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Basics ofNuclear Data Evaluation andPerspectives

H. Leeb

Atominstitut,TU Wien, Austria

NuPECCMeeting,Vienna, March 13, 2009

Research atthe Atominstitut

atomicphysics, quantumoptics

(J. Schmiedmayer)

radiationphysics

(Ch. Streli)

low-temperaturephysics,

Super conductivity

(H. Weber)

appliedquantumphysics

(N.N.)

neutronandquantumphysics

(H. Abele)

nuclearandparticlephysics

(H. Leeb)

NuPECC Meeting,Vienna, March 13, 2009

NuclearandParticlePhysics

NuclearPhysicsandNuclearAstrophysics(H. Leeb)

scatteringandreactiontheory, nucleardataevaluation

HadronPhysicsand Fundamental Interactions (M.Faber,

H. Markum)

exoticatoms, latticegaugetheory

Experimental ParticlePhysics(Ch. Fabjan)

detectordevelopments, dataanalysistechniques

directlylinkedtothe Institute of High EnergyPhysics

ofthe Austrian AcademyofSciences

NuPECC Meeting,Vienna, March 13, 2009

NuclearPhysicsandNuclearAstrophysics

Theoreticaldescriptionofscatteringandreactionprocesses

andtheinterpretationof observables withregardtointeractions

andunderlyingstructures in basicandappliedphysics

Scatteringandreactiontheory

- inverse scatteringtechniques
- opticalpotentialsandspecificreactions
- phaseproblem in quantummechanics

Neutron-inducedreactions

- nucleardataevaluation
- nuclearastrophysics

involvement in theexperiments

atn_TOF@CERNand in Geel

NuPECC Meeting,Vienna, March 13, 2009

Experiments: n-inducedcrosssections

n_TOF@CERN

(n,g) crosssectionsfortransmutationandastrophysics

GELINA (JRC)

(n,2n) crosssections via prompt g-decay

Experiments performedwithincollaboration:

TU Wien and University of Vienna

G. Badurek, E. Jericha, H. Leeb, A. Pavlik, A. Wallner

NuPECC Meeting,Vienna, March 13, 2009

(n,xn) crosssections

E. Jericha (TU Wien)

A. Pavlik (Univ. Wien)

GELINA (JRC)

209Bi(n,2n) crosssections

Measurement of prompt

g-raysofthe residual

nucleus (even A)

4+

2 +

0 +

Mihailescu et al. ND2007

NuPECC Meeting,Vienna, March 13, 2009

(n,g) crosssections

n_TOF@CERN

(n,g) (n,f)

4p total absorption

calorimeter (TAC)

astrophysicalrelevance

s-process

mainresponsibilityof TU Wien: proper uncertaintyanalysis

NuPECC Meeting,Vienna, March 13, 2009

Experimental uncertaintiesatn_TOF

232Th(n,g)

151Sm(n,g)

E‘ MeV

E MeV

151Sm(n,g)

232Th(n,g)

E‘ MeV

E‘ MeV

normalizedcovariancematrixofthen_TOFexperiment

NuPECC Meeting,Vienna, March 13, 2009

Nucleardataevaluation

Start of Modern Data Evaluation:

recommendedvaluesof fundamental physicsconstants (c, h, af, ... )

Dunnington (1939); Du Mond and Cohen (1953)

Present Status:

AtpresentEvaluatedNuclear Data Files represent a consistentsetof

crosssectionsandassociatedquantitiesfor all relevant reaction

processes. Most datafilesare limited totheenergyregionbelow

20MeV.

Thereexistseveralnucleardatalibrarieswithevaluatedcrosssection

data, but onlyfewfilescontainuncertaintyinformation thereliability

Is still an open question.

