H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 1 Basics of Nuclear Data Evaluation and Perspectives H. Leeb Atominstitut,TU

H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 1

Basics of Nuclear Data Evaluation and Perspectives

H. LeebAtominstitut,TU Wien, Austria

NuPECC Meeting,Vienna, March 13, 2009

Research at the Atominstitut

H. Leeb Atominstitut, TU Wien, Austria 2

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


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 techniquesdirectly linked to the Institute of High Energy Physicsof the Austrian Academy of Sciences


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

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 experimentsat n_TOF@CERN and in Geel


Experiments: n-induced cross sections


GELINA (JRC)

(n,2n) cross sections via prompt g-decay

Experiments performed within collaboration: TU Wien and University of ViennaG. Badurek, E. Jericha, H. Leeb, A. Pavlik, A. Wallner

n_TOF@CERN

(n,g) cross sections for transmutation and astrophysics


(n,xn) cross sections


GELINA (JRC)

209Bi(n,2n) cross sectionsMeasurement of promptg-rays of the residual nucleus (even A)

4+

2 +

0 +

Mihailescu et al. ND2007

E. Jericha (TU Wien)A. Pavlik (Univ. Wien)


(n,g) cross sections


n_TOF@CERN

astrophysical relevance s-process

main responsibility of TU Wien: proper uncertainty analysis

(n,g) (n,f)

4p total absorption calorimeter (TAC)


Experimental uncertainties at n_TOF


normalized covariance matrix of the n_TOF experiment

232Th(n,g)

151Sm(n,g)151Sm(n,g)232Th(n,g) E‘ MeV

E‘ MeV E‘ MeV

E MeV


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 sectiondata, but only few files contain uncertainty information the reliabilityIs still an open question.

JEFF3.1, ENDF/B-VII, JENDL, CENDL, …


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

- covariance matrices of observables (cross sections)

BAYESIAN STATISTICS

modelnuclear of parameters sections, cross x

energy channel, ... ,


Bayes theorem


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 ?

Expectation value:

Covariance matrix element:

MxMxpxd n , | modelapriori

MxMxMxpxd n ,, | modelmodelapriori


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


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, …


Bayes theorem





from experiment Choice of proper prior ?

Expectation value:

Covariance matrix element:

MxMxpxd n , | modelapriori

MxMxMxpxd n ,, | modelmodelapriori


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


Sources of uncertainties


The contributions to the covariance matrix of the model are

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

parameter uncertainties numerical

implementation error

Model defectsnon-statistical error

= ( ) d d p

EFFDOC-1047


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.1

( ) lnN

i ii

H p K p p

Assumption: Besides the marginalisation we know an expection value

0 1 0 11 1 1

( , , ) ln 1 0N N N

i i i i ii i i

H p K p p K p K p f f

0 1 0 11 1 1

( , , ) ln 1 0N N N

i i i i ii i i

H p K p p K p K p f f


Theory for prior determination


1

0 11

( ) log( )

( ) 1 ( ) 0

N

K

N k kk

p ada da p a

m a

da da p a G p a

Information Entropy

Constraints

1( ) m(x)exp ( )

p x f xZ

( ) exp ( ) Z dx m x f x

ln

f Z

2

22

ln

f Z

prior

partitionfunction

Determination of Lagrange par. l

variance

Invariant measure to account for continuous parameters:

for scaling parameters: 1( ) m x x

Principle of maximal information entropy


Admissible range of parameters


dependence on av of admissible range in rv

admissible range in av

z defines lower boundary

2 2 2 2

arg arg

3 2

2

3

ch e OM ch e forcer r r r

d r r V rr

d r V r


Parameter distribution for 208Pb


potential parameters

rv (fm)

v1 (MeV)


Parameter uncertainties-correlations


phenomenological optical potentials microscopic optical potentials

stotal

selastic


Model defects - scaling


Global scaling factor for each reaction channel c

isotopesm

cnccEE

cn

cn

cn

cn

cth

cthdef

cc

mcn

m

ncm

cn

mcn

rcth

rcex

rallrall

rcth

rcth

mcn

EN

rcth

rcex

rallrall

rcth

rcth

rallr

cth

rallr

cex

mcn

ENNENNENEEEE

ENwN

ENE

E

E

EEN

E

E

E

E

E

EEN

r

2',',

''''

