Advances in the analysis of resonance cross section data

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


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)


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


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


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’


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


Au-disc1mm thick80 mm diameter


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



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


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


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


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


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


Powder sample

Probability that a neutron “sees” n particle,given by Poisson-statistics

N=1 N=3.5


•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


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


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)


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


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


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


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


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


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


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)

Documents

Advances in the analysis of resonance cross section data