JEFF3.1, ENDF/B-VII, JENDL, CENDL, …

NuPECC Meeting,Vienna, March 13, 2009

Conceptofevaluation

Nucleardataevaluationisessentially a procedurefollowing

therulesofBayesianstatisticswithin a subjectiveinterpretationtheprobabilityreflectsourexpectation no experimental verification

Evaluation isgiven in termsof

- expectationvaluesof observables- covariancematricesof observables (crosssections)

BAYESIAN STATISTICS

NuPECC Meeting,Vienna, March 13, 2009

Bayestheorem

Bayes Theorem (1763):

p(x|s M) = p(s |xM) p(x|M) / p(s |M)

posterior = likelihood x prior / evidence

x ... model parameter s ... data M ... other information

from experiment

Choice of proper prior ?

Expectationvalue:

Covariancematrixelement:

NuPECC Meeting,Vienna, March 13, 2009

Evaluations donebyVonach et al.

First evaluations in thefieldofnucleardatewhichincludeuncertaintieswereperformedbyVonach et al. (Univ. Vienna) about 1990

Theyconsiderednucleiwheremany experimental datahavebeenavailable

choiceofprior not essential

S. Tagesen, H. Vonach, A. Wallner, ND2007

NuPECC Meeting,Vienna, March 13, 2009

Developments in nucleardataevaluation

- CurrentDemands:
- Inclusionofuncertaintyinformation covariancematrices
- Extension ofenergyrangeto ~150MeV

- Challenges:
- Evaluation processandcovariancematrices – scarcityof experimental datafor E > 20 MeV quest ofuncertaintyofnuclearmodels
- Improvementofmodels: nuclearreactions, fission, …

NuPECC Meeting,Vienna, March 13, 2009

Bayestheorem

Bayes Theorem (1763):

p(x|s M) = p(s |xM) p(x|M) / p(s |M)

posterior = likelihood x prior / evidence

x ... model parameter s ... data M ... other information

from experiment

Choice of proper prior ?

Expectationvalue:

Covariancematrixelement:

NuPECC Meeting,Vienna, March 13, 2009

Choice of proper prior

GOAL

quantitative estimateofthereliabilityofnuclear model

basedevaluations

- Define an almostunbiasedprior
- Accountfor all aprioriknowledge
- Minimal useof experimental data

NuPECC Meeting,Vienna, March 13, 2009

Sourcesofuncertainties

The contributions to the covariance matrix of the model are

M(mod) = M(par) + M(num) + M(def)

parameter uncertainties

Model defects

non-statistical error

numerical

implementation

error

EFFDOC-1047

NuPECC Meeting,Vienna, March 13, 2009

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)

Information entropy:

The amount of uncertainty is maximal if the entropy is maximal.

Assumption: Besides the marginalisation we know an expection value

NuPECC Meeting,Vienna, March 13, 2009

Theoryforpriordetermination

Principleof maximal informationentropy

Information Entropy

Constraints

Determination of

Lagrange par. l

prior

partition

function

variance

Invariant measure to account for continuous parameters:

for scaling parameters:

NuPECC Meeting,Vienna, March 13, 2009

Admissiblerangeofparameters

dependence on av of

admissible range in rv

admissible range in av

z defines lower boundary

NuPECC Meeting,Vienna, March 13, 2009

Parameter distributionfor208Pb

potential parameters

rv(fm)

v1(MeV)

NuPECC Meeting,Vienna, March 13, 2009

Parameter uncertainties-correlations

stotal

selastic

phenomenologicalopticalpotentials

microscopicopticalpotentials

NuPECC Meeting,Vienna, March 13, 2009

Model defects - scaling

Global scaling factor for

each reaction channel c

Mean value and vairance for

each energy bin Em and

isotope n

This coarse approximation provides a covariance matrix

PROBLEM: not statistically defined

NuPECC Meeting,Vienna, March 13, 2009

Model defectsof16O

Example16O

total crosssection

experimental datafor

12C,14N,19F,20Ne,23Na,24Mg

E MeV

E‘ MeV

0

30%

relative variance in %

E MeV

20%

60 10 60

NuPECC Meeting,Vienna, March 13, 2009

Correlations - comparison

correlationsof total crosssection 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