,

2

weight

2

scale local

weight

)')(( ''

reactiongiven and isotopeeach for scalemean

This coarse approximation provides a covariance matrix

PROBLEM: not statistically defined

Mean value and vairance for each energy bin Em and isotope n


Model defects of 16O


E‘ MeV

E

MeV

Example 16Ototal cross section

experimental data for12C,14N,19F,20Ne,23Na,24Mg

60 10 60

E MeV

030%

20%

rela

tive

varia

nce

in %


Correlations - comparison


correlations of total cross section uncertainties16Ocut: E+E‘=const

complete prior

parameter uncertainties

0.6

0.6

0.0

60 10 60

E MeV

60 10 60

E MeV

more details inFinal report ofEFDA-TW6-TTMN-001B-D7a


Importance of uncertainty information


2

Example: uncertainty of is requReli iredable

e

f

f

ef

fk

k

K K

cross section covariances

Safety margins – commissioningReduce the number of experimental tests

significant economic impact


Implementation of Bayesian statistics






Bayesian update procedure


Exp-01

Exp-02

Exp-m

Exp-03

x0 M0

x2 M2

x3 M3

xm Mm

x1 M1

prior

experimentposterior


Problem of update procedure


erdcxbxaxf 121 2

statistical errorsystematic

error

Bayes theorem Bayesian update

prior


Origin of the difference


Standard Bayesian update procedure – no correlationsbetween experiments

The ‚experiments‘ covariance matrix V contains all experimentsand all correlations

Systematic errors are treated like a statistical uncertainty i.e. m

1


Evaluation Tool GENEUS


TALYSPRIOR

SCALE

SC2COV BAYES

EXFORJanis-Tables

graphicsENDF-file

EXPCOV

tables

semi-automatic for singleisotope and restricted reaction channels

still manual

not available

one-step procedure


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, …


Topics in nuclear reactions


Future research will focus on challenges in reaction theory:

• Reactions involving charged composite nucleiembrittlement due to gas production in structure materials p-process reactions in nuclear astrophysics, ( ,a g), (p,g)

• Reactions involving weakly bound nucleibreak-up contributions in deuteron involving reactionsreaction processes with exotic weakly bound nuclei

• (Microscopic) modelling of nuclear fission microscopic understanding of fission processmodelling of fission cross sections experimentally not accessibleisotopes (MA)


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


Working Group


J. Gundacker (Master)J. Haidvogl (PhD)D. Neudecker (PhD)Th. Srdinko (Master)V. Wildpaner

Former studentsK. NikolicsM.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

NuPECC Meeting,Vienna, March 13, 2009H. Leeb Atominstitut, TU Wien, Austria 35

THANK YOU FOR YOUR ATTENTION


a-nucleus optical potentials


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

Optical Potential: , , ,optV r r U r r iW r r

, T TU r r r PVPA r Direct part:

evaluated within RGM in order to account correctly for the antisymmetrisation

,

1

opt T T

T T

V r r r PVPA r

r PVQ QVPA rE QHQ i

direct term

coupling term


Imaginary a-nucleus optical potentials


0 02 , Im , ;M M

TT N M M NM

T TW r r r V r g r r E r V r

Imaginary Part:

Intermediate states in RPA

Green function at intermediate state

It can be considered as a nuclear structure approach to a-nucleusoptical potential, which should work satisfactory at low energies

calculations for a-16O and a-40Ca and a-208Pb are in progress


Reactions of weakly bound nuclei


deuteron breaks up easily (EB=2,2 MeV)

breakup leads to additional flux loss

Neglecting breakup leads to non-standard parameters in fitted potentials

nonelastic due to n-collisionBreakup of the deuteron

nonelastic due to p-collision

Elastic d-A channel

Incoming channel outgoing channel

Incomingd-A channel

Keaton, Armstrong (1973)Ansatz of a complete wave function of the d-A system

300, r r d

��

deuteron wave function p-n scattering wave function (continuum)


Breakup contribution for d-6Li


Documents

H. Leeb Atominstitut, TU Wien, Austria NuPECC Meeting,Vienna, March 13, 2009 1 Basics of Nuclear Data Evaluation and Perspectives H. Leeb Atominstitut,TU