1 1 Complete calculation of evaluated 0 2 Maxwellian-averaged cross sections and their n a uncertainties for s-process nucleosynthesis J 0 1 ] R S . h Boris Pritychenko ∗ p NationalNuclearDataCenter,BrookhavenNationalLaboratory,Upton,NY11973-5000,USA - o E-mail: [email protected] r t s a Present contribution represents a significant improvement of our previous calculation of [ Maxwellian-averaged cross sections and astrophysical reaction rates. Addition of newly- 2 v evaluated neutron reaction libraries, such as ROSFOND and Low-Fidelity Covariance Project, 2 and improvements in data processing techniques allowed us to extend it for entire range of s- 7 7 processnuclei, calculate Maxwellian-averagedcrosssectionuncertaintiesforthefirst time, and 4 provideadditionalinsightsonallcurrentlyavailableneutron-inducedreactiondata. Nuclearre- . 8 actioncalculationsusingENDFlibrariesandcurrentJavatechnologieswillbediscussedandnew 0 0 resultswillbepresented. 1 : v i X r a 11thSymposiumonNucleiintheCosmos,NICXI July19-23,2010 Heidelberg,Germany Speaker. ∗ (cid:13)c Copyrightownedbytheauthor(s)underthetermsoftheCreativeCommonsAttribution-NonCommercial-ShareAlikeLicence. http://pos.sissa.it/ CompletecalculationofevaluatedMaxwellian-averagedcrosssectionsandtheiruncertainties BorisPritychenko 1. Introduction Nuclearreactionsplayanimportantroleinstellarnucleosynthesis andareresponsibleforpro- ducingheavychemicalelementsfromlightelementsthatweregeneratedintheBigBang. Present- day calculations of s-process nucleosynthesis are often based on dedicated nuclear astrophysics data tables, such as work of Bao et al. [1], or its successor KADONIS [2], however it is essen- tial to produce complementary neutron-induced reaction data sets. ENDF-6 formatted evaluated neutron libraries contain various data for all known nuclei, including neutron capture cross sec- tions for more than 680 individual nuclei from 1H to 257Fm in the range of neutron energy from 10 5eVto20MeV.Nuclear-reactorandnational-security applicationcommunitiesusedthesedata − extensively in the eV and MeV energy ranges, while keV data were less utilized. This creates a unique opportunity to utilize evaluated neutron data for non-traditional intermediate-energy ap- plications, such as s-process nucleosynthesis, and create a new set of ENDF benchmarks. This work represents a significant upgrade of our previous calculation of Maxwellian-averaged cross sections and astrophysical reaction rates [3]. In addition of newly-evaluated neutron reaction li- braries, such as JENDL-4, CENDL-3.1, ROSFOND 2010 and Low-Fidelity Covariance Project [4,5],improvements indataprocessing techniques allowedustoextendcalculations fortheentire rangeofs-processnucleiandproduceMaxwellian-averaged crosssectionuncertainties forthefirst time. Nuclearreactioncalculations usingevaluatedneutronlibrariesandcurrentJavatechnologies willbediscussed andnewresultswillbepresented. 2. CalculationofMaxwellian-averagedCrossSections andUncertainties ENDFlibrariesarebasedontheoreticalcalculations thatareoftenadjustedtofitexperimental data [6]. There are two kinds of ENDF cross section data representations: groupwise (averaged over energy interval) and pointwise. The first kind is often used in reactor physics calculations, whilethesecondoneisbettersuitedfornuclear physicsapplications. GenericENDFlibrarycross sections (MF=3) do not contain information on neutron resonances. To resolve this problem