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Improved Full Bayesian Evaluation of Neutron- induced Reactions on 55 Mn

Improved Full Bayesian Evaluation of Neutron- induced Reactions on 55 Mn. H. Leeb, St. Gundacker , D. Neudecker, Th . Srdinko , V. Wildpaner Atominstitut, Vienna University of Technology, Vienna, Austria. EFNUDAT 2010, CERN ID29.

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Improved Full Bayesian Evaluation of Neutron- induced Reactions on 55 Mn

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  1. ImprovedFullBayesian Evaluation of Neutron-inducedReactions on 55Mn H. Leeb, St. Gundacker, D. Neudecker, Th. Srdinko, V. Wildpaner Atominstitut, Vienna University of Technology, Vienna, Austria EFNUDAT 2010, CERN ID29 Work supported by EURATOM via the F4E grant F4E-GRT-014 NUDATA_FILES. The views and opinions expressed herein do not reflect necessarily those of the European Commission ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  2. Content • Motivation • The Full Bayesian Evaluation Technique – GENEUS 0.0 • Choice of Nuclear Model • Determination of Prior- Parameter uncertainties- Model defects • Experimental data • Bayesian evaluation procedure • Evaluated cross section data • Summary EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  3. Motivation • Mn-55 is an importantcomponentofstructuralmaterials • usedfor a futurefusionfacilityas well asforfissionreactors • andcurrentlydiscussedacceleratordrivensystems (ADS). • Therearetwodemandstothenucleardatacommunity • Extension oftheenergyrangeuptoabout 150 MeV • Inclusionofuncertaintyinformation in form ofcrosssectionuncertainties • PROBLEM • The generationofreliablecovariancematricesis still an open • Questionandtherefore a topicofresearchregarding • Development ofmethods • Validation ofreliability EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  4. Concept of Nuclear Data Evaluation Concept: Nuclear Data Evaluation should provide a consistent set of cross section and spectral data and associated uncertainty information. At present it is well accepted that consistency can be best achieved via application of Bayesian statistics. Development of FULL BAYESIAN EVALUATION TECHNIQE • Characteristics: • Evaluation fully based on Bayesian statistics • Consistent inclusion of apriori knowledge associated with nuclear model • Inclusion of Model defects in the prior • Inclusion of proper covariance matrices of experiments • Proper treatment of systematic errors EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  5. The Full Bayesian Evaluation Technique EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  6. Evaluation Tool - GENEUS EXFOR Data Base Underlying Model: TALYS 1.0 parameters optimized for the nucleus PRIOR parameter uncertainties model defects ICE Estimatecovariancematricesforexperiments Parallel Parallel BAYESIAN UPDATE EFNUDAT 2010, CERN ID29 Bayesian Evaluation MF=3 and MF=33 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  7. Objective of the present work Application of the Full Bayesian Evaluation Technique to neutron-induced cross sections of 55Mn • Status reportedatthe ND2010 Conference • Atthe ND2010 in Jeju (April 2010) a firstapplicationoftheFullBayesian • Evaluation Technique (GENEUS 0.0) on neutron-inducedcrosssectionsof • Mn-55 was presented. Itdifferedfrompreviousevaluationsbyfollowingfeatures • Model Defectsincluded, • Estimateof experimental covariancematricesincluded, • Cross experimentcorrelationsincluded. • Advances in themeantime • Uncertaintiesof p-, d- anda-nucleusoptical potential parametersincluded • Uncertainties in theleveldensitiesincluded • Improvedextrapolationsofmodeldefects in energyregionswithoutexperimental crosssectiondata EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  8. Choice of Nuclear Model The code TALYS with slightly different optical model and level density parameters was used. To optimize the parameters the cross section data of neighboring nuclei (not 55Mn) were used. EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  9. Model Parameters Parametrisation form of optical potential of Koning and Delaroche and level Densities (CTM – TALYS) have been used. Optimisation on the cross sections of neighboring nuclei (40<A<60) EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  10. Descriptive power of the model EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  11. Determination of Prior Nuclear model calculations are used to determine the PRIOR: EFNUDAT 2010, CERN ID29 Improved method developed and first application to 55Mn Method and code based on complete ignorance and transformation group invariance developed by Pigni and Leeb neglected ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  12. Parameter uncertainties • In comparisontotheevaluationpresentedat ND2010 we • considered a wider classofnuclearmodels • neutronoptical potential • proton-, deuteron- andalpha-optical potential • leveldensity • Assumptionofequally • distributedparametervalues • boundariesaremoreimportant Probabilitydensitydistribution an EFNUDAT 2010, CERN ID29 a< a> Simple probabilitysufficientforpriordetermination Important: choiceofphysicalandmathematicalboundaries ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  13. Effect of increased parameter space n,p, d,a + Level densities tot,tot (n,2n),(n,2n) only n EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  14. Formulation of Model Defects Basic idea: introduction of scaling factor for each channel c with a scaling factor per isotope (n) Scaling factor in the energy bin M Covariance matrix EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  15. Scaling factors and uncertainties EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  16. Correlation matrix <stot(E)stot(E‘)> EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  17. Problems with limited data (n,2n) – (n,2n) correlationmatrix Extrapolation because of lack of data EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  18. Extrapolation of Model Defects C correlations Phenomenological extrapolation in area C Interpolation EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  19. Impact of improved extrapolation total cross section (n,a) cross section OLD NEW ND2010-1352: Bayesian based uncertainties of neutron-induced reaction cross sections of Mn-55

