Present contribution represents a significant improvement of our previous
calculation of Maxwellian-averaged cross sections and astrophysical reaction
rates. Addition of newly-evaluated neutron reaction libraries, such as ROSFOND
and Low-Fidelity Covariance Project, and improvements in data processing
techniques allowed us to extend it for entire range of s-process nuclei,
calculate Maxwellian-averaged cross section uncertainties for the first time,
and provide additional insights on all currently available neutron-induced
reaction data. Nuclear reaction calculations using ENDF libraries and current
Java technologies will be discussed and new results will be presented.Comment: 6 pages, 2 figure

Pritychenko, Boris

English

arXiv

Present contribution represents a significant improvement of our previous calculation of Maxwellian-averaged cross sections and astrophysical reaction rates. Addition of newly-evaluated neutron reaction libraries, such as ROSFOND and Low-Fidelity Covariance Project, and improvements in data processing techniques allowed us to extend it for entire range of sprocess nuclei, calculate Maxwellian-averaged cross section uncertainties for the first time, and provide additional insights on all currently available neutron-induced reaction data. Nuclear reaction calculations using ENDF libraries and current Java technologies will be discussed and new results will be presented

Pritychenko, B.

UNT (University of North Texas) Digital Library

     BNL-93963-2010-CP     Complete calculation of evaluated Maxwellian-averaged cross sections and their uncertainties for s-process nucleosynthesis    Boris Pritychenko    National Nuclear Data Center, Brookhaven National Laboratory, Upton, NY 11973-5000, USA E-mail: pritychenko@bnl.gov      National Nuclear Data Center  Energy Sciences & Technology Department  Brookhaven National Laboratory  P.O. Box 5000  Upton, NY 11973-5000  www.bnl.gov            Notice: This manuscript has been co-authored by employees of Brookhaven Science Associates, LLC under Contract No. DE-AC02-98CH10886 with the U.S. Department of Energy. The publisher by accepting the manuscript for publication acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.  This preprint is intended for publication in a journal or proceedings. Since changes may be made before publication, it may not be cited or reproduced without the author’s permission.      DISCLAIMER  This report was prepared as an account of work sponsored by an agency of the United States Government.  Neither the United States Government nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or any third party’s use or the results of such use of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof or its contractors or subcontractors.  The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.  Complete calculation of evaluatedMaxwellian-averaged cross sections and theiruncertainties for s-process nucleosynthesisBoris Pritychenko∗National Nuclear Data Center, Brookhaven National Laboratory, Upton, NY 11973-5000, USAE-mail: pritychenko@bnl.govPresent contribution represents a significant improvementof our previous calculation ofMaxwellian-averaged cross sections and astrophysical reaction rates. Addition of newly-evaluated neutron reaction libraries, such as ROSFOND and Low-Fidelity Covariance Project,and improvements in data processing techniques allowed us to extend it for entire range of s-process nuclei, calculate Maxwellian-averaged cross section uncertainties for the first time, andprovide additional insights on all currently available neutron-induced reaction data. Nuclear re-action calculations using ENDF libraries and current Java technologies will be discussed and newresults will be