already in Fröhner et al.'s [17] evaluation; the present Γ _f value (0.093 meV) being equal to one-third of the original Fröhner et al.'s [17] value (0.290 meV).

Figure 12. Comparison of the one- (JEFF-3.1.1) or two-steps fitted fission cross sections with both the major evaluated data files released in 2006 and the relevant differential data sets over the two lowest resonances energy domain. The Γ _f value extracted from Fröhner et al. [17] evaluation for the second resonance is abnormally high (0.290 meV rather than 0.093 meV).

Figure 13. Comparison of the one- (JEFF-3.1.1) or two-steps fitted fission cross sections with both the major evaluated data files released in 2006 and the relevant differential data sets in the neighborhood of the third resonance.

Figure 14. Comparison of the one- (JEFF-3.1.1) or two-steps fitted fission cross sections with both the major evaluated data files released in 2006 and the relevant differential data sets in the neighborhood of the fourth resonance.

3. Capture isomeric ratio to ^242gAm and energy dependency

As mentioned in the introduction, an underestimation of the ²⁴¹Am capture cross section is not the only cause for the underestimation of the fuel inventory prediction on ^242m Am. The ^242m Am absorption cross section, poorly known, is another significant source of uncertainty ( b [28]) but this question is not developed in this article. The third source of uncertainty is the capture ISO _γ which is definitively a sensitive key parameter especially because its energy dependency is approximately modeled in the application libraries by using only one weighted average value (so-called “effective”) corresponding somehow to the relevant reactor spectrum. Our goal is to supply, in particular in the JEFF-3 framework, an ISO _γ factor with an energy dependency over the whole reactor spectrum [(0–20)MeV], associated with plausible uncertainties, to allow each time as possible a direct use of pointwise ISO _γ data or, at worse a much better determination of the relevant effective ISO _γ value for reactor code calculations. This option has been made available since the JEFF-3.1 release (by means of MF = 9 and 40 with MT = 102 in ENDF-6 format) and the coming sections will trace back the spirit of our study which has been broken in two parts. The first one “pragmatic” is straightforward and based essentially on a regular error weighted cubic spline fit between all sources of information and the second one relies on a Monte Carlo-type prediction; although perfectible but bringing supplement information on the ISO _γ energy variation over the resonances.

3.1. Pragmatic approach by weighted polynomial adjustment

3.1.1. Experimental database content

The review made on the experimental data released at the time of JEFF-3.1 shows that the low energy range was pretty well covered by a large amount of measurements but the information in the fast energy domain was pretty scarce. Most of the results are derived from integral measurements performed in reactors (P.I.E. experiments based on so-called “radiochemical” analyses; report to Table 14 ). Only two datasets ( Table 15 ) obtained by Wisshak et al. [43] are extracted from differential techniques. As already debated in preamble, differential techniques bring more precise information in energy (with mono-energetic neutrons) than integral measurements which cover a broad energy range. However, the measurement by Wisshak et al. [43] performed by ²⁴¹Am sample activation, using a Van de Graaff accelerator to produce quasi-monoenergetic neutrons at 30 keV, remains strongly in disagreement with all the other trends. The authors have reviewed all experimental sources of uncertainties as well as prior input parameters for their model calculations and did not find any significant reasons for their low ISO _γ fast energy value except that “a direct comparison is difficult with integral data since it covers a very broad range.” This is definitively true but as their trend remains isolated, the value of (0.64 ± 0.05) at 30 keV was disregarded for the present fit. We will keep in mind that the post-treatment method, chosen by the authors and following the sample activation, involves the observation of the electrons emitted by beta-decay of ^242g Am to ²⁴²Cm in a high background of α-, γ-, and X-radiations. Such a task remains very difficult to achieve and is a possible source of errors (as was demonstrated by the study on the Pandemonium fictional nucleus β-decay scheme [44]). By consequence, definitive experimental results remain fragile to extract. On the contrary to their measurement at 30 keV, the second activation differential measurement performed at 14.75 meV using a graphite monochromatic spectrometer at the Karlsruhe FR2 reactor gives a result compatible with the others and was therefore included in our database.

Table 14. Integral feedback used as guideline for JEFF-3.1.1.

Authors		ISO γ and estimated uncertainty	Flux type or range	Approximate mean energy [eV]
Shinohara et al. [31]		0.90 ± 0.09	Thermal	0.0253
Fioni et al. [9]		0.914 ± 0.01	Thermal	0.0253
Gavrilov et al. [24]		0.914 ± 0.081	Thermal	0.0253
Maidana et al. [33]		0.909 ± 0.019*	Thermal	0.0253
Dovbenko et al. [32]		0.89 ± 0.029	Thermal	0.0253
Harbour et al. [23]		0.899 ± 0.032	Epithermal	0.1
Bak et al. [22]		0.905 ± 0.109	Epithermal	0.1
Ihle et al. [45]		0.891 ± 0.07	Epithermal	0.3
Shinohara et al. [31]		0.89 ± 0.07	Epithermal	0.45
Harbour et al. [23]		0.865 ± 0.101	Epithermal	0.66
Bak et al. [22]		0.875 ± 0.111	Epithermal	0.66
Dovbenko et al. [32]		0.84 ± 0.02	Fast	300,000
Tommasi [46]		0.85 ± 0.01	Fast	110,000
CEA
Bernard et al. [15]		0.86 ± 0.01	Epithermal	0.6
Several		0.86		1,000
LANL
CriticalAssemblies [47]		0.82	5,000–3,000,000	200,000**
Note: *The ISO7 value assigned to Maidana et al. [33] was extrapolated again assuming Fioni's capture value to metastable; . **The ISOγ value quoted in [47] is mis-plotted and should be associated to a mean energy of 500 keV [48].

Table 15. Differential data released as support to ISO _γ prediction. The value from Wisshak et al. [43] at 30 keV was disregarded for the present fit.

Authors	ISO γ	Energy [eV]
	0.92 ± 0.06	0.01475
Wisshak et al. [43]
	0.64 ± 0.05	30,000

3.1.2. Methodology

3.1.2.1. Low energy asymptote

Although there is no reason (see section 3.2.) to consider a constant ISO _γ ratio over the sub-thermal energy range, a conservative approach was chosen below 0.022 eV which consisted in imposing an asymptotic value equal to the experimental error weighted average made over “thermal” ISO _γ results (those listed in Table 14 including the subthermal measurement by Wisshak et al. [43] and printed in Table 15). The resulting ISO _γ mean value is (0.91 ± 0.01).