for neutron physics calculations the codes PREPRO [7] and NJOY [8] are often used to produce a pointwise version of the libraries that include the resonance region data and provide cross section information within ENDF range of energies from 10 5 eV to 20 MeV. Here, we used the code − PREPROtoreconstruct theresonance regionwithaprecision of0.1%. Maxwellian-averaged crosssectionscanbeexpressedas[3] s Maxw(kT)= √2p (m2/((mk1T+)2m2))2Z ¥ s (EnL)EnLe−kT(EmnL1m+2m2)dEnL (2.1) 0 wherekandTaretheBoltzmann constant andtemperature ofthesystem, respectively andE isan energy ofrelative motion ofthe neutron with respect tothe target. Here EL isaneutron energy in n thelaboratory systemandm andm aremassesofaneutronandtargetnucleus, respectively. 1 2 Previously[3],Maxwellian-averaged crosssectionsandastrophysicalreactionrateswerepro- ducedusingtheSimpsonmethodonlinearized ENDFcrosssections(MF=3). Thissimplemethod allowedquickcalculatedintegralvalueswithgoodprecision. Howeverthedegreeofprecisionwas within 1%[3, 9]. Thisgeneral limitation can be overcome inthe linearized ENDFfilesbecause ∼ 2 CompletecalculationofevaluatedMaxwellian-averagedcrosssectionsandtheiruncertainties BorisPritychenko Table1:EvaluatednuclearlibrariesandKADONISMaxwellian-averagedneutroncapturecrosssectionsin mbatkT=30keVfors-processnuclei. Isotope JENDL-4.0 ROSFOND2010 ENDF/B-VII.0 KADONIS[2] 36-Kr-82 9.582E+1 9.483E+1 1.027E+2 2.097E+1 9.000E+1 6.000E+0 ± ± 42-Mo-96 1.052E+2 1.035E+2 1.036E+2 1.690E+1 1.120E+2 8.000E+0 ± ± 44-Ru-100 2.065E+2 2.062E+2 2.035E+2 3.949E+1 2.060E+2 1.300E+1 ± ± 46-Pd-104 2.700E+2 2.809E+2 2.809E+2 4.488E+1 2.890E+2 2.900E+1 ± ± 48-Cd-110 2.260E+2 2.346E+2 2.346E+2 4.219E+1 2.370E+2 2.000E+0 ± ± 50-Sn-116 9.115E+1 1.002E+2 1.002E+2 1.875E+1 9.160E+1 6.000E-1 ± ± 52-Te-122 2.644E+2 2.639E+2 2.349E+2 4.883E+1 2.950E+2 3.000E+0 ± ± 52-Te-123 8.138E+2 8.128E+2 8.063E+2 1.063E+2 8.320E+2 8.000E+0 ± ± 52-Te-124 1.474E+2 1.473E+2 1.351E+2 2.682E+1 1.550E+2 2.000E+0 ± ± 54-Xe-128 2.582E+2 2.826E+2 2.826E+2 6.823E+1 2.625E+2 3.700E+0 ± ± 54-Xe-130 1.333E+2 1.518E+2 1.518E+2 2.993E+1 1.320E+2 2.100E+0 ± ± 56-Ba-134 2.301E+2 2.270E+2 2.270E+2 4.038E+1 1.760E+2 5.600E+0 ± ± 56-Ba-136 7.071E+1 7.001E+1 7.001E+1 1.087E+1 6.120E+1 2.000E+0 ± ± 60-Nd-142 3.557E+1 3.701E+1 3.341E+1 4.252E+1 3.500E+1 7.000E-1 ± ± 62-Sm-148 2.361E+2 2.444E+2 2.449E+2 4.416E+1 2.410E+2 2.000E+0 ± ± 62-Sm-150 4.217E+2 4.079E+2 4.227E+2 3.601E+2 4.220E+2 4.000E+0 ± ± 64-Gd-154 9.926E+2 1.010E+3 9.511E+2 1.070E+2 1.028E+3 1.200E+1 ± ± 66-Dy-160 8.702E+2 8.293E+2 8.328E+2 6.769E+1 8.900E+2 1.200E+1 ± ± 72-Hf-176 5.930E+2 4.529E+2 4.571E+2 4.811E+1 6.260E+2 1.100E+1 ± ± 80-Hg-198 1.612E+2 1.612E+2 1.612E+2 1.621E+1 1.730E+2 1.500E+1 ± ± 82-Pb-204 8.355E+1 7.242E+1 7.242E+1 7.699E+0 8.100E+1 2.300E+0 ± ± thecrosssectionvalueislinearly-dependent onenergywithinaparticular bin[10] s (E ) s (E ) s (E)=s +(E E ) 2 − 1 (2.2) 1 1 − E E 2 1 − wheres (E ),E ands (E ),E arepointwisecrosssectionandenergyvaluesforthecorresponding 1 1 2 2 energybin. Lastequationisagoodapproximationofneutroncrosssectionvaluesforasufficiently dense grid. This allowed us to calculate definite integrals using Wolfram Mathematica online integrator [11]. Summing integrals for all energy bins will produce an exact integral value for Maxwellian-averaged crosssection. Low-Fidelitycrosssectioncovariances wereusedtocalculate uncertainties for ENDF/B-VII.0 data [5, 12]. Final results for