Calculations of Nuclear Astrophysics and Californium Fission Neutron Spectrum Averaged Cross Section Uncertainties using ENDF/B-VII.1, JEFF-3.1.2, JENDL-4.0 and Low-Fidelity Covariances
aa r X i v : . [ a s t r o - ph . S R ] J un Calculations of Nuclear Astrophysics and Californium Fission Neutron SpectrumAveraged Cross Section Uncertainties using ENDF/B-VII.1, JEFF-3.1.2, JENDL-4.0and Low-Fidelity Covariances
Boris Pritychenko ∗ National Nuclear Data Center, Brookhaven National Laboratory, Upton, NY 11973, USA (Dated: April 3, 2018; Received XX May 2014; revised received XX August 2014; accepted XX September 2014)Nuclear astrophysics and californium fission neutron spectrum averaged cross sections and theiruncertainties for ENDF materials have been calculated. Absolute values were deduced withMaxwellian and Mannhart spectra, while uncertainties are based on ENDF/B-VII.1, JEFF-3.1.2,JENDL-4.0 and Low-Fidelity covariances. These quantities are compared with available data, in-dependent benchmarks, EXFOR library, and analyzed for a wide range of cases. Recommendationsfor neutron cross section covariances are given and implications are discussed.
I. INTRODUCTION
Calculations of integral values at NNDC have been con-ducted in parallel with the ENDF/B-VII library releases[1, 2]. These values represent the complementary datasets for nuclear astrophysics, industry, and data evalua-tion applications. First results on reaction rates and neu-tron cross sections [3] have demonstrated a large potentialof ENDF/B-VII for applications, such as KADoNiS stel-lar nucleosynthesis library [4]. Further interactions withthe fundamental and applied science communities haveinitiated work on the extended list of integral values andtheir uncertainties [5–7]. Calculations of nuclear astro-physics and californium fission neutron spectrum aver-aged cross section ( i.e. californium spectrum) uncertain-ties are presented in the following sections.
II. MAXWELLIAN-AVERAGED CROSSSECTIONS UNCERTAINTIES
Nuclear data covariances are essential for fundamentaland applied nuclear science and technology. They providethe experimentally-observable uncertainties that are nec-essary for application development. Maxwellian-averagedcross sections and their uncertainties have been calcu-lated in recent years [3, 5]. Fig. 1 shows cross sectionuncertainties for ENDF/B-VII.1 evaluated library, LowFidelity project, and KADoNiS database [2, 4, 8] demon-strate nuclear astrophysics value of ENDF and Low Fi-delity covariances for stellar nucleosynthesis research. At ∗ Corresponding author: [email protected] the same time, the ENDF/B-VII.1 and Low Fidelity un-certainties are relatively large for precise calculations.The stellar nucleosynthesis calculations require the strin-gent cross section uncertainties in order <
3% to final-ize the branching of the s -process path. However, evena specially-designated KADoNiS library, at the presentstate, cannot satisfy this requirement, and further re-search is necessary. Atomic Mass
KADoNiS M a x w e lli an - a v e r aged C r o ss S e c t i on U n c e r t a i n t i e s , % Low-Fidelity
ENDF/B-VII.1
FIG. 1. (Color online) Maxwellian-averaged neutron capturecross section, kT =30 keV, uncertainties for ENDF/B-VII.1library, Low-Fidelity project and KADoNiS database [2, 4, 8].Data are taken from [5]. alculations of Nuclear Astrophysics . . . NUCLEAR DATA SHEETS Boris Pritychenko
III.
CF FISSION NEUTRON SPECTRUMAVERAGED CROSS SECTIONS AND THEIRUNCERTAINTIES σ ( M a x w e lli an ( k T = k e V )) / σ ( M annha r t ) Atomic Mass
ENDF/B-VII.1 Capture
ENDF/B-VII.1 Fission
FIG. 2. (Color online) The ratio of calculated ENDF/B-VII.1 californium spectrum neutron cross sections usingMaxwellian, kT =1420 keV, and Mannhart spectra [5, 10]. Cf is often used in nuclear physics as a compact,portable and intense neutron source. Its neutron energyspectrum is similar to a fission reactor, with an averageenergy of 2.13 MeV. This is very convenient for ENDFlibraries validation tests in the fast region, even thoughit is not exactly representative of a fast reactor spectrum(being hotter) [9].For evaluation purposes,
Cf spectrum neutron fis-sion and capture averaged cross sections were calculatedusing Maxwellian-averaged ( kT =1420 keV) spectrum andMannhart evaluation [5, 10]. Fig. 2 shows the ra-tio of calculated californium spectra cross sections us-ing Maxwellian, and Mannhart approaches for ENDF/B-VII.1 library. This ratio indicates that Maxwellian spec-trum provides a reasonable fit of californium data, how-ever, it falls short of being used for nuclear standardsand dosimetry purposes. Consequently, the Mannhartevaluation has been chosen for calculation of californiumspectrum cross sections.Presently, the original and 640-group representationsof Mannhart evaluation are frequently considered. Toevaluate a possible spectrum representation impact, neu-tron cross sections have been calculated using the bothformats. Figs. 3, 4 show the ratios of californium fis-sion and capture cross sections for both representations ofthe linearized ENDF libraries. The plotted ratios clearlydemonstrate the impact of different representations.