3.1.2.2. High energy constraint

Since no experimental results are available at very high energy, we must rely either on theoretical support or on systematic considerations depending, for instance, on the spin of the final state. The temptation is strong to tend toward an ISO _γ value equal to 0.5 but if we look over the entire periodic table and the data pertaining to ISO _γ, there is no universal law that leads to 0.5. Proves are the various (1-ISO _γ)/ISO _γ ratios compiled in the JEFF-3.0/A activation file at 20 MeV incident neutron energy. Examples of values are the following: 0.67/0.33 (¹⁰⁷Ag^*), 0.38/0.62 (¹⁶⁴Ho^*), 0.19/0.81 (¹⁵⁰Eu^*), 0.44/0.56 (¹³⁷Ce^*), 0.11/0.89 (¹²⁰Sb^*), 0.44/0.56 (¹¹⁷Sn^*), 0.60/0.40 (¹⁰¹Rd^*), 0.24/0.76 (⁹⁶Tc^*), etc. Indeed we do not expect an even asymptotic value since below the continuum range within the excited nucleus, the γ-ray cascade must keep going through the discrete level scheme. Thus, level branching ratios determine to a large extend what the ISO _γ value is. To that piece of information must be added the spin knowledge on discrete levels and the spin distribution in the near-continuum. Table 16 lists the adopted levels structure and γ-ray in the ENSDF [49] database. We see that already above the fourth excited level, γ-ray branching values are seldom known even with, sometimes, unknown excited state spin and parity assignments. In order to estimate the sensibility to discrete levels information and to get an order of magnitude on the ISO _γ value at the very far end of the neutron spectrum (20 MeV), two TALYS 10 calculations [50], involving the ²⁴²Am excited nucleus and integrating the coupled-channels optical model code ECIS, were performed. The first calculation was made on a 10 discrete levels basis description with continuum level density above and the second one included only four discrete levels. The resulting ISO _γ values at 20 MeV were 0.77 and 0.49, respectively. This well demonstrates the strong sensitivity to the ²⁴²Am actual level scheme. This question is emphasized at high energy by the direct capture dominating process which exhibits an unlike prior spin distribution and so involves different γ-ray cascades. The choice of the convergence point at 20 MeV remains matter of arbitrariness. An ISO _γ value of 0.75 at 20 MeV was finally imposed during the present task.

Table 16. Overview of the lowest level structure adopted for the ²⁴²Am excited nucleus and corresponding γ-rays. Possible decay modes are α, β, internal transition (IT), and electronic capture (EC). The uncertainties on the least significant digit(s) are printed in subscripts. The complete diagram is available from the ENSDF [49] database.

Level index	Level energy [keV]	J ^π		Energy of γ-ray(s) [keV]	De-excitation mode [%]
0	0.	1^–	16h022		β^- = 82.73, EC = 17.33
1	44.0923	0^–		44.0923
2	48.603	5^–	141y2	48.635	IT = 99.552, α = 0.452
3	52.704	3^–		52.774
4	75.821	2^–		75.8234
5	99
6	114	6^–
7	148	5^–
8	149.692	4^–		73.86411 and 96.9942
9	171
10	190	7^–

3.1.2.3. Main fitting process

An error weighted polynomial adjustment of third degree order was performed over the whole neutron spectrum [0 – 20 MeV] using as guideline the set of experimental results commented above. Table 17 gives the parameter values obtained during the present fit and their uncertainties. The χ² obtained was close to 1. The low energy tail was cut at 0.022 eV to match the desired low energy asymptotic ISO _γ value (i.e. 0.91) whereas the high energy constraint, described right above, was imposed during the fit on the ISO _γ curve. Figure 15 plots the resulting fitted curve (released as JEFF-3.1 and maintained in JEFF-3.1.1), the supporting experimental data (listed in Tables 14 and 15), and the 10 discrete levels TALYS calculation (early version; made in 2005) for reference. Experimental uncertainties and representative mean energies were carefully examined during this work and tuned whenever needed. Older theoretical calculations by Mann et al. [51] (1977), Wisshak et al. [43] (1982) and Gardner et al. [52] (1984) are plotted to illustrate the difficulty of finding the right ISO _γ magnitude. However, all these calculations agree on the ISO _γ descent above 1 MeV due to higher relative orbital momentum openings with the excitation energy increase. Indeed high relative orbital momentum occurrences increase the possibility to reach the isomeric metastable state of large total angular momentum (I ^π = 5⁻) whereas that problem does not raise for the ground state of smaller total angular momentum value (I ^π = 1⁻).

Table 17. Posterior parameter values (and uncertainties) obtained by a three degrees polynomial regression over a set of 18 experimental data points weighted by their uncertainties. Parameters A, B ₁, B ₂ and B ₃ are defined as follows: ISO _γ (E _n ) = A + B ₁ logE _n  + B ₂(logE _n )² + B ₃(logE _n )³ where E_n stands for the neutron energy.

Parameter	Value	Standard error
A	0.85962	0.00523
B 1	−0.01516	0.00238
B 2	0.00789	0.0012
B 3	−0.00108	1.19173 10^–4

Figure 15. ISO _γ dependency versus energy: present JEFF-3.1.1 fit (purple thick solid curve), experimental data base used for the present fit (black full circles) and theoretical support: Talys calculations with 10 discrete levels [50] (orange dash line), calculations by Mann et al. [51] (green dot line), Wisshak et al. [43] (red double dot and dash line) and Gardner et al. [52] (blue dash-dot line).

3.1.3. ISO _γ variances from estimated experimental uncertainties propagation

As far as the resonance energy range is concerned, the total variances are supplied by the present error weighted cubic spline fit which includes three components:

•	the square of the standard deviation resulting of the fitting process and classically equal to the ratio of the sum of residuals between calculated and experimental ISO γ values, and the number of experimental data points (i.e. 18; normalization value [ISO γ = (0.75 ± 0.001)] at 20 MeV included) minus 2,
•	the variance resulting of the relevance on the choice of the fitting law (here a three degrees polynomial) and,
•	the standard deviation increase due to small sample statistical theory (student's “t-test” by Gosset [53]).

At very low neutron energy, where no experimental ISO _γ data or trends exist, the variance is arbitrarily set to the experimental uncertainty weighted average made over the “thermal” ISO _γ results (those listed in Table 14 with the inclusion of the Wisshak et al. [43] differential measurement at 14.75 meV).

