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Advances in the analysis of resonance cross section data. S. Kopecky, P. Schillebeeckx M. Moxon, I. Sirakov. Topics. URR (I. Sirakov visitor 2 x 3 months) ENDF-6 compatible evaluation procedures optical model calculation Self shielding and multiple scattering corrections - PowerPoint PPT Presentation
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IRMM - Institute for Reference Materials and MeasurementsGeel - Belgium
http://irmm.jrc.ec.europa.eu/
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 1
Advances in the analysis of resonance cross section data
S. Kopecky, P. SchillebeeckxM. Moxon, I. Sirakov
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 2
Topics
URR (I. Sirakov visitor 2 x 3 months)•ENDF-6 compatible evaluation procedures optical model calculation•Self shielding and multiple scattering corrections
RRR ( M. Moxon visitor 1.5 month)•Varying Weighting function according to resonance strength •Corrections for powder samples•Investigation of Multiple Scattering Corrections (collaboration with KIT)
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 3
URR Cross Section
'secc
'' ' ' '2
se c ccc cc cc c cc
c
T Tg F
k T
',c cT T
Shape elastic scattering cross sectionENDF-6 compatibility lead to approximations
'ccF Fluctuation factor
Transmission coefficient
Transmission factors and shape elastic cross section calculated by optical model
Sl(E) Strength functionR’(E) scattering radius
0( ) ( )J J JTT E T f E
Adjustment of Sl(0) and Tto experimental cross section data
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 4
URR Th-232
0 50 100 150
10
15
20
25
CRP-evaluation Iwasaki et al. Poenitz et al. Uttley et al. Vertebnyj et al. Kobyashi et al. Gregoriev et al.
(n,
tot)
/ b
Neutron Energy / keV0 50 100 150
60
70
80
90
100
(n,)
E1
/2 /
(b
eV
1/2)
CRP-evaluation Borella et al. Aerts et al. Kobayshi et al. Macklin et al.
Neutron Energy / keV
Sirakov et al., Annals of Nuclear Energy 35 (2008) 128
(n,tot) & (n,) + covariance matrix in ENDF/B-VII
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 5
URR – ENDF-6
Programs & Procedures to determine average parameters and their covariance matrix
Derive cross sections linked to optical model calculations
NJOY has been modified to accommodate energy dependent R’
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 6
URR - MCNP-Flux Geometry
0 20 40 60 80 100
1.00
1.05
1.10
Yc /
(n
Beam diameter 60 mm 78 mm 84 mm
Neutron energy / keV
Au-disc1mm thickdiameter mm
0 20 40 60 80 100
1.00
1.05
1.10
Yc /
(n
(E)dE = 1/E dE(E)dE = C dE
Neutron energy / keV
Au-disc1mm thick80 mm diameter
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 7
Comparison SESH-MCNP
Tested influence of experimental conditions on shelf-shielding and multiple scattering
SESH & MCNP similar results
Procedures established to derive corrections and fitting of average parameters
0 20 40 60 80 100
1.00
1.05
1.10
SESH SESH
Yc /
(n
MCNP 1.0 mm MCNP 0.5 mm
Neutron energy / keV
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 8
Weighting Function
WF1 WF2
Reliable WF’s can be obtained by Monte Carlo simulations provided that the geometry input reflects the experimental conditions, i.e. accounts for –ray transport in sample(started with Perey et al. at ORELA)
Weak resonance : WF1
Strong resonance : WF2(Affects also the observed shape)
Procedure :(1) Apply WF1 on experimental data
(2) Correction factor on calculated yield
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 9
Verification of WF and normalization by experiment1.15 keV of 56Fe + n
1140 1150 11600.0
0.1
0.2
0.3
0.4 Exp. REFIT
Yie
ldNeutron energy / eV
1140 1150 11600.0
0.1
0.2
0.3
0.4 natFe
natFenatW
natWnatFe
natFenatZr
natZrnatFe
Yie
ld
Neutron energy (eV)
n = 61.7 0.9 meV
= 574 meV
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 10
Normalization capture data: 1.15 keV of 56Fe + n
Sample Length / m Normalization
REFIT MCNP resolution
REFIT MCNP resolution
SAMMY Analytical resolution
natFe 58.5660 0.0004 28.16 0.25 27.80 0.25 natFe / natW 58.5670 0.0004 27.88 0.25 28.50 0.25 natFe / natZr 58.5671 0.0004 27.68 0.25 28.10 0.25 natW / natFe 58.5678 0.0004 27.41 0.25 28.30 0.25 natZr / natFe 58.5674 0.0004 27.19 0.25 27.70 0.25
Average 58.5671 27.67 28.08
Stdev 0.0007 0.38 0.34
Stdev (%) 0.0011 1.4 1.2
natW natFe
WF calculated with -rays distributed in Fe
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 11
Correction Factor
10-2 10-1 100 101 1020.85
0.90
0.95
1.00
C6D6- detectors at 125o
Kc
Au- thickness 0.11 mm 0.53 mm 1.10 mm
ntot
2
1tc WF
WF)n(K
nnnwccwcnnexp dE)YYK()E,T(RNY
DICE-box for gamma spectrumFold calculated spectrum with WF
Derive Correction Factor
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 12
Influence of Kc on normalization
1 10 10010-3
10-2
10-1
100
Yexp YM, REFIT (+ att.) YM, REFIT (no att.)