presented.11th Symposium on Nuclei in the Cosmos, NIC XIJuly 19-23, 2010Heidelberg, Germany∗Speaker.c© Copyright owned by the author(s) under the terms of the Creativ Commons Attribution-NonCommercial-ShareAlike Licen. http://pos.sissa.it/Complete calculation of evaluated Maxwellian-averaged cross sections and their uncertaintiesBoris Pritychenko1. IntroductionNuclear reactions play an important role in stellar nucleosynthesis and are responsible for pro-ducing heavy chemical elements from light elements that were g nerated in the Big Bang. Present-day calculations of s-process nucleosynthesis are often based on the dedicated nuclear astrophysicsdata tables, such as work of Bao et al. [1], however it is essential to produce complementaryneutron-induced reaction data sets. ENDF-6 formatted evaluated neutron libraries contain variousdata for all known nuclei, including neutron capture cross sections for more than 680 individ-ual nuclei from1H to 257Fm in the range of neutron energy from 10−5 eV to 20 MeV. Nuclear-reactor and national-security application communities have used these data extensively in the eVand MeV energy ranges while keV data were less utilized. Thiscreates a unique opportunity to uti-lize intermediate-energy evaluated neutron data for non-traditional applications, such as s-processnucleosynthesis, and create a new set of ENDF benchmarks. Pre ent work represents a significantupgrade of our previous calculation of Maxwellian-averaged cross sections (MACS) and astrophys-ical reaction rates [2]. Addition of newly-evaluated neutron reaction libraries, such as JENDL-4,CENDL-3.1, ROSFOND 2010 and Low-Fidelity Covariance Project [3, 4], and improvements indata processing techniques allowed us to extend it for the entire range of s-process nuclei andcalculate Maxwellian-averaged cross section uncertainties for the first time. Nuclear reaction cal-culations using evaluated neutron libraries and current Java technologies will be discussed and newresults will be presented.2. Calculation of Maxwellian-averaged Cross Sections and UncertaintiesENDF libraries are based on theoretical calculations that are often adjusted to fit experimentaldata [5]. There are two kinds of ENDF cross section data representations: groupwise (averagedover energy interval) and pointwise. The first kind is often used in reactor physics calculations,while the second one is better suited for nuclear physics applications. Generic ENDF library crosssections (MF=3) do not contain information on neutron resonances. To resolve this problem forneutron physics calculations, codes PREPRO [6] and NJOY [7]are often used to produce a point-wise version of the libraries that include resonance regiondata and provide cross section informa-tion within ENDF range of energies from 10−5 eV to 20 MeV. Here, we used code PREPRO toreconstruct resonance region with 10−3 precision.Maxwellian-averaged cross sections (MACS) can be expressed a [2]σ Maxw(kT ) =2√π(m2/(m1 + m2))2(kT )2∫ ∞0σ(ELn )ELn e− ELn m2kT(m1+m2) dELn (2.1)wherek andT are the Boltzmann constant and temperature of the system, respectively andE is anenergy of relative motion of the neutron with respect to the target. HereELn is a neutron energy inthe laboratory system andm1 andm2 are masses of a neutron and target nucleus, respectively.Previously [2], Maxwellian-averaged cross sections and astrophysical reaction rates were pro-duced using the Simpson method on linearized ENDF cross sections (MF=3). This simple methodallowed quick calculated integral values with good precision. However the degree of precision waswithin ∼ 1 % [2, 8]. This general limitation can be solved in the linearized ENDF files because2Complete calculation of evaluated Maxwellian-averaged cross