Above 300 keV where, again, we are facing to the same problem (no experimental ISO _γ data or trends are available), the variance resulting from the cubic spline fit is combined with half the difference between our final ISO _γ fit normalized to 0.75 at 20 MeV and an extreme choice relying on an equiprobable ISO _γ normalization value of 0.5. For practical user purpose and because the variances obtained rely on estimated uncertainties, it was decided to average the point-wise variances over 11 energy groups which were chosen accordingly to both the various energy domains and the feedbacks involved by this study. Table 18 lists the energy group boundaries, the relative variances on the isomeric ratio to the ground state (ISO _γ) and to the metastable state (1-ISO _γ) and the last column indicates the energy range covered by each group. The uncertainties are much smaller on ISO _γ than on (1-ISO _γ) because the actual ISO _γ ratio is in the resonance range up to 10 times larger than the ratio (1-ISO _γ) with an absolute uncertainty identical on the two ratios. The final uncertainty on ISO _γ in the resonance range remains small (<1%) and much better than the uncertainties on the partial or total capture cross sections because we treat here a ratio making the errors on the entrance neutron channel (acting as a normalization) to cancel. At high energy, the lack of integral feedback is undeniable. In addition we deal with both small capture values difficult to measure and direct capture involving another physics area. Feedback from neutron reactor physics is unlikely since the neutron reaction rate is poor above 2 MeV and so, we rely on high energy physics experiments (such as deuterium–tritium experiments).

Table 18. Relative ISO _γ variances derived from the present data uncertainty propagation. These data were released as JEFF-3.1 and maintained in JEFF-3.1.1. The last column recalls the energy range covered by each group involving six main energy regions: sub-thermal, thermal, epithermal resonances, upper resolved resonance range, unresolved resonance range, and continuum. Results are stored in record MF = 40, MT = 102, under ENDF-6 format conventions [42].

Group number	Energy group boundaries [eV]	[%]	[%]	Group relevance
1	10^–5–0.022	0.69	7.05	Low energy asymptote
2	0.022–0.1	0.42	3.54	Thermal
3	0.1–0.45	0.49	3.38	First level
4	0.45–0.8	0.58	3.88	Second level
5	0.8–1.6	0.64	4.06	Third level
6	1.6–2.1	0.68	4.56	Fourth level
7	2.1–150	0.71	4.08	Upper RRR
8	150–4.10^4	0.54	3.15	URR
9	4.10^4–3.10^5	0.51	2.75	Fast range feedback
10	3.10^5–1.10^6	1.75	8.47	Slope change
11	1.10^6–2.10^7	11.36	38.77	Constrained at 20MeV

3.2. ISO _γ Monte Carlo-type prediction over resonance range

3.2.1. Framework

In order to get an estimate of what could be the magnitude of the associated uncertainty and of the energy dependency on ISO _γ over the RRR, a series of Monte Carlo calculations based on compound nucleus level density statistics has been performed. The following framework was considered:

•	A slow energy neutron impinges a 241Am target nucleus to form a 242Am* compound nucleus (CN) which de-excites in particular by γ-ray transitions. The energy Ei (J π) of the initial excited level of spin and parity (J π) in the CN is the sum of both the neutron separation energy Sn and the neutron kinetic energy En . Over the epithermal range, En remains small relatively to Sn and so, Ei (J π) ≈ Sn ≡ 5.5376 MeV. According to the vectorial combination of the intrinsic spins (respectively, I and i) of the target and the neutron incident particle, the total spin J of the system is either equal to 2 or 3 with negative parity π (defined as π = (−1) l  × π i  × π I ) for a relative orbital angular momentum l = 0. Consistently, the set of J π values corresponding to a p-wave excited state (l = 1) is spread between 1+ to 4+ by steps of 1 unit.
•	The de-excitation from an initial excited level of J π given down to either the ground state I π = 1− or the metastable state I π = 5− (see respective characteristics on Table 16) occurs through sequences of electric E1, E2, and magnetic M1, M2 single-particle and collective transitions over intermediate states upon electromagnetic selection rules. Transitions come by continuum spectrum and subsequent discrete level scheme. Among the discrete levels in the 242Am* compound nucleus, nearly all the 44 lowest lying levels exhibit known spin and parity but the next 43 discrete levels, spread from 915 keV up to 2.2 MeV, have essentially been identified in energy [49] only.
•	ISO γ is deduced from the calculated branching ratio (γBR) using the relationship

and γ BR is calculated as the ratio () of the total probabilities leading, respectively, to the metastable (ms) and ground (gs) states starting from the same initial excited level (i). The total probability, considering all possible γ-ray cascade stories leading to the ground state (index = 1) or the metastable state (index = 3), is calculated as follows:

with being the individual normalized probability defined as with , the photon transition probability between an initial state i and a final state j; is set to unity.

The mean γ-multiplicity (⟨v _γ⟩) from an initial state (i) down to the final ground or metastable state (characterized by their index number) is simply given by

The corresponding mean γ-energy is

3.2.2. Models and assumptions

In this context, the ISO _γ calculation was conducted under classical models and plausible assumptions. In the present calculation, the internal electronic conversion probability in the excited nucleus is assumed to be small relatively to the radiative decay probability. The electric (E1) and magnetic (M1) dipole (l = 1) contributions to the total photon transition probability, as well as the electric quadruple (l = 2) contribution (E2), are calculated 11 as having the corrected Lorentzian form [54] of the so-called giant dipole resonance (GDR), where all protons vibrate against all neutrons such as

where ε_γ stands for the photon energy of the transition, E ₀ and Γ₀ are, respectively, the energy and the width of the giant resonance. Γ _K acts as an energy- and temperature-dependent damping width. The temperature Θ corresponds to the temperature of the state on which the giant resonance is built. The GDR parameters used were those empirically estimated for a spherical compound nucleus as listed on Table 19 and the relationship between Γ _K and Γ₀ is .

Table 19. Parameters of the corrected Lorentzian shape of the “Giant Dipole Resonance” for electric (El) and magnetic (Ml) dipole (l = 1) and quadruple (l = 2) radiations in the ²⁴²Am excited nucleus reconstructed from systematics [54].

	E1	E2	M1
E 0 [MeV]	13.25	10.11	6.58
Γ0 [MeV]	3.61	3.21	4.00
σ0 [mb]	731.86	24.83	20.85
Θ [MeV]	5.00	0.	0.

The magnetic quadruple (M2) contributions are smaller in magnitude and are approximated by the simple Weisskopf estimate

with l = 2 and the nuclear radius r = 1.45A ^1/3 [fm].

The levels whose spin is unknown were assigned following the standard Gilbert–Cameron empirical level density law [19], ρ(U, J, σ), function of the effective excitation energy U in the CN, the level total angular momentum J, and the spin cut-off parameter σ. In practice, the calculation was carried on from a Rayleigh spin type probability density function such as . The parity was chosen on a negative–positive equiprobability basis. Finally, an average over the total transition probabilities was made over thousand drawings to account for the J ^π spin-parity statistical distributions of the second sequence of low-lying levels. This spin-parity drawing propagates the main source of uncertainty in our ISO _γ calculation. Thereof a special care has been made on the estimation of the ISO _γ uncertainty originated from this process. One must note that the 43rd excited level at E_L  = 2.2 MeV, confining this second sequence and exhibiting a 14 ms half-life with a spontaneous fission decay mode, is assumed to be stable from the point of view of the γ-cascade stories calculation and consequently no transitions were allowed from this level.

