covariance data of experimental observables in the ...€¦ · wonder 2009, cea cadarache, 29...

WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx 1

Joint Research Centre (JRC)IRMM - Institute for Reference Materials and MeasurementsGeel - Belgiumhttp://irmm.jrc.ec.europa.eu/http://www.jrc.ec.europa.eu/

Covariance data of experimental

observables in the resonance region WONDER 2009

29 September – 2 October, 2009CEA, Cadarache

P. Schillebeeckx1), A. Borella1), S. Kopecky1), C. Lampoudis1), C. Massimi1,2), M. Moxon, N. Otsuka3), I. Sirakov1,4)

1) EC- JRC – IRMM, Geel Belgium2) INFN, Bologna, Italy3) IAEA – NDS, Vienna, Austria4) INRNE – Sofia, Bulgaria

2WONDER 2009, CEA Cadarache, 29 September – 2 October 2009, P. Schillebeeckx

Problem

( σ, Vσ ) determined by :• Reaction model : σ = F(θ)

– R-Matrix; HF+WF; Optical Model

• Calculation Method for Vσ

– Simple model (transformation of variables): P(σ) dσ = Q(θ)dθ

– MC-simulations

– Vσ ≈ Gθ Vθ GθT with Gθ = δF/δθ

• Input parameters : (θ, Vθ)– (θ, Vθ) determined by adjustment to experiment (χ2- minimization)

Reaction Model(σ, Vσ) (θ, Vθ)

θ θ θθ ≈ μ + θ − μF( ) F( ) G ( )


Reliable model parameters by adjustment to experiment

Requirements:

• Experimental observables and relations to model parameters are

defined

• All uncertainty components are identified, quantified and

documented (uncorrelated & correlated)

• Verify the impact of correlations due to calibration (normalization)

uncertainties on the minimization of χ2


Experimental observables

Capture (fission) Transmission

Self-indication

tneT σ−≈ ...)e1(Yt

n t +σ

σ−≈ γσ−

γ

...))e1((e,Yt

nnSI tt1 +

σ

σ−≈γ γσ−σ−

n1 n


σ(n,γ) measurements 103Rh(n,γ)

104 105 106 107100

102

104

Bi AuNa

C'w

B'w

Res

pons

e / (

1/ns

)Time Of Flight / ns

104 105 106 10710-4

10-2

100

C'ϕ

B'ϕ

Res

pons

e / (

1/ns

)

Time Of Flight / ns

Flux measurement Capture measurement

''

'w

'w

rexp

BCBCNY

ϕϕ

ϕ

−

−ε

σ=


AGS: Data reduction + uncertainty propagation

C’ dead time corrected counts

B’ background contribution

N normalization factor''

'w

'w

rexp

BCBCNY

ϕϕ

ϕ

−

−ε

σ= '

out'out

'in

'in

expBCBCNT

−

−=

Reaction yield + Self-indication Transmission

Histogram operations + Covariance information (AGS)

Models

Yexp + covarianceYSI,exp + covarianceTexp + covariance

input

WONDER 2006


SZ : correlated partdim. (n x k)

DZ : uncorrelated partn values

Analysis of Geel Spectra (AGS)

• Transform count rate spectra into observables (transmission, yields + SI )

• Full uncertainty propagation starting from counting statistics

• Output: complete covariance matrix

• Special format for covariance matrix– Reduce space for data storage (EXFOR)– Document the sources of uncertainties due to

each step in the data reduction processX Z Dz Sz

Special format for full covariance information

Observable Z (dimension n) with k sources of correlated uncertainties

TZZZZ SSDC +=


10-1 100 10110-3

10-2

10-1

100

101

Cap

ture

Yie

ld

Energy [eV]

n + 197Au 0.5 mm ENDF/B-VII

197Au: σ(nth , γ) = (99.0 ± 1.0) b <--> (98.7 ± 0.1) b

4x100 5x100 6x100

10-1

100

Cap

ture

Yie

ld

Energy [eV]


