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Basics of Nuclear Data Evaluation and Perspectives H. Leeb Atominstitut,TU Wien, Austria H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 1 Research at the Atominstitut atomic physics, quantum optics (J. Schmiedmayer) radiation physics (Ch. Streli) low-temperature physics, Super conductivity (H. Weber) applied quantum physics (N.N.) nuclear and particle physics (H. Leeb) H. Leeb Atominstitut, TU Wien, Austria neutron and quantum physics (H. Abele) NuPECC Meeting,Vienna, March 13, 2009 2 Nuclear and Particle Physics Nuclear Physics and Nuclear Astrophysics (H. Leeb) scattering and reaction theory, nuclear data evaluation Hadron Physics and Fundamental Interactions (M.Faber, H. Markum) exotic atoms, lattice gauge theory Experimental Particle Physics (Ch. Fabjan) detector developments, data analysis techniques directly linked to the Institute of High Energy Physics of the Austrian Academy of Sciences H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 3 Nuclear Physics and Nuclear Astrophysics Theoretical description of scattering and reaction processes and the interpretation of observables with regard to interactions and underlying structures in basic and applied physics Scattering and reaction theory • inverse scattering techniques • optical potentials and specific reactions • phase problem in quantum mechanics Neutron-induced reactions • nuclear data evaluation • nuclear astrophysics involvement in the experiments at n_TOF@CERN and in Geel H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 4 Experiments: n-induced cross sections n_TOF@CERN (n,g) cross sections for transmutation and astrophysics GELINA (JRC) (n,2n) cross sections via prompt g-decay Experiments performed within collaboration: TU Wien and University of Vienna G. Badurek, E. Jericha, H. Leeb, A. Pavlik, A. Wallner H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 5 (n,xn) cross sections E. Jericha (TU Wien) A. Pavlik (Univ. Wien) GELINA (JRC) 209Bi(n,2n) cross sections Measurement of prompt g-rays of the residual nucleus (even A) 4+ 2+ 0+ Mihailescu et al. ND2007 H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 6 (n,g) cross sections n_TOF@CERN (n,g) (n,f) 4p total absorption calorimeter (TAC) astrophysical relevance s-process main responsibility of TU Wien: proper uncertainty analysis H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 7 Experimental uncertainties at n_TOF E MeV 232Th(n,g) E‘ 151 MeV Sm(n,g) 151Sm(n,g) 232Th(n,g) E‘ MeV E‘ MeV normalized covariance matrix of the n_TOF experiment H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 8 Nuclear data evaluation Start of Modern Data Evaluation: recommended values of fundamental physics constants (c, h, af, ... ) Dunnington (1939); Du Mond and Cohen (1953) Present Status: At present Evaluated Nuclear Data Files represent a consistent set of cross sections and associated quantities for all relevant reaction processes. Most data files are limited to the energy region below 20MeV. There exist several nuclear data libraries with evaluated cross section data, but only few files contain uncertainty information the reliability Is still an open question. JEFF3.1, ENDF/B-VII, JENDL, CENDL, … H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 9 Concept of evaluation Nuclear data evaluation is essentially a procedure following the rules of Bayesian statistics within a subjective interpretation the probability reflects our expectation no experimental verification Evaluation is given in terms of - expectation values of observables cross sections, x parameters of nuclear model - covariance matrices of observables (cross sections) , ... channel, energy BAYESIAN STATISTICS H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 10 Bayes theorem Bayes Theorem (1763): p(x| M) = p( |xM) p(x|M) / p( |M) posterior = likelihood x prior / evidence ... data x ... model parameter from experiment Expectation value: Covariance matrix element: apriori H. Leeb Atominstitut, TU Wien, Austria apriori M ... other information Choice of proper prior ? d nx px | M model x, M d nx px | M model x, M model x, M NuPECC Meeting,Vienna, March 13, 2009 11 Evaluations done by Vonach et al. First evaluations in the field of nuclear date which include uncertainties were performed by Vonach et al. (Univ. Vienna) about 1990 They considered nuclei where many experimental data have been available choice of prior not essential S. Tagesen, H. Vonach, A. Wallner, ND2007 H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 12 Developments