Yie
ld
Neutron Energy / eV
4 5 60.0
0.5
1.0
Yie
ld
Neutron Energy / eV
0 1 2 30.00
0.05
0.10
0.15
0.20
0.25
0.30
Yie
ld
Neutron Energy / eV
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 13
Powder sample
Probability that a neutron “sees” n particle,given by Poisson-statistics
N=1 N=3.5
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 14
•Poisson distribution
•Spheres
•Radius lognormal
•Black line MC
•Red line lognormal fit
0 2 40
700
1400
2100
2800
3500
arb.
units
thickness (mean=1)
N=1=0.69
0 2 40
5000
10000
N=10=0.36
arb.
uni
tsthickness
0 2 40
1000
2000
3000
N=50=0.16
arb.
uni
ts
thickness
0 2 40
2000
4000
N=100=0.11
Yar
b. u
nits
thickness
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 15
Influence of Power Sample on Transmission
1.0 1.1
0.4
0.5
0.6
0.7
0.8
0.9
1
Tra
nsm
issi
on
energy [eV]
242Pu - sample thickness 2.10-4 at/barn
of thickness distribution is varied between 0 to 0.6in steps of 0.1
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 16
Experminentally observed effects
2.5 2.6 2.7 2.8
-4
0
4
Re
sid
ua
ls
0.4
0.6
0.8
1.0
Literature = 25 meV
n = 2.00 meV
FIT = 36.5 meV
n = 1.46 meV
Tra
nsm
issi
on
2.5 2.6 2.7 2.8
-4
0
4
Re
sid
ua
ls
Neutron Energy / eV
0.4
0.6
0.8
1.0
Holes = 0.33
LN = 0.47
= 25 meV
n = 1.90 meV
Tra
nsm
issi
on
2.5 2.6 2.7 2.8
-4
0
4
Re
sid
ua
ls
0.4
0.6
0.8
1.0
Literature = 25 meV
n = 2.00 meV
FIT = 36.5 meV
n = 1.46 meV
Tra
nsm
issi
on
2.5 2.6 2.7 2.8
-4
0
4
Res
idua
ls
Neutron Energy / eV
0.4
0.6
0.8
1.0
Holes = 0.33
LN = 0.47
= 25 meV
n = 1.90 meV
Tra
nsm
issi
on
REFIT: accounting for the powder grain size (EFNUDAT project : IRMM - Moxon)
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 17
Sample dimensions are determined by a 2D-optical scanning system including a height measurement
Area (also for irregular shapes) Circularity of a disc Height profile
totnexp eT
n : areal density
sample dimensions
Sample characterization: discs and foils
...e1Ytot
nexp
tot
area
weight
m
Nn
X
A
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 18
Sample characterization : homogeneity186W (metal disc)
0 20 40 603.6
3.8
4.0
H
eigh
t /
mm
Position / mm
3.7 3.8 3.9 4.00.00
0.05
0.10
0.15
0.20
Pro
babi
lity
Height / mm
Probability distribution P(h)dhinput to REFIT
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 19
Multiple Scattering
n nn’
n n’
n’’
j
jm YY
2
22
n
A2
nA
nn
'n sin
m
mcos
mm
mEE
YoY1 Y2
)e1(Y totn
toto
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 20
Multiple Scattering
67 68 69 70 71 7210-3
10-2
10-1
100
Y = Yi
Y0
Y1
Y2
Exp REFIT (full Doppler) SAMMY
Yie
ld
Energy / eV68.8 69.0 69.2 69.4 69.6
0.3
0.4
0.5
0.6
Yie
ldEnergy / eV
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 21
Mn-55 Multiple Scattering
Mn sputtering target77 mm diameter
3 mm thick0 2000 4000 6000
10-6
10-5
10-4
10-3
10-2
10-1
100
Exp. Y = Y
i
Y0
Y1
Y2
Yie
ld
Neutron energy / eV
200 300 400 500 60010-3
10-2
10-1
100
Neutron energy / eV
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 22
Conclusions
Procedures and Programs to derive average parameters and their covariance matrix in the URR
Parameters are compatible with ENDF-6 procedures
NJOY has been modified to be ENDF-6 compatible
programs and procedures have been established to calculate self-shielding and multiple scattering in the URR
CERN 29.8.-2.9. 2010 – EFNUDAT workshop 23
Conclusions
Modification to RSA REFITCorrections of WF depending on the resonance strengthCorrection due to powder samples
Investigation of Multiple Scattering in RSAStarted project to incorporate MC approach (EFNUDAT, Sept. 2010)
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