JENDL-4.0, ROSFOND 2010 and ENDF/B-VII.0 libraries [13, 4, 12] are shown in Table 1. Due to space limitations only selected dataareshownandCENDL-3.1,JEFF-3.1crosssectionsareomitted. In s-process nucleosynthesis, we assume that product of neutron-capture cross section (at 30 keVinmb)timessolarsystemabundances(relativetoSi=106)asafunctionofatomicmassshould beconstant forequilibrium nuclei[14]: s N =s N =constant (2.3) A A A 1 A 1 − − 3 CompletecalculationofevaluatedMaxwellian-averagedcrosssectionsandtheiruncertainties BorisPritychenko 103 ENDF/B-VII.0 Si) 102 6 0 1 N(/ b)* m σ( 101 100 80 100 120 140 160 180 200 220 Atomic Mass Figure 1: ENDF/B-VII.0 product of neutron-capturecross section (at 30 keV in mb) times solar system abundances(relativetoSi=106)asafunctionofatomicmassfornucleiproducedonlyinthes-process. To verify this phenomenon, the calculated s gMaxw(30keV) from the ENDF/B-VII.0 library h i [12] were multiplied by solar abundances taken from Anders and Grevesse [15], and plotted in Figure1. VisualinspectionoftheFigureindicatestwolocalequilibrium andledge-precipice break atA 138fortheENDF/B-VII.0fit. Relativelyhighproductvaluefor116Snisduetothefactthat ∼ 116Snhasr-process contribution [15]. InFY2011, present contribution resultswillbeusedtoupgrade ‘Maxwellian-averaged Cross Sections and Astrophysical Reaction Rates’ Web application http://www.nndc.bnl.gov/astro. The Webapplication frontpage isshowninFigure2. 3. Conclusion& Outlook Maxwellian-averagedcrosssectionsforneutroncapturehavebeencalculatedusingJENDL-4, CENDL-3.1, ROSFOND2010, ENDF/B-VII.0and JEFF-3.1 libraries using Low-Fidelity covari- anceprojectdata. ROSFOND2010library(686materials)[4]providesthemostcompletecoverage alongthes-processpath. Infact,itcontainsinformationon347outof354isotopes(98%coverage). The only s-process isotopes that are missing in ROSFOND are: 12C, 110Ag, 132,133,135,137Ce and 142Pr. Carbon and Praseodymium cross sections can be found in the CENDL-3.1 and ENDF/B- VII.0 or JEFF-3.1 libraries, respectively. Typical neutron library, such as ENDF/B-VII.0 (393 materials), provides 80%coverageofthes-process path. The comparison of Maxwellian-averaged cross section values from Table 1 indicates a good agreement between KADONIS and evaluated nuclear libraries. Future work on ENDF libraries will provide additional improvements and benefits for nuclear astrophysics and applications com- munities. 4 CompletecalculationofevaluatedMaxwellian-averagedcrosssectionsandtheiruncertainties BorisPritychenko Figure 2: ‘Maxwellian-averaged Cross Sections and Astrophysical Reaction Rates’ Web application, http://www.nndc.bnl.gov/astro. 4. Acknowledgments The author thanks Drs. V. Zerkin (IAEA), M.W. Herman, C.M. Mattoon, S.F. Mughabghab, and M. Pigni (BNL)for productive discussions and help on ROSFONDand Low-Fidelity project data,respectively. WearealsogratefultoM.Blennauforacarefulreadingofthemanuscript. This workwassponsoredbytheOfficeofNuclearPhysics,OfficeofScienceoftheU.S.Departmentof Energy, underContractNo. DE-AC02-98CH10886 withBrookhaven ScienceAssociates, LLC. References [1] Z.Y.Bao,H.Beer,F.Käppeleretal.,ATOMICDATA ANDNUCLEAR DATATABLES76,70(2000). [2] I.Dillmann,M.Heil,F.Käppeleretal.,AIPConf.Proc.819,123(2006).Datadownloadedfrom http://www.kadonis.org onApril7,2010. h i [3] B.Pritychenko,S.F.Mughabghab,andA.A.Sonzogni,ATOMICDATAAND NUCLEARDATA TABLES96,645(2010). 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