sections and their uncertaintiesBoris PritychenkoTable 1: Evaluated nuclear libraries and KADONIS Maxwellian-averaged neutron capture cross sections inmb atkT=30 keV fors-process nuclei.Isotope JENDL-4.0 ROSFOND 2010 ENDF/B-VII.0 KADONIS [13]36-Kr- 82 9.582E+1 9.483E+1 1.027E+2±3.308E+1 9.000E+1±6.000E+042-Mo- 96 1.052E+2 1.035E+2 1.036E+2±3.281E+1 1.120E+2±8.000E+044-Ru-100 2.065E+2 2.062E+2 2.035E+2±6.716E+1 2.060E+2±1.300E+146-Pd-104 2.700E+2 2.809E+2 2.809E+2±7.551E+1 2.890E+2±2.900E+148-Cd-110 2.260E+2 2.346E+2 2.346E+2±7.266E+1 2.370E+2±2.000E+050-Sn-116 9.115E+1 1.002E+2 1.002E+2±3.402E+1 9.160E+1±6.000E-152-Te-122 2.644E+2 2.639E+2 2.349E+2±8.648E+1 2.950E+2±3.000E+052-Te-123 8.138E+2 8.128E+2 8.063E+2± .857E+2 8.320E+2±8.000E+052-Te-124 1.474E+2 1.473E+2 1.351E+2±4.689E+1 1.550E+2±2.000E+054-Xe-128 2.582E+2 2.826E+2 2.826E+2±9.991E+1 2.625E+2±3.700E+054-Xe-130 1.333E+2 1.518E+2 1.518E+2±4.913E+1 1.320E+2±2.100E+056-Ba-134 2.301E+2 2.270E+2 2.270E+2±8.311E+1 1.760E+2±5.600E+056-Ba-136 7.071E+1 7.001E+1 7.001E+1±2.389E+1 6.120E+1±2.000E+060-Nd-142 3.557E+1 3.701E+1 3.341E+1± .147E+1 3.500E+1±7.000E-162-Sm-148 2.361E+2 2.444E+2 2.449E+2±7.331E+1 2.410E+2±2.000E+062-Sm-150 4.217E+2 4.079E+2 4.227E+2±1.452E+2 4.220E+2±4.000E+064-Gd-154 9.926E+2 1.010E+3 9.511E+2± .901E+2 1.028E+3±1.200E+166-Dy-160 8.702E+2 8.293E+2 8.328E+2± .900E+2 8.900E+2±1.200E+172-Hf-176 5.930E+2 4.529E+2 4.571E+2±1.459E+2 6.260E+2±1.100E+180-Hg-198 1.612E+2 1.612E+2 1.612E+2±5.392E+1 1.730E+2±1.500E+182-Pb-204 8.355E+1 7.242E+1 7.242E+1±2.084E+1 8.100E+1±2.300E+0cross section value is linearly-dependent on energy withina particular bin [9]σ(E) = σ1 +(E −E1)σ(E2)−σ(E1)E2−E1(2.2)whereσ(E1),E1 andσ(E2),E2 are pointwise cross section and energy values for the energybin.This allowed us to calculate definite integrals using Wolfram Mathematica online integrator [10].Summing integrals for all energy bins will produce an exact integral value for Maxwellian-averagedcross section. Low-Fidelity cross section covariances were used to calculate uncertainties forENDF/B-VII.0 data [4, 11]. Final results for JENDL-4.0, ROSFOND 2010 and ENDF/B-VII.0libraries [12, 3, 11] are shown in Table 1. Due to space limitations only selected data are shownand CENDL-3.1, JEFF-3.1 cross sections are omitted.In s-process nucleosynthesis, the product of neutron-capture cross section (at 30 keV in mb)times solar system abundances (relative to Si = 106) as a function of atomic mass should be constantfor equilibrium nuclei [14]:σANA = σA−1NA−1 = constant (2.3)To verify this phenomenon, the calculated〈σ Maxwγ (30keV )〉 from the ENDF/B-VII.0 library[11] were multiplied by solar abundances taken from Anders and Grevesse [15], and plotted in3Complete calculation of evaluated Maxwellian-averaged cross sections and their uncertaintiesBoris Pritychenko80 100 120 140 160 180 200 220100101102103σ(mb)*N(/106 Si)  Atomic Mass ENDF/B-VII.0Figure 1: ENDF/B-VII.0 product of neutron-capture cross section (at30 keV in mb) times solar systemabundances (relative to Si = 106) as a function of atomic mass for nuclei produced only in thes-process.Figure 1. Visual inspection of the Figure indicates two locaequilibrium and ledge-precipice breakat A ∼ 138 for the ENDF/B-VII.0 fit. Relatively high product value for 116Sn is due to the fact that116Sn hasr-process contribution [15].In FY 2011, present contribution results will be used to upgrade ‘Maxwellian-averaged CrossSections and Astrophysical Reaction Rates’ Web application http://www.nndc.bnl.gov/astro. TheWeb application frontpage is shown in Figure 2.3. Conclusion & OutlookMaxwellian-averaged cross sections (MACS) for capture andfission have been calculated us-ing JENDL-4, CENDL-3.1, ROSFOND 2010, ENDF/B-VII.0 and