  20. Model defects: (n,2n) reaction edgebecauseof lack ofdata EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  21. Combination to complete prior EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  22. Analysis of experiments Block 1 Block 3 EFNUDAT 2010, CERN ID29 Block 2 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  23. Analysis of each experiment Eachexperimenthasbeenconsideredwithregardto uncertaintiesandreliabilities on thebasisoftheavailable literature. The information was fedintotheprogramme ICE (Interactive CovarianceEstimator) toestimatecovariance matricesofcrosssectionuncertaintiesforeachexperiment Generate a fullcovariancematrixforeach block in order to includecorrelationsofdataandtoavoidstatisticaltreatment ofsystematicerrors. EFNUDAT 2010, CERN ID29 Block Covariance Matrices ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  24. Covariance Matrix of Experiments Block 1 correlationmatrix Block 3 correlationmatrix EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  25. Available covariance matrices Prior covariance matrix: cov.matrix + prob. distr. only cov. matrix Covariance matrix of experiments: energycalcibrationerror measurement uncertainties Likelyhood function: EFNUDAT 2010, CERN ID29 V =<Dsc(E) Dsc‘(E‘)>Expexperimental covariance matrixsModel=SM(x) model value ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  26. Bayesian Update Procedure At present normal probability distributions are assumed  linearized expression for Bayes theorem can be applied parameter vector covariance matrixG sensitivity matrix EFNUDAT 2010, CERN ID29 Differencetopreviousapproaches: V =<Dsc(E)Dsc‘(E‘)>Expcontainsthecovariancematricesof all availablecorrelated experimental dataforthesystem. ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  27. Evaluated stot EFNUDAT 2010, CERN ID29 106 107 108 E eV 109 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  28. Evaluated selastic EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  29. Evaluated (n,xn) cross sections (n,2n) (n,4n) EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  30. Correlations <stot(E),stot(E‘)> Model defects Parameter uncertainties evaluation EFNUDAT 2010, CERN ID29 prior ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  31. Correlations <s(n,2n)(E),s(n,2n)(E‘)> NEW EVALUATION OLD EVALUATION EFNUDAT 2010, CERN ID29 model defects ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  32. Cross channel correlations All crosschannelcorrelationshavebeendetermined n,inl – n,2n NEW EVALUATION EFNUDAT 2010, CERN ID29 n,inl – n,2n OLD EVALUATION ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  33. Cross channel correlations NEW EVALUATION <Dsela(E) Dsinl(E‘)> EFNUDAT 2010, CERN ID29 OLD EVALUATION ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  34. Evaluated (n,p)-cross section EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  35. Evaluated (n,pa)-cross section EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  36. Impact of increased model space (n,a) crosssection Uncertaintiesof n-, p-, d-, a-nucleusoptical model parametersand leveldensitiesincluded Uncertaintiesonly in n-nucleusoptical model Parameters included EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  37. Importance of Prior correlations elastic cross section

  38. Summary • neutron-inducedreactioncrosssectionfor55Mn in theenergy • rangebetween 5-150 MeVhavebeenre-evaluatedwithin an • ImprovedFullBayesian Evaluation Technique • Angle integratedcrosssections (MF=3) • Covariancematricesforcrosssectionuncertainties (MF=33) • total, elastic, inelastic, (n,2n),(n,3n),(n,4n),(n,p),(n,t),(n,pa),(n,a) • Parameter uncertaintiesfor n-, p-, d-anda-nucleusopticalpotentialsas well asleveldensitiesaretakenintoaccount • Model defectsaretakenintoaccount – improvedextrapolation • Covariancematricesofexperimentsareestimated • ENDF Files (MF=3 and 33) havebeengenerated EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  39. Outlook • Further improvementsare in progress: • Extension tofissionablenucleiwithin ANDES • Inclusionof angle differential dataintotheevaluation • Improvemethodfordeterminationofcorrelationsofexp. • Improvedautomatisationofdeterminationof model defects EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  40. Co-workers Denise NEUDECKER Thomas SRDINKO Thankyouforyourattention EFNUDAT 2010, CERN ID29 Volker WILDPANER Stefan GUNDACKER ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  41. Parameter boundaries: potential depths Potential should be within one family characterized by the number of bound states sustained by the potential EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  42. Parameter boundaries: geometry Physics constraints on the geometry: rms-radius must lie between charge radius and charge radius + 2 nuclear range These uncertainties are transferred to other parameters EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  43. Scaling factors and uncertainties EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

  44. Scaling factors and uncertainties EFNUDAT 2010, CERN ID29 ImprovedFullBayesian Evaluation of Neutron-inducedReactions on Mn-55

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