220 230 240 250 2601.001.021.041.001.021.041.001.021.04 F i ss i on σ ( M annha r t ) / σ ( G r oup s ) Atomic Mass
ENDF/B-VII.1
JEFF-3.1.2
JENDL-4.0
FIG. 3. (Color online) The ratio of ENDF, JEFF, and JENDLcalculated californium spectrum neutron fission cross sectionsusing the original and 640-group Mannhart spectra [10]. C ap t u r e σ ( M annha r t ) / σ ( G r oup ) Atomic Mass
ENDF/B-VII.1
JEFF-3.1.2
JENDL-4.0
FIG. 4. (Color online) The ratio of ENDF, JEFF, and JENDLcalculated californium spectrum neutron capture cross sec-tions using the original and 640-group Mannhart spectra [10].
Following the nuclear dosimetry example,
Cf spec-trum neutron fission averaged cross sections for ma-jor evaluated libraries: ENDF/B-VII.1, JEFF-3.1.2, andJENDL-4.0 [2, 11, 12] have been produced using the 640-group format and shown in the Table I. These data are ina good agreement with the previously-published CIELOvalues [9]. Californium spectrum neutron capture aver-aged cross sections are available upon request.2alculations of Nuclear Astrophysics . . .
NUCLEAR DATA SHEETS Boris Pritychenko
TABLE I: 640-group californium spectrum neutron fission averaged crosssections for ENDF, JEFF, and JENDL major evaluated libraries, andEXFOR (experimental nuclear reaction) data ( kT ∼ Material ENDF/B-VII.1 JEFF-3.1.2 JENDL-4.0 EXFOR (barns) (barns) (barns) (barns)88-Ra-223 5.485E-2 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± . . . NUCLEAR DATA SHEETS Boris Pritychenko
TABLE I: 640-group californium spectrum neutron . . . (continued).
Material ENDF/B-VII.1 JEFF-3.1.2 JENDL-4.0 EXFOR (barns) (barns) (barns) (barns)98-Cf-253 7.674E-1 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± IV. CROSS SECTION UNCERTAINTIESANALYSIS AND RECOMMENDATIONS
To evaluate ENDF libraries covariances in the fast neu-trons region I will consider Maxwellian, and californiumspectra cross sections uncertainties, and deduce recom-mendations.
220 230 240 250 260040801200.00.404080120
Atomic Mass
ENDF/B-VII.1
JEFF-3.1.2 C f δ σ ( n ,f i ss i on ) , % JENDL-4.0
FIG. 5. (Color online) The ENDF, JEFF, and JENDL calcu-lated californium spectrum neutron fission cross section un-certainties using the 640-group Mannhart spectrum [10].
Visual inspection of the shown in Figs. 5, 6 data al-lows to spot the “suspect” cases, where uncertainties arenot very useful for application development. These some-what unrealistic uncertainties of above 100 and below 1 %originate from theoretical models and fitting procedures,respectively. The summary of re-analysis of the previ-ous Maxwellian data ( kT =30 keV) [5] and analysis of thecurrent Mannhart spectrum uncertainties for ENDF/B-VII.1 library is shown in the Table II.The present analysis suggests the following recommen-dations for ENDF integral values and covariances: C f δ σ ( n , γ ) , % Atomic Mass
ENDF/B-VII.1
JEFF-3.1.2
JENDL-4.0
FIG. 6. (Color online) The ENDF, JEFF, and JENDL cal-culated californium spectrum neutron capture cross sectionuncertainties using the 640-group Mannhart spectrum [10].
1. Absolute cross section values for linearized files aresensitive to the changes of Mannhart evaluationgroup structure. Calculated values are model de-pendent and may vary within 1-5%.2. Nuclear astrophysics and energy applications re-quire covariances for all ENDF materials.3. Realistic covariances are needed: • Covariance matrices that result in >
100 %cross section uncertainties should be avoided,such large uncertainties are not very useful forapplication development. • Covariance matrices that result in < • Presently, covariance matrices produce widevariations of cross section uncertainties within0.5-120 % range. This spread should be keptwithin 3-50 % range.4alculations of Nuclear Astrophysics . . .
NUCLEAR DATA SHEETS Boris Pritychenko
TABLE II. The summary of the ENDF/B-VII.1 library cross section uncertainties analysis.Reaction Maxwellian spectrum, kT =30 keV Mannhart spectrum [10]Uncertainty <
1% Uncertainty > <
1% Uncertainty > U, , Pu , Ac,
Th,
Pa,
Np,
Pu,
Cm, , Bk, , , , Cf, , , Es , U, , Pu , Ac,
Th(n, γ ) Pa,
Pu,
Cm,
Bk, Fm Cr Pa, U, , , Np, Pu
4. Multiple MF=33 covariance matrices can be con-fusing.
V. CONCLUSIONS
The previously-calculated ENDF/B-VII.1 and Low-Fidelity Maxwellian-averaged cross section uncertaintieshave been re-analyzed. Californium spectrum neutronfission and capture averaged cross sections and theiruncertainties have been calculated for ENDF/B-VII.1, JEFF-3.1.2, and JENDL-4.0 nuclear data libraries.Recommendations for ENDF covariances have beendeduced using the application development needs.
Acknowledgements:
The author thanks M. Herman(BNL) for support of this work, R. Capote, A. Trkov andV. Zerkin (IAEA) for help with Mannhart spectra anddata processing, and Mrs. M. Blennau (BNL) for carefulreading of the manuscript and useful suggestions. Workat BNL was funded by the Office of Nuclear Physics,US DoE under Contract No. DE-AC02-98CH10886 withBrookhaven Science Associates, LLC. [1] M.B. Chadwick, P. Obloˇzinsk´y, M. Herman et al. ,“ENDF/B-VII.0: Next Generation Evaluated NuclearData Library for Nuclear Science and Technology,”
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