in nuclear data evaluation Current Demands: • Inclusion of uncertainty information covariance matrices • Extension of energy range to ~150MeV Challenges: Evaluation process and covariance matrices – scarcity of experimental data for E > 20 MeV quest of uncertainty of nuclear models Improvement of models: nuclear reactions, fission, … H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 13 Bayes theorem Bayes Theorem (1763): p(x| M) = p( |xM) p(x|M) / p( |M) posterior = likelihood x prior / evidence ... data x ... model parameter from experiment Expectation value: Covariance matrix element: apriori H. Leeb Atominstitut, TU Wien, Austria apriori M ... other information Choice of proper prior ? d nx px | M model x, M d nx px | M model x, M model x, M NuPECC Meeting,Vienna, March 13, 2009 14 Choice of proper prior GOAL quantitative estimate of the reliability of nuclear model based evaluations • Define an almost unbiased prior • Account for all apriori knowledge • Minimal use of experimental data H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 15 Sources of uncertainties d d = p ( ) The contributions to the covariance matrix of the model are M(mod) = M(par) + M(num) + M(def) parameter uncertainties EFFDOC-1047 H. Leeb Atominstitut, TU Wien, Austria numerical implementation error Model defects non-statistical error NuPECC Meeting,Vienna, March 13, 2009 16 Parameter uncertainties For most cases where there is no obvious prior Baye proposed to apply Laplace principle of insufficient reasoning, i.e. a uniform distribution Main criticism from objectivist: the choice of prior is arbitrary !!! INFORMATION THEORY (Shannon 1949) N Information entropy: H ( p) K pi ln pi H ( p, 0 , 1 ) K pi ln pi 0 K pi 1 1K i 1 pi fi f 0 N N N The amount of uncertainty is maximal if the entropy is maximal. i 1 i 1 i 1 Assumption: Besides the marginalisation we know an expection value N N N H ( p, 0 , 1 ) K pi ln pi 0 K pi 1 1K pi fi i 1 i 1 i 1 H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 f 0 17 Theory for prior determination Principle of maximal information entropy da1 0 p a daN p(a) log m(a ) daN p ( a ) 1 k Gk p( a ) 0 k 1 da1 prior p( x) Information Entropy 1 Z K m(x) exp f ( x) Determination of Lagrange par. partition Z dx m( x) exp f ( x) variance function Constraints f ln Z 2 f 2 ln Z 2 Invariant measure to account for continuous parameters: m( x ) 1 for scaling parameters: x H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 18 Admissible range of parameters dependence on av of admissible range in rv r2 ch arg e r OM r2 ch arg e r2 force d r r V r d r V r 3 2 r2 2 3 admissible range in av z defines lower boundary H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 19 Parameter distribution for 208Pb potential parameters rv (fm) v1 (MeV) H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 20 Parameter uncertainties-correlations total elastic phenomenological optical potentials H. Leeb Atominstitut, TU Wien, Austria microscopic optical potentials NuPECC Meeting,Vienna, March 13, 2009 21 Model defects - scaling local scale N Er weight Er c c E ex Er N nc Em all r c th c r th Er all r th Er thc Er c ex all r all r weight 2 c c E E 2 N nc Em th c r exc r N nc Em all r th Er th Er Global scaling factor for each reaction channel c Mean value and vairance for each energy bin Em and isotope n all r N nc wmc ,n N nc Em mean scale for each isotope and given reaction m This coarse approximation provides a covariance matrix c E c ' E ' thc E thc ' E ' ( N nc E N nc )( N nc ' E ' N nc ' ) E , E ' c ,c ' 2 N nc Em def isotopes PROBLEM: not statistically defined H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 22 Model defects of 16O relative variance in % E MeV Example 16O total cross section E‘ MeV H. Leeb Atominstitut, TU Wien, Austria experimental data for 12C,14N,19F,20Ne,23Na,24Mg 0 30% E MeV 20% 60 10 NuPECC Meeting,Vienna, March 13, 2009 60 23 Correlations - comparison correlations of total cross section uncertainties16O cut: E+E‘=const 0.6 0.0 complete prior E MeV 60 10 60 more details in Final report of EFDA-TW6-TTMN-001B-D7a 0.6 E MeV 60 H. Leeb Atominstitut, TU Wien, Austria parameter uncertainties 10 60 NuPECC Meeting,Vienna, March 13, 2009 24 Importance of uncertainty information Example: Reliable uncertainty of keff is required keff 2 K K cross section covariances Safety margins – commissioning Reduce the number of experimental tests significant economic impact H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 25 Implementation of Bayesian statistics Bayes Theorem (1763): p(x| M) = p( |xM) p(x|M) / p( |M) posterior = likelihood x prior / evidence x ... model parameter H. Leeb Atominstitut, TU Wien, Austria ... data M ... other information NuPECC Meeting,Vienna, March 13, 2009 26 Bayesian update procedure prior x0 M0 Exp-01 x1 M1 Exp-02 x2 M2 Exp-03 x3 M3 Exp-m xm Mm posterior H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 experiment 27 Problem of update procedure prior statistical error Bayes theorem H. Leeb Atominstitut, TU Wien, Austria f x a bx cx 2 1 d 2r 1 e systematic error Bayesian update NuPECC Meeting,Vienna, March 13, 2009 28 Origin of the difference The ‚experiments‘ covariance matrix V contains all experiments and all correlations Standard Bayesian update procedure – no correlations between experiments Systematic errors are treated like a statistical uncertainty i.e. 1 H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 m 29 Evaluation Tool GENEUS still manual semi-automatic for single isotope and restricted reaction channels not available ENDF-file tables graphics PRIOR TALYS SC2COV BAYES SCALE one-step procedure EXFOR Janis-Tables H. Leeb Atominstitut, TU Wien, Austria EXPCOV NuPECC Meeting,Vienna, March 13, 2009 30 Perspectives Current Demands: • Inclusion of uncertainty information covariance matrices • Extension of energy range to ~150MeV Challenges: Evaluation process and covariance matrices – scarcity of experimental data for E > 20 MeV quest of uncertainty of nuclear models Improvement of models: nuclear reactions, fission, … H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 31 Topics in nuclear reactions Future research will focus on challenges in reaction theory: • Reactions involving charged composite nuclei embrittlement due to gas production in structure materials p-process reactions in nuclear astrophysics, (a,g), (p,g) • Reactions involving weakly bound nuclei break-up contributions in deuteron involving reactions reaction processes with exotic weakly bound nuclei • (Microscopic) modelling of nuclear fission microscopic understanding of fission process modelling of fission cross sections experimentally not accessible isotopes (MA) H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 32 Summary and outlook Summary: • Neutron-induced cross section measured • Well defined evaluation procedure based on modelling developed • General evaluation tool GENEUS is under construction Outlook: Focus is currently changing to topics on reaction theory - composite particle scattering theory - reactions involving weakly bound nuclei H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 33 Working Group J. Gundacker (Master) J. Haidvogl (PhD) D. Neudecker (PhD) Th. Srdinko (Master) V. Wildpaner EU Research Projects: EURATOM P&T: n_TOF,IP_EUROTRANS EURATOM Fusion: EFDA-Projrects, F4E-Grants EU I3-Project: EURONS Former students K. Nikolics M.T. Pigni (PhD) I. Raskinyte (PostDoc) H. Leeb Atominstitut, TU Wien, Austria Strong collaboration with the nuclear data centers NEA, IAEA NuPECC Meeting,Vienna, March 13, 2009 34 THANK YOU FOR YOUR ATTENTION H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 35 a-nucleus optical potentials (semi)microscopic approach for low energies (relevant to astrophysics) Optical Potential: Vopt r ,r U r ,r iW r ,r Vopt r ,r r a T PVPA T a r r a T PVQ coupling term Direct part: direct term 1 E QHQ i QVPA T a r U r ,r r a T PVPA T ar evaluated within RGM in order to account correctly for the antisymmetrisation H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 36 Imaginary a-nucleus optical potentials Imaginary Part: W 2 r ,r Im r T0 VN a TM r g M r ,r ;E M r TM VN a T0 r M Intermediate states in RPA Green function at intermediate state It can be considered as a nuclear structure approach to a-nucleus optical potential, which should work satisfactory at low energies calculations for a-16O and a-40Ca and a-208Pb are in progress H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 37 Reactions of weakly bound nuclei deuteron breaks up easily (EB=2,2 MeV) breakup leads to additional flux loss Incoming channel outgoing channel Elastic d-A channel Incoming d-A channel Breakup of the deuteron nonelastic due to n-collision nonelastic due to p-collision Neglecting breakup leads to non-standard parameters in fitted potentials Keaton, Armstrong (1973) Ansatz of a complete wave function of the d-A system r , 0 0 r d 3 deuteron wave function H. Leeb Atominstitut, TU Wien, Austria p-n scattering wave function (continuum) NuPECC Meeting,Vienna, March 13, 2009 38 H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 39