The discrete sequence of 87 low-lying levels (44+43) was expanded by a fraction of continuum (spread between 2.25 and 2.75 MeV) of which total level density is assumed to follow again the Gilbert–Cameron total level density law ρ(U, σ). The value of the Fermi gas level density parameter a_F was adjusted accordingly to the incident neutron s-wave resonance mean spacing value (D ₀ = (0.55 ± 0.05) eV) at S_n recommended by the “Atlas of Neutron Resonances” [28]. No nucleon pairing energy corrections were needed since the ²⁴²Am^* excited nucleus is an odd-odd compound nucleus. An ultimate sequence of 4523 levels have been generated, including the 87 experimentally observed discrete levels and 4436 levels simulating the lowest part of the continuum. This near-continuum is built upon a number of predicted levels at U = 2.5 MeV and picket fence model with large Gaussian-type spacing fluctuations (centered around the mean spacing value with a full width at half maximum equal to 0.8). Again, it was assumed that the continuum level parities are equally distributed among the two parities although recent theoretical Hartree-Fock-Bogolyubov calculations, compiled in RIPL3 [55], bring some hints for non-equal level parity densities. With this ultimate sequence of levels, an average total transition probability was again considered to take account of sampling statistics. The number of drawings was limited to 50 accordingly to both final statistic uncertainty and computing time.

Caveat: For the purpose of the present study, the choice has been made to simulate photon transition intensities from evaluated nuclear structure data, basic models, and Monte Carlo-type calculations with fluctuations from both mean level spacing and level capture width. However, no allowance has been granted for the width fluctuation correlations between reaction channels other than capture. Since the actual width fluctuation correction factor affects mainly the magnitude of the average cross sections, we expect limited impact in terms of isomer ratio; effect that should be even smaller because of the narrow energy range involved (RRR).

3.2.3. Results

3.2.3.1. First feelings on ISO _γ

A preliminary ISO _γ calculation, accounting only for the first 44 well-known levels and the physics described above, has revealed the general trend expressed in Figure 16 in function of the spin-parity couple of the initial excited level. Clearly no significant parity effect shows up although the parity tends to be more sensitive with total angular momentum increase. Higher the relative orbital momentum is, more equiprobable are the cascade stories down to the ground state (I ^π = 1⁻) and to the metastable state. This is the direct consequence of an increase of the incident neutron energy bringing a larger relative orbital momentum value which favors the metastable state of high spin value (I ^π = 5⁻).

Figure 16. Isomeric ratio profile versus excited level J ^π. Those values are extracted from a first stage calculation involving only the 44 well-known low-lying levels in the ²⁴²Am excited nucleus.

3.2.3.2. Nature of the transitions leading to metastable and ground states

Table 20 presents the ISO _γ values depending on the nature of the transitions (single-particle or collective motions) allowed during the γ-ray cascade stories to ground state. The impact of the various types of γ-transition is tested by suppressing successively the E1, E2, E1 + M1, M1, M2 and E2 + M2 transitions. Clearly, ISO _γ results are non-sensitive to M2 transitions as expected. The inclusion of E2 second-order collective motions in the photon transition coefficient calculation become essential for the highest total angular momentum values (J ^π = 3⁻,4⁺).

Table 20. ISO _γ calculated values [%] in function of both the nature of the transitions (single-particle or/and collective motions) and the spin-parity of the initial excited state. Each column represents the ISOγ value obtained without a particular type of γ-transition. The ISOγ listed values account only for the first 44 well-known discrete levels.

		Single-particle			Collective		Single and Collective
J ^Π	No E1	No M1	No E1 + M1	No E2	No M2	No E2 + M2	all allowed
2^–	93.6	90.6	75.3	88.5	93.2	88.5	93.2
3^–	76.6	86.0	64.8	61.1	79.1	61.1	79.1
1^+	99.9	98.8	98.3	99.1	99.3	99.2	99.3
2^+	99.6	93.2	98.2	87.5	92.3	87.5	92.3
3^+	99.5	80.6	96.0	70.0	83.1	70.0	83.1
4^+	99.2	63.0	95.5	29.3	60.5	29.3	60.5

3.2.3.3. ISO _γ second stage calculation

An additional sequence of discrete levels (as numerous as 43), of mainly unknown spins and parities, is now included in the ISO _γ calculation path. The spin assignment of these levels is made on a Rayleigh probability density function basis with a parity assumption set up on a negative–positive equiprobability basis.

Figure 17 plots the sampled ISO _γ distributions associated to either a 2⁻ or 3⁻ excited resonance and the net difference. These distributions are obtained from 14,000 spin-parity samplings accounting for both known energy and unknown J ^π level values. The predicted average ISO _γ values are (92.86 ± 0.43)% and (78.59 ± 0.90)%, respectively, for a 2⁻ and a 3⁻ s-wave resonance. The net difference between these distributions reveals that the ISO _γ value corresponding to a 2⁻ s-wave resonance is on average much large, (14.27 ± 0.99)%, than the value obtained from a 3⁻ excited level radiative decay. It confirms the trend obtained by Wisshak et al. [43] whose calculation was predicting a net difference of about 13% in the same direction at thermal neutron energy. The ISO _γ values obtained in this second stage are close to the corresponding first stage values. It seems to demonstrate that ISO _γ is mostly dependent on the low lying level sequence. This is also the conclusion brought to us by Wisshak et al. [43].

Figure 17. Capture isomeric ratio distributions (left-hand side of the picture) related to 2⁻ and 3⁻ s-waves neutron resonances and obtained from a discrete sequence of 87 levels after spin-parity assignments. The right-hand side plot expresses the net difference between these 2⁻ and 3⁻ distributions.

In terms of average number of emitted γ and mean energies, 12 Figures 18 and 19 summarize the results obtained for γ-ray cascades to the ground state. γ-multiplicities are significantly different between the two types of s-wave resonances ((2.76 ± 0.04) from a 2⁻ level compared to (3.02 ± 0.03) from a 3⁻ level); fact which is also verified in terms of mean γ-energies ((2.01 ± 0.03) MeV compared to (1.83 ± 0.02) MeV). Corresponding multiplicity values relatively to the metastable state are and , respectively, from a 2⁻ level and a 3⁻ level. It might suggest feasible experimental spin discrimination on the lowest neutron resonances in the ²⁴²Am^* compound nucleus by γ-ray measurements.

Figure 18. Mean γ-multiplicity distributions (left-hand side of the picture) accordingly to a γ decay from either a 2⁻ or a 3⁻ s-wave neutron resonance down to the ground state and obtained from a discrete sequence of 87 levels after spin-parity assignments. The right-hand side plot expresses the net difference between these 2⁻ and 3⁻ distributions.

