H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, Basics of Nuclear Data Evaluation and Perspectives H. Leeb Atominstitut,TU Wien, Austria

Research at the Atominstitut H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, radiation physics (Ch. Streli) applied quantum physics (N.N.) atomic physics, quantum optics (J. Schmiedmayer) low-temperature physics, Super conductivity (H. Weber) neutron and quantum physics (H. Abele) nuclear and particle physics (H. Leeb)

Nuclear and Particle Physics H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 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

Nuclear Physics and Nuclear Astrophysics H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, Theoretical description of scattering and reaction processes and the interpretation of observables with regard to interactions and underlying structures in basic and applied physics Neutron-induced reactions Scattering and reaction theory nuclear data evaluation nuclear astrophysics inverse scattering techniques optical potentials and specific reactions phase problem in quantum mechanics involvement in the experiments at and in Geel

Experiments: n-induced cross sections H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, GELINA (JRC) (n,2n) cross sections via prompt  -decay Experiments performed within collaboration: TU Wien and University of Vienna G. Badurek, E. Jericha, H. Leeb, A. Pavlik, A. Wallner (n,  ) cross sections for transmutation and astrophysics

(n,xn) cross sections H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, GELINA (JRC) 209 Bi(n,2n) cross sections Measurement of prompt  -rays of the residual nucleus (even A) Mihailescu et al. ND2007 E. Jericha (TU Wien) A. Pavlik (Univ. Wien)

(n,  ) cross sections H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, astrophysical relevance s-process main responsibility of TU Wien: proper uncertainty analysis (n,  ) (n,f) 4  total absorption calorimeter (TAC)

Experimental uncertainties at n_TOF H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, normalized covariance matrix of the n_TOF experiment 232 Th(n,  ) 151 Sm(n,  ) 232 Th(n,  ) E‘ MeV E MeV

Nuclear data evaluation H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, Start of Modern Data Evaluation: recommended values of fundamental physics constants (c, ,  f,... ) 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, …

Concept of evaluation H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 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 - covariance matrices of observables (cross sections) BAYESIAN STATISTICS

Bayes theorem H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, Bayes Theorem (1763): p(x|  M) = p(  |xM) p(x|M) / p(  |M) posterior = likelihood x prior / evidence x... model parameter ... data M... other information from experimentChoice of proper prior ? Expectation value: Covariance matrix element:

Evaluations done by Vonach et al. H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 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

Developments in nuclear data evaluation H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 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, …

Bayes theorem H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, Bayes Theorem (1763): p(x|  M) = p(  |xM) p(x|M) / p(  |M) posterior = likelihood x prior / evidence x... model parameter ... data M... other information from experimentChoice of proper prior ? Expectation value: Covariance matrix element:

Choice of proper prior H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 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

Sources of uncertainties H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, The contributions to the covariance matrix of the model are M (mod) = M (par) + M (num) + M (def) parameter uncertainties numerical implementation error Model defects non-statistical error EFFDOC-1047

Parameter uncertainties H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 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) Information entropy: The amount of uncertainty is maximal if the entropy is maximal. Assumption: Besides the marginalisation we know an expection value

Theory for prior determination H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, Information Entropy Constraints prior partition function Determination of Lagrange par. variance Invariant measure to account for continuous parameters: for scaling parameters: Principle of maximal information entropy

Admissible range of parameters H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, dependence on a v of admissible range in r v admissible range in a v z defines lower boundary

Parameter distribution for 208 Pb H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, potential parameters r v (fm) v 1 (MeV)

Parameter uncertainties-correlations H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, phenomenological optical potentialsmicroscopic optical potentials  total  elastic

Model defects - scaling H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, Global scaling factor for each reaction channel c This coarse approximation provides a covariance matrix PROBLEM: not statistically defined Mean value and vairance for each energy bin E m and isotope n

Model defects of 16 O H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, E‘ MeV E MeV Example 16 O total cross section experimental data for 12 C, 14 N, 19 F, 20 Ne, 23 Na, 24 Mg E MeV 0 30% 20% relative variance in %

Correlations - comparison H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, correlations of total cross section uncertainties 16 O cut: E+E‘=const complete prior parameter uncertainties E MeV E MeV more details in Final report of EFDA-TW6-TTMN-001B-D7a

Importance of uncertainty information H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, cross section covariances Safety margins – commissioning Reduce the number of experimental tests  significant economic impact

Implementation of Bayesian statistics H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, Bayes Theorem (1763): p(x|  M) = p(  |xM) p(x|M) / p(  |M) posterior = likelihood x prior / evidence x... model parameter ... data M... other information

Bayesian update procedure H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, Exp-01 Exp-02 Exp-m Exp-03 x 0 M 0 x 2 M 2 x 3 M 3 x m M m x 1 M 1 prior experiment posterior

Problem of update procedure H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, statistical error systematic error Bayes theorem Bayesian update prior

Origin of the difference H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, Standard Bayesian update procedure – no correlations between experiments The ‚experiments‘ covariance matrix V contains all experiments and all correlations Systematic errors are treated like a statistical uncertainty i.e.

Evaluation Tool GENEUS H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, TALYS PRIOR SCALE SC2COVBAYES EXFOR Janis-Tables graphicsENDF-file EXPCOV tables semi-automatic for single isotope and restricted reaction channels still manual not available one-step procedure

Perspectives H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 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, …

Topics in nuclear reactions H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 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, (  ), (p,  ) 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)

Summary and outlook H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 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

Working Group H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, J. Gundacker (Master) J. Haidvogl (PhD) D. Neudecker (PhD) Th. Srdinko (Master) V. Wildpaner Former students K. Nikolics M.T. Pigni (PhD) I. Raskinyte (PostDoc) EU Research Projects: EURATOM P&T: n_TOF,IP_EUROTRANS EURATOM Fusion: EFDA-Projrects, F4E-Grants EU I3-Project: EURONS Strong collaboration with the nuclear data centers NEA, IAEA

H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, THANK YOU FOR YOUR ATTENTION

 -nucleus optical potentials H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, (semi)microscopic approach for low energies (relevant to astrophysics) Optical Potential: Direct part: evaluated within RGM in order to account correctly for the antisymmetrisation direct term coupling term

Imaginary  -nucleus optical potentials H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, Imaginary Part: Intermediate states in RPA Green function at intermediate state It can be considered as a nuclear structure approach to  -nucleus optical potential, which should work satisfactory at low energies calculations for  - 16 O and  - 40 Ca and  Pb are in progress

Reactions of weakly bound nuclei H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, deuteron breaks up easily (E B =2,2 MeV) breakup leads to additional flux loss Neglecting breakup leads to non-standard parameters in fitted potentials nonelastic due to n-collision Breakup of the deuteron nonelastic due to p-collision Elastic d-A channel Incoming channel outgoing channel Incoming d-A channel Keaton, Armstrong (1973) Ansatz of a complete wave function of the d-A system deuteron wave functionp-n scattering wave function (continuum)

Breakup contribution for d- 6 Li H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13,