2x10-2 3x10-2 4x10-21.5x10-1

2.0x10-1

2.5x10-1

3.0x10-1

3.5x10-1

4.0x10-1

Cap

ture

Yie

ld

Energy [eV]


Absolute determination of σ(n,γ)


Correction for n- and γ-transportimplemented in REFIT

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

ldNeutron Energy / eV

0 1 2 30.00

0.05

0.10

0.15

0.20

0.25

0.30

Yie

ld

Neutron Energy / eV

WF depending on σtot, WONDER 2006

Borella et al., NIMA 577 (2007) 626


Resonance shape analysis

FM is a model describing the transmission observable TM, with model parameters:

RP resonance parameters σtot(RP)

Experimental parameters θ:R resolution TOF-spectrometer

TD Debye temperature (Doppler effect)

n number of atoms per unit area ⇒ Resonance parameters adjustable parameters

)TT(V)TT()RP( Mexp1,T

TMexp

2 −−=χ −θ10000 20000 30000 40000 50000

-4

4

Res

idua

ls

Neutron Energy / eV

0.2

0.4

0.6

0.8

1.0

Tran

smis

sion

10000 20000 30000 40000 50000

-404

Sputtering target n = 1.92 10-2

Res

iuda

ls

0.2

0.4

0.6

0.8

1.0

Tran

msm

issi

on

Mn powder n = 9.94 10-3

Time-of-flight11

,TT

RP )DVD(V −θ

−θθ=

,...)R,n,T,RP(FT DMM =


nΓ<<Γγ nΓ>>Γγ

Γ

ΓΓ∝ γ

γn

JngA ngn ΓγΓgn• Capture(weak resonances)

ngn Γ γΓΓngn

thin,tA ngn Γ• Transmission ngn Γ

For (Γ >> ΔD and ΔR) ⇒ Γ = Γn + Γγ directly from observed shape

• Self-indication(thick – thin)

Resonance parameters: (ER, Γn, Γγ , J(π), l )

n1,SI gn

AΓ

Γ∝γ

γΓΓ∝ nthick,t gnA

gn11 n1 gn Γ

Γγ

)1I2(21J2g

++

=

l from transmission

Fröhner, ND1966, p. 55


Spin of 4.9 eV resonance for 197Au + n

4 5 6

0

Res

.

0.0

0.5

1.0

J = 2

Tran

smis

sion

4 5 6

0Res

.Neutron Energy / eV

0.0

0.5

1.0J = 2

Tran

smis

sion

4 5 6

0

Res

.

Neutron Energy / eV

0.0

0.5

1.0

J = 1

Tran

smis

sion

4 5 6

0 Res

.

0.0

0.5

1.0

J = 1

Tran

smis

sion Only gΓn

Γn can be wrong by 40%

Uncertainty on Γn ?

83g =

85g =

Simultaneous RSA using REFIT


Spin of 4.9 eV resonance for 197Au + n

J = 1 J = 2

Simultaneous RSA using REFIT


0.0

0.2

0.4

0.6

0.8

1.0

Texp TM,REFIT

Tran

smis

sion

Dependence of VRP on measurement type4.9 eV resonance for 197Au+n

4.0 4.5 5.0 5.5 6.00.0

0.2

0.4

0.6

0.8

1.0

Texp TM,REFIT

Tran

smis

sion

Neutron Energy / eV

10 μm

50 μm

Γn = ( 15.06 ± 0.08) meV

Γγ = (121.7 ± 1.3 ) meV

ρ(Γn, Γγ) = 0.55

⇒

⇒

Γn = ( 14.66 ± 0.30) meV

Γγ = (124.8 ± 3.7 ) meV

ρ(Γn, Γγ) = - 0.96

VT,exp: only uncorrelated uncertainties due to counting statistics

ΔD ∼ 80 meV

L = 50 m ΔR ∼ 5 meV


4.0 4.5 5.0 5.510-3

10-2

10-1

100

Yexp YM,REFIT

Yie

ld

Neutron Energy / eV

10-3

10-2

10-1

100

Yexp YM,REFIT

Yie