Figure 19. Mean γ -energy distributions (left-hand side of the picture) accordingly to a γ decay from either a 2⁻ or a 3⁻ s-wave neutron resonance down to the ground state and obtained from a discrete sequence of 87 levels after spin-parity assignments. The right-hand side plot expresses the net difference between these 2⁻ and 3⁻ distributions.

3.2.3.4. ISO _γ final refinement

In order to quantify the impact of γ-ray cascades over the near-continuum region in the ²⁴²Am excited nucleus, an attempt of continuum sequence generation was made using the method described above (see section 3.2.2). Results show a slight drift as the number of extra continuum levels increases. For 4436 levels added right above the discrete region, the ISO _γ values tend toward (90.22 ± 0.20)% and (75.90 ± 0.32)%, respectively, for a 2⁻ and a 3⁻ s-wave resonance, to be compared to the values obtained without near-continuum (92.86 ± 0.43)% and (78.59 ± 0.90)%. The addition of extra levels increases logically the average number of emitted γ up to 3.43 compared to the original 2.76 value for a γ decay from a 2⁻ s-wave neutron resonance down to the ground state, bringing a large source of uncertainty (20%) on the γ-multiplicity prediction (multiplicity values associated to the metastable state are, respectively, and ; 20% systematic uncertainties not included). Consistently, the adjunction of many levels of higher spin values (an example of J ^π sampling in near-continuum with 4436 levels is presented in Figure 20 ) favors γ decays to the metastable state of high total momentum value; the 2⁻ and 3⁻ ISO _γ values to the ground state are altered accordingly. The ISO _γ values obtained with our largest level sequence (discrete + near-continuum states) are going in the direction pointed out by Wisshak et al. [43] who got (84)% and (71)%, respectively, for a 2⁻ and a 3⁻ resonance, on a conventional approach involving statistical model and coupled-channels calculations. In addition to a Gilbert and Cameron total level density law, the authors used a simple density formula with temperature dependency at low excitation energy. It must be noted that only the knowledge on the first 22 levels (i.e. up to 590 keV) in the ²⁴²Am excited nucleus was available at that time. In the continuum, Wisshak et al. [43] assumed only E1 transition types and classical equiprobable parity distribution. Noting the slight drift on our ISO _γ global results (and the associated sensitivities) as the number of extra continuum levels increases, we have decided to assign a systematic absolute uncertainty of about 3% on ISO _γ such as to be equal to (90 ± 3)% and (76 ± 3)%, respectively, for a 2⁻ and a 3⁻ s-wave resonance.

Figure 20. Example of spin sampling made in the near-continuum. The distribution is centered around a large spin value (6 ).

3.3. Resonant cross sections upon ISO _γ spin dependency

The ²⁴¹Am neutron cross section over the resolved resonance energy range is described by R-matrix theory under multi-level Breit–Wigner (MLBW) approximation (in the ENDF-6 sense [18]) which considers isolated (λ) resonances with no interferences as far as the capture reaction channel is involved. This MLBW-ENDF-6 formalism (in short MLBWe) implies the use of a unique total capture resonance width collapsing the sum of all individual γ-transition widths with the implicit assumption of interference cancellation between all reduced capture resonance width amplitudes. In this context, the total capture resonance width () can be split in two major average capture contributions (i.e. two partial capture channel widths) with the assumption of no interferences between those two exit channels which will collapse for the present application from one side the γ-ray cascade all the way down to the ground state () and from the other side the cascade to the metastable state (). The two partial capture cross sections are then directly reconstructed from the corresponding partial capture width parameters such as (the energy variable has been dropped off for a better display)

with c covering the neutron incident channels and , the total resonance width such as with a unique fission channel (f ₁). The partial capture resonance widths can be estimated following the relationship

for each resonance on a total angular momentum J dependency basis.

Sticking to the isomeric ratio definition, we can recover the isomer total ratio from the fluctuating partial and total capture cross sections (i.e. ) and then apply this formula to the ²⁴²Am excited nucleus exhibiting a significant isomer level contribution for instance. From the ISO _γ total angular momentum dependent values obtained in our study (i.e. and for s-wave resonances), we obtain the total capture and partial ground and isomeric states capture cross sections plotted in Figure 21 . 13 Although we did not try to fit the thermal partial capture cross sections, their values are closed to the marked values (the present calculation of gives 78b) relatively to the thermal total capture cross section value imposed ( b).

Figure 21. ²⁴¹Am total capture and partial capture to both ground and isomeric states neutron cross sections assuming two major spin dependent partial capture widths extracted from the present work. These curves are reconstructed at room temperature (293K).

The resulting isomer total ratio curve exhibits strong fluctuations induced by the narrow level nuclear structure in the ²⁴²Am compound nucleus and the presence of two types of s-wave resonances characterized by very different isomer ratios. Figure 22 well displays this behavior. The above resonance parameter representation allows us to estimate the Doppler broadening impact on the isomer total ratio. Pending on cross section ratios, the net effect between two suitable temperatures (room (293 K) and operating power reactor (873 K)) is damped ( Figure 23 ) but shows up in case of a dramatic stellar temperature (e.g. 100,000 K) because of strong overlaps between the resonances originally well isolated. However, the latter remark can apply between closer temperatures (293 K relatively to 873 K) in the upper resonance range (E > 20 eV on Figure 24 ) where resonances cannot be considered as isolated. These elements of conclusion highlight three important points:

Figure 22. ²⁴¹Am reconstructed capture isomeric ratio vs energy using two major spin dependent partial capture widths extracted from the present work. The two dash lines display the total uncertainty contour on the pointwise ISO _γ average data. These curves correspond to the room temperature (293K).

Figure 23. ²⁴¹Am reconstructed capture isomeric ratio vs energy (E < 20 eV) using two major spin dependent partial capture widths extracted from the present work. These curves are reconstructed at room temperature (293K) , at operating power reactor temperature (873K) and at a dramatic stellar temperature (100,000K).

Figure 24. ²⁴¹Am reconstructed capture isomeric ratio vs energy (20 eV < E < 150 eV) using two major spin dependent partial capture widths extracted from the present work. These curves are reconstructed at room temperature (293K), at operating power reactor temperature (873K), and at a dramatic stellar temperature (100,000K).

1.	the isomer ratio value at a precise energy might be much different from an average ratio over the neutron spectrum energy range,
2.	it might be of importance of storing the isomer ratio data in terms of pointwise partial capture cross sections which will be more frequently Doppler broadened at the temperature corresponding to the simulated experiment,
3.	the user must be aware that using unbroadened isomer ratio data might alter the comparison between room temperature differential data and microscopic integral quantities which post irradiation activated samples are still hot (i.e. at the operating reactor temperature of 873 K).

