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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
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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 px | M   model x, M 
  d nx px | M   model x, M  model x, M 
NuPECC Meeting,Vienna, March 13, 2009
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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 px | M   model x, M 
  d nx px | M   model x, M  model x, M 
NuPECC Meeting,Vienna, March 13, 2009
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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
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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
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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
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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
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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