JEFF-3.1 libraries using Low-Fidelity covariance project data. ROSFOND 2010 library (686 materials) [3] provides the mostcomplete coverage along the s-process path. In fact, it contains information on 347 out of 354isotopes (98% coverage). The onlys-process isotopes that are missing in ROSFOND are:12C,110Ag, 132,133,135,137Ce and142Pr. Carbon and Praseodymium cross sections can be found in theCENDL-3.1 and ENDF/B-VII.0 or JEFF-3.1 libraries, respectively. Typical neutron library, suchas ENDF/B-VII.0 (393 materials), provides 80% coverage of thes-process path.The comparison of Maxwellian-averaged cross section values from Table 1 indicates a goodagreement between KADONIS and evaluated nuclear libraries. Future work on ENDF librarieswill provide additional improvements and benefits for nuclear astrophysics and applications com-munities.4. AcknowledgmentsThe author thanks Drs. V. Zerkin (IAEA), M.W. Herman, C.M. Mattoon, S.F. Mughabghab,4Complete calculation of evaluated Maxwellian-averaged cross sections and their uncertaintiesBoris PritychenkoFigure 2: ‘Maxwellian-averaged Cross Sections and Astrophysical Reaction Rates’ Web application,http://www.nndc.bnl.gov/astro.and M. Pigni (BNL) for productive discussions and help on ROSF ND and Low-Fidelity projectdata, respectively. We are also grateful to M. Blennau for a careful reading of the manuscript. Thiswork was sponsored by the Office of Nuclear Physics, Office of Science of the U.S. Department ofEnergy, under Contract No. DE-AC02-98CH10886 with Brookhaven Science Associates, LLC.References[1] Z.Y. Bao, H. Beer, F. Käppeleret al., ATOMIC DATA AND NUCLEAR DATA TABLES 76, 70 (2000).[2] B. Pritychenko, S.F. Mughabghab, and A.A. Sonzogni, ATOMIC DATA AND NUCLEAR DATATABLES (2010), in press; doi:10.1016/j.adt.2010.05.002.[3] S.V. Zabrodskaya, A.V. Ignatyuk , V.N. Koscheevt al., VANT, Nuclear Constants 1-2 3 (2007).[4] R.C. Little, T. Kawano, G.D. Halet al., NUCLEAR DATA SHEETS109 2828 (2008). Available from〈http://www.nndc.bnl.gov/lowfi/〉.[5] EXPERIMENTAL NUCLEAR REACTION DATA (EXFOR/CSISRS), Available from〈http://www.nndc.bnl.gov/exfor〉.5Complete calculation of evaluated Maxwellian-averaged cross sections and their uncertaintiesBoris Pritychenko[6] D.E. Cullen, “The ENDF/B Pre-processing codes (PREPRO)," Available from〈http://www-nds.iaea.org/ ndspub/endf/prepro/〉.[7] R.E. MacFarlane and D.W. Muir, “The NJOY nuclear data processing system, version 91," Tech. Rep.LA-12740-M, Los Alamos National Lab, 1994.[8] T. Nakagawa, S. Chiba, T. Hayakawa, T. Kajino, ATOMIC DATA AND NUCLEAR DATA TABLES 91,77 (2005).[9] B. Pritychenko, PROCEEDINGS OF59th CSEWG MEETING, Upton, NY, USA, November 3-5(2009), Available from〈http://www.nndc.bnl.gov/proceedings/2009csewgusndp/Tuesday/csewg/PritychenkoCSEWG09.pdf〉.[10] Wolfram Mathematica Online Integrator, Available from 〈http://integrals.wolfram.com〉.[11] M.B. Chadwick, P. Obložinský, M.W. Hermanet al., NUCLEAR DATA SHEETS107, 2931 (2006).[12] JAPANESEEVALUATED NUCLEAR DATA L IBRARY (JENDL-4.0), Available from〈http://wwwndc.jaea.go.jp/index.html〉.[13] I. Dillmann, M. Heil, F. Käppeleret al., AIP Conf. Proc.819, 123 (2006). Data downloaded from〈http://www.kadonis.org〉 on April 7, 2010.[14] C.E. Rolfs and W.S. Rodney, CAULDRONS IN THE COSMOS, The University of Chicago Press (1988).[15] E. Anders and N. Grevesse, GEOCHIMICA ET COSMOCHIMICA ACTA 53, 53 (1989).6

Complete Calculation of Evaluated Maxwellian-Averaged Cross Sections and Their Uncertainties for S-Process Nucleosynthesis

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Complete calculation of evaluated Maxwellian-averaged cross sections and their uncertainties for s-process nucleosynthesis

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