4. Performances overview from present ISO _γ data and cross sections

The JEFF-3.1.1 study has been performed with the constant objective to improve significantly the agreement with P.I.E. feedback while preserving a reasonable agreement between differential and integral microscopic measurements. This goal was reached by a rigorous data base selection and a trial-error iterative process involving from one side improved RRP and evaluated ISO _γ data and, from the other side several APOLLO2 cell code calculations. At the end of the day, a quite satisfactory compromise was reached within the limits of the available information. Table 21 presents the prior and posterior fitting results obtained in terms of few integral representative indexes (spectral indices, Pu ageing, and multiplication factor) for both UO _x and MO _x cores. The expected overall improvement is close to a factor 2.

Table 21. Discrepancies observed between calculated (C) and experimental (E) results on the ²⁴¹Am, ^242mAm, and ²⁴²Cm fuel inventory predictions using the whole JEFF-3.0 library and after the substitution of the present evaluation. The differences expressed in terms of ((C-E)/E ± δE/E) ratios, at 1σ are given in percentage. Concentration ratios are supplied either at the Beginning (BoC) or at the End of the Cycle (EoC).

	Indexes	JEFF-3.0	JEFF-3.1.1
	241Am/241Pu EoC	13 ± 6	3 ± 6
UO x	^242mAm/^241Am	−28 ± 7	−11 ± 7
P.I.E	^242Cm/^241Am BoC	−33 ± 10	−26 ± 10
	241Am/241Pu EoC	12 ± 6	3 ± 6
MO x	^242mAm/^241Am	−28 ± 3	−12 ± 3
P.I.E	^242Cm/^241Am BoC	−26 ± 6	−20 ± 6
	Pu ageing	−7 ± 3	−3 ± 3
	keff MO x	720 ± 300	470 ± 300

Table 23. Total cross section values at the peak of the three lowest ²⁴¹Am resonances; retrieved respectively from JEFF-3.1.1, JENDL-4.0, and Slaughter et al. The corresponding resonance area increase estimated to fit the new data from Sage [61] is given as well.

	Resonance #1		Resonance #2		Resonance #3
	Resonance value [b]	Area ratio increase [%]	Resonance value [b]	Area ratio increase [%]	Resonance value [b]	Area ratio increase [%]
Slaughter et al. [38]	6500	8	5200	11.5	6800	12
JEFF-3.1.1	6400	9	5200	11.5	5500	38
JENDL-4.0	5900	19	5000	16	6500	17
Sage [61]	7000	1	5800	1	7600	1

5. Next americium 241 phase-II: a major step forward

Several years have passed since the beginning of the present study, here fully described, and a few new microscopic results have been released which confirm the direction followed by JEFF-3.1.1 but demonstrate that we can go further. This is also the attitude adopted by the recent JENDL-4.0 ²⁴¹Am data revision (+7% on and +9% on I _γ relatively to JENDL-3.3). In this context, it has been decided to start an enlarged and comprehensive ²⁴¹Am data evaluation using this time the modern and large capabilities of the CONRAD tool associated to both TALYS and AVXSF codes [56]. As preamble to this next step and conclusion to our JEFF-3.1.1 study, the coming paragraphs will inventory the new experimental results and list the few evaluations performed in the meantime and will propose some directions for the next stage occurring in the JEFF-3.2 context.

5.1. JEFF-3.1.1 comparison with up-to-date evaluations

Since the release of JEFF-3.1, three full or partial evaluation works are worth to be quoted: JENDL-4.0 [14], which agrees on the trend to increase the thermal capture cross section ( b to be compared to 647 b for JEFF-3.1.1), and both RUSFOND-2010 [57] and BRC-2009 [58], which well complement the information on the ISO _γ behavior.

5.1.1. Resonance parameters set

The low energy RRP set from JENDL-4.0 was revised on the basis of the capture cross section measurement performed recently by Jandel et al. [12] after applying a +3% re-normalization factor. Figures 25 – 27 compare the absorption cross section reconstructed from the JENDL-4.0 file relatively to JEFF-3.1.1 and the differential measurements by Jandel et al. [12] and Weston and Todd [29]. Even with a significant renormalization (a +11.6% factor having been already applied at the time of JEFF-3.1), the absorption cross section observed by Weston and Todd [29] remains significantly smaller than the one exhibited by Jandel et al. [12] at the peak of the resonances. It could prove that Weston and Todd's [29] data have to be enhanced again. However, we point out that this trend showing up for the three lowest resonances is being reversed from the fourth resonance. A difference showing up between the present two-steps analysis and JENDL-4.0 is the presence of four bound levels (three of 3⁻ and one of 2⁻ spin-parity values) in the latter file compared to only one 2⁻ bound level in the case of the former. We recall that our point of view is supported by the present ISO _γ study which demonstrates a large sub-thermal ISO _γ value carried by the tail of a 2⁻ bound level. However, the JENDL-4.0 evaluation is built such as reproducing correctly the observed isomer ratio at thermal energy. This was already the objective of JENDL-3.3 [27] which was including one more bound level than JENDL-4.0 (three 3⁻ and two 2⁻).

Figure 25. Absorption cross section comparison between JEFF-3.1.1, JENDL-4.0 and the differential measurements performed by Weston et al. in 1976 and Jandel et al. in 2008 (the capture data are combined with the present two-steps fission cross section) over the two lowest resonances energy domain.

Figure 26. Absorption cross section comparison between JEFF-3.1.1, JENDL-4.0, and the differential measurements performed by Weston and Todd [29]. in 1976 and Jandel et al. [12] in 2008 (the capture data are combined with the present two-steps fission cross section) in the neighborhood of the third resonance.

Figure 27. Absorption cross section comparison between JEFF-3.1.1, JENDL-4.0, and the differential measurements performed by Weston and Todd [29]. in 1976 and Jandel et al. [12]. in 2008 (the capture data are combined with the present two-steps fission cross section) in the neighborhood of the fourth resonance.

Figure 28. ISO _γ dependency versus energy: JEFF-3.1.1 vs JENDL-4.0, RUSFOND-2010 and BRC-2009.

Figure 29. Comparison of the one- (JEFF-3.1.1) or two-steps fitted total cross sections with the most recent transmission measurement by Sage et al. [61] and the new JENDL-4.0 evaluation over the two ²⁴¹Am lowest resonances energy domain.

Figure 30. Comparison of the one- (JEFF-3.1.1) or two-steps fitted total cross sections with the most recent transmission measurement by Sage et al. [61] and the new JENDL-4.0 evaluation in the neighborhood of the ²⁴¹Am third resonance.

The present two-steps analysis and JENDL-4.0 are in agreement as far as the fission cross section is concerned since both converge on a thermal value close to 3.14b and the old measurement by Dabbs et al. [39].

5.1.2. ISO _γ ratio data

More precise information on the ISO _γ behavior at above URR energy is now available from two independent calculations based on standard high energy formalisms (Hauser-Feshbach statistical theory with coupled channel optical model calculations and pre-equilibrium/equilibrium corrections). The first calculated ISO _γ curve, using the CCONE code [62] (developed in the JENDL-4.0 framework [14]), is drawn on graphic 28 (orange dash curve) and compared to the predicted ISO _γ ratio (green solid curve) by Morillon et al. [58] using the TALYS-ECIS06 system of codes. These two calculations converge toward a similar asymptotic ISO _γ value close to 0.64. Since they both treat simultaneously all open channels and reactions and, in particular, the direct capture preponderant at high energy, we can assume that an asymptotic ratio close to 0.64 is likely within the present knowledge on the ²⁴²Am excited level scheme. For completeness we plot on the same figure the ENDF/B-VII.1 evaluated isomer ratio which is unchanged since ENDF/B-VII.0.

The oscillating ISO _γ branching ratio proposed by RUSFOND-2010 [57] in the resonance range strengthens our feeling, already expressed in 2006 [63], about this eventuality. No special comments are joined with the RUSFOND-2010 file but we can cast that this is derived from a spin-dependent ISO _γ calculation which from our conclusion is much larger for a 2⁻ than for a 3⁻ s-wave resonance. Beyond the fluctuations, the special step-like curve promoted by RUSFOND-2010 manifests a deep investigation by the authors of the capture decay process from a particular excited resonance above the neutron separation energy. An interesting topic of investigation would be the impact of the unlikely individual weak γ-transitions between neighboring neutron spectroscopy resonances of spacing less than 1 eV. Such weak γ-transitions might be substituted by an electronic conversion process 14 which could delay the switching point between a particular ISO _γ value to another (e.g. from the to the and reciprocally).

5.2. Foreseen improvements from recent microscopic results

Among the recent microscopic results released are from one side those supplying information on thermal cross sections and from the other side those bringing feedback on resonance integrals. Table 22 gives an updated list on the former measurement type whose error weighted average gives  = (670 ± 8)b. The very large value quoted by Shinohara et al. [31] was excluded from this average because it relies on the Cd ratio technique which has demonstrated difficulties to be interpreted. The latest experimental result quoted by Letourneau et al. [59] is also excluded from the average since we can assess a certain degree of confidence on it. We will use this result as ultimate “cross-checking value” and double-cross this result by a re-calculation of the effective cross section () representative of the reaction rate measured by Letourneau et al. [59] in the fission chamber located in the so-called “V4 canal” of the ILL-Grenoble high flux reactor. This re-calculation, performed by Leconte [64] and using the whole certified JEFF-3.1.1 application library based on  = 647b, results in a value of  = (573 ± 14)b. On a direct proportionality 15 basis between thermal and effective cross section, we would recover from Letourneau et al.'s [59] experimental data, a corresponding thermal value of b consistent with our cross section averaging, b, from the quoted results. It indicates a slight thermal capture cross section overestimation in JENDL-4.0 which suggests another balance between and capture resonance integral. This also means that the normalization applied by Jandel et al. [12] on their capture yields measurement and leads to a thermal cross section value of (665 ± 33)b was adequately established.

Another piece of information is carried by the most recent transmission measurement by Sage et al. [66] performed in 2007 (first data acquisition set) at the IRMM Geel which focussed on the first three resonances of the ²⁴¹Am neutron induced cross section. Figures 29 and 30 present Sage et al. results in terms of reconstructed total cross section from the resonance parameter set quoted in their MLBWe analysis (Ref. [66] page 124). This new measurement reveals a total cross section still significantly larger than the one quoted by Slaughter et al. (JEFF-3.1.1 basis) and much larger than Belanova et al. as far as the two lowest resonances are concerned. Both JEFF-3.1.1 and JENDL-4.0 RRP must be revised accordingly. The JEFF-3.1.1 result in the neighborhood of the third resonance is poor since it is calibrated on Derrien et al. whose data are likely altered within the resonance peak. JENDL-4.0 is better since it was designed such as reproducing the recent data from Jandel et al. Nonetheless JENDL-4.0 must be also significantly increased in the neighborhood of the third resonance. Table 23 shows for these three resonances the values of the total cross section at the peak of the resonances and the corresponding resonance area increase estimates requested to fit Sage et al. data. The enhancement factors encountered are up to 38% for JEFF-3.1.1 across the third resonance and up to 19% for JENDL-4.0 across the first resonance. The correction to apply to Derrien et al.'s data, measured above the second resonance energy, to be in agreement with Sage et al. new measurement will require a 31% increase of Derrien et al.'s total cross section area across the third resonance.

The final piece confirming the above elements of conclusion is brought by the validation feedback of JEFF-3.1.1 through specific neutron integral experiments carried in the critical zero power reactor facilities of the CEA Cadarache. Among those experiments, the results [65] of the “OSMOSE” program, performed in the MINERVE pool reactor and devoted to the improvement on the knowledge of the actinide absorption cross sections, reveal an underestimation of over the thermal and the epithermal neutron energy range by about (−6 ± 2)%.

6. Conclusions and perspectives for JEFF-3.2

This study has carefully reviewed the reasons of the disagreements between differential and microscopic data. Both types of results nowadays tend to be more consistent especially because more attention can be brought to the experimental data post-treatment with full uncertainty propagation. However, this study has brought to our attention the fact that differential measurements, relying on transmission experiments, could be in some cases not as absolute as the standard belief would postulate it. Differential results must be compared, as often as possible, to integral trends to tend toward a very precise and self-validated nuclear data evaluation.

Regarding the ²⁴¹Am nucleus, the recent experimental efforts spent in terms of integral [59,65] and differential [12,61] have enriched quite significantly the neutron database allowing a breakthrough on the knowledge relative to this minor actinide. The new JENDL-4.0 [14] evaluated file testifies of this progress. However, our study on thermal and epithermal cross sections shows well that there is still some room for improvement, recommending in particular a thermal capture cross section around (662 ± 20)b larger than JEFF-3.1.1 ( = 647b) but lower than JENDL-4.0 ( = (684 ± 15)b). This choice and the present epithermal feedback suggest another balance in terms of resonance integral requesting an additional increase of this latter over the resonance range, even for JENDL-4.0 which includes the recent capture measurement by Jandel et al. [12]. The brand new differential transmission measurement by Sage [61] reveals a cross-sectional area even larger than the old poor, but rather fair, measurement by Slaughter et al. [38] (JEFF-3.1.1 reference over the two lowest resonances). From the third resonance, the JEFF-3.1.1 total cross section needs a larger renormalization than JENDL-4.0 because it relies on Derrien and Lucas's data [37] assumed to be of good quality. The inclusion of the new transmission dataset in the fitting base suggests a subsequent correction on Derrien and Lucas's [37] data since the observed area under the third resonance is 38% smaller than the area measured by Sage [61].

This article traces back the ²⁴¹Am capture isomeric ratio evaluation performed at Cadarache for JEFF-3.1 (and maintained for JEFF-3.1.1) from 0 to 20 MeV relying essentially on the integral data feedback which gives suitable results in terms of reactor physics and addresses a valuable estimation of the associated variances. The constraint point at 20 MeV on the isomer ratio (ISO _γ = 0.75) aims to recall the lack of high energy experimental information in the energy region where the capture cross section is small and dominated by direct processes. Recent more precise theoretical calculations involving high energy physics (Hauser-Feshbach statistical theory with coupled channel optical model calculations and pre-equilibrium/equilibrium corrections) such as those performed with the CCONE code [62] (developed in the JENDL-4.0 framework [14]) or the TALYS-ECIS06 system of codes [58] converge toward a similar asymptotic ISO _γ value around 0.64. Since they both treat simultaneously all open channels and reactions and in particular direct capture processes preponderant at high energy, we can assume that an asymptotic ratio value close to 0.64 is plausible within the present knowledge on the ²⁴²Am level scheme.

Over the energy region of the resolved resonances, we support our pragmatic ISO _γ evaluation by photon transition intensity simulations from evaluated nuclear structure data, basic models, and Monte Carlo-type calculations in order to quantify the impact due the presence of two s-wave types. Our study has confirmed and has refined the results obtained by Wisshak et al. [43] who had shown a significant modification of both the ISO _γ and the average number of emitted γ (multiplicities) depending on the resonance total angular spin and parity involved. The values estimated from our Monte Carlo calculations are equal to (90 ± 3)% and (76 ± 3)%, respectively, for 2⁻ and 3⁻ resonances, including simulated γ transitions over a near-continuum level sequence. These results remain consistent with those of Wisshak et al. [43] who found, respectively, 84% and 71% using a more conventional approach. In terms of γ-multiplicities, the average values fulfill the same trend with well-resolved results leading to (3.43 ± 0.3) and (3.67 ± 0.3) for decays, respectively, from 2⁻ and 3⁻ s-wave neutron resonances. This feature suggests workable experimental spin discrimination from resonance observation. Comforted by Wisshak et al.'s [43] results, we decided to quantify the impact of the two different s-wave ISO _γ values on the isomeric total ratio versus energy in a MLBWe framework. The resulting total ISO _γ shows strong fluctuations over the resonance range; that trend, already stated in a preliminary study [63], is also apparent in the recent RUSFOND-2010 [57] library. The present study proposes to convert this ISO _γ behavior in terms of MLBWe resonance parameters upon resonance spin and assuming two additional non-interfering partial exit capture channels corresponding to the two main γ-ray cascade stories all the way down, respectively, to the ground and metastable states. Since the current MLBWe representation does not allow more than two non-elastic non-capture exit reaction channels whose one is already occupied by the single fission channel in the ²⁴²Am compound nucleus, we suggest the development of an MLBWe extended format well dedicated to fertile isotopes with narrow resonances. An alternative choice would be the existing Reich–Moore extended format (LRF = 7 in ENDF-6 convention [42]) which will have to deal with capture interferences between these two major capture channels. At final, the resonance reconstruction allows systematic ISO _γ Doppler broadening for a better comparison between differential and integral measurements. However, the net impact of the broadening on a ratio of capture cross sections remains small except when the isolated resonance approximation is not valid (upper part of the RRR) or when the Doppler broadening is so dramatic (temperature observed in astrophysics) that isolated resonances overlap strongly. In addition to this broadening treatment, we recommend the use in reactor calculations of pointwise ISO _γ data rather than an effective ISO _γ value for more accurate calculations. However, if the LWR JEFF-3.1.1 data application library user is willing to use such an average for practical purpose, we have obtained the value of (84.6 ± 2.9)% after weighting the evaluated pointwise ISO _γ data by the ²⁴¹Am capture reaction rate encountered in a neutron epithermal flux.

The present study 16 paves the way for the next JEFF-3.2 stage which will be based on both our JEFF-3.1.1 exhaustive feedback and an updated database combining the most valuable results from both differential and integral sources.

Acknowledgments

One author of this work (O. Bouland) would like to gratefully acknowledge H. Weigmann and A. Plompen for fruitful comments made in the early times of this work. The authors also wish to thank G. Noguère and P. Leconte for valuable exchanges. Part of this work has relied on the SAMMY code which was dutifully maintained and developed by Dr. Nancy Larson at ORNL. The authors are also deeply indebted to Prof. A. Santamarina for directions during this study.

Notes

 1. The appellation “isomeric ratio”, referring solely to the relative population of the ground state to the total capture cross section, is less frequently used than the expression “branching ratio” (γBR) which is the ratio of two partial capture cross sections leading to distinct states (e.g. ).

 2. Since JEF-2.2 and JEFF-3.0 data are identical as far as the ²⁴¹Am neutron data are concerned, the stage JEFF-3.0 will not be mentioned anymore in this article if not explicitly needed.

 3. In this article, the term “integral” refers to microscopic information derived from experiments performed in reactors.

 4. Institute for Reference Materials and Measurements (IRMM), Forschungszentrum Karlsruhe (FZK), and Budapest Neutron Center (BNC).

 5. Since JEFF-3.1 and JEFF-3.1.1 data are identical as far as the ²⁴¹Am neutron data are concerned, we will keep the present appellation JEFF-3.1.1 for the rest of this article if not explicitly needed.

 6. Unphysical spin values are in general not supported by neutron application data library processing systems, such as NJOY [25].

 7. After a slight renormalization on the updated gold reference cross section value of 98.66 b (instead of 98b quoted by the authors).

 8. The inner fundamental barrier height in the (²⁴¹Am + n) compound system is about 1 MeV larger than the neutron separation energy.

 9. This is the value adopted by the “Atlas of Neutron Resonances.”

10. Using an early version of the TALYS code.

11. For the purpose of this study, the choice has been made to stick with purely calculated individual photon transition intensities even if the most intense γ-rays have been measured and compiled in standard databases as for instance in ENSDF [49].

12. Mean energies' values mentioned in this article are relative to level transition intensities whatever the exact transition nature is either by γ decay or by electronic conversion process.

13. The present ground state partial capture of ²⁴¹Am cross section calculation under MLBWe convention was performed using the SAMMY code by setting for each individual resonance with a fictitious second fission channel to preserve the total width of the resonance. The reciprocal widths were applied to the metastable state partial capture cross section.

14. In our calculation developed in section 3.2.2, we assume no competitive electronic conversion process.

15. Assuming that the effective cross section is simply derived from the weighting of the thermal cross section by a Maxwellian-type flux.

16. Pending on an improved knowledge of the 242 Americium absorption cross section, the recommendations expressed in this article could be slightly modified.