parameter uncertainties

E MeV

60 10 60

NuPECC Meeting,Vienna, March 13, 2009

Importanceofuncertaintyinformation

cross section covariances

Safetymargins – commissioning

Reducethenumberof experimental tests

significanteconomicimpact

NuPECC Meeting,Vienna, March 13, 2009

ImplementationofBayesianstatistics

Bayes Theorem (1763):

p(x|s M) = p(s |xM) p(x|M) / p(s |M)

posterior = likelihood x prior/ evidence

x ... model parameters ... dataM ... otherinformation

NuPECC Meeting,Vienna, March 13, 2009

Bayesian update procedure

prior

x0 M0

Exp-01

x1 M1

Exp-02

x2 M2

Exp-03

x3 M3

Exp-m

xm Mm

experiment

posterior

NuPECC Meeting,Vienna, March 13, 2009

Problem of update procedure

prior

systematic

error

statistical error

Bayes theorem

Bayesian update

NuPECC Meeting,Vienna, March 13, 2009

Origin ofthedifference

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.

NuPECC Meeting,Vienna, March 13, 2009

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

EXPCOV

NuPECC Meeting,Vienna, March 13, 2009

Perspectives

- CurrentDemands:
- Inclusionofuncertaintyinformation covariancematrices
- Extension ofenergyrangeto ~150MeV

- Challenges:
- Evaluation processandcovariancematrices – scarcityof experimental datafor E > 20 MeV quest ofuncertaintyofnuclearmodels
- Improvementofmodels: nuclearreactions, fission, …

NuPECC Meeting,Vienna, March 13, 2009

Topics in nuclearreactions

- Future research will focus on challenges in reactiontheory:
- Reactionsinvolvingchargedcompositenucleiembrittlement due to gas production in structurematerials p-processreactions in nuclearastrophysics, (a,g), (p,g)
- Reactionsinvolvingweaklyboundnucleibreak-upcontributions in deuteroninvolvingreactionsreactionprocesseswithexoticweaklyboundnuclei
- (Microscopic) modellingofnuclearfissionmicroscopicunderstandingoffissionprocessmodellingoffissioncrosssectionsexperimentally not accessible isotopes (MA)

NuPECC Meeting,Vienna, March 13, 2009

Summaryandoutlook

- Summary:
- Neutron-inducedcrosssectionmeasured
- Well definedevaluationprocedurebased on modellingdeveloped
- General evaluationtool GENEUS isunderconstruction

Outlook:

Focus iscurrentlychangingtotopics on reactiontheory - compositeparticlescatteringtheory - reactionsinvolvingweaklyboundnuclei

NuPECC Meeting,Vienna, March 13, 2009

Working Group

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 collaborationwiththe

nucleardatacenters NEA, IAEA

NuPECC Meeting,Vienna, March 13, 2009

NuPECC Meeting,Vienna, March 13, 2009

a-nucleusopticalpotentials

(semi)microscopic approach for low energies (relevant to astrophysics)

Optical Potential:

direct term

coupling term

Direct part:

evaluated within RGM in order to account

correctly for the antisymmetrisation

NuPECC Meeting,Vienna, March 13, 2009

Imaginarya-nucleusopticalpotentials

Imaginary Part:

Intermediate states in RPA

Green functionat intermediate state

Itcanbeconsideredas a nuclearstructureapproachtoa-nucleus

optical potential, whichshouldworksatisfactoryatlowenergies

calculationsfora-16O anda-40Ca anda-208Pb are in progress

NuPECC Meeting,Vienna, March 13, 2009

Reactionsofweaklyboundnuclei

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

deuteron wave function

p-n scattering wave function (continuum)

NuPECC Meeting,Vienna, March 13, 2009

Breakupcontributionford-6Li

NuPECC Meeting,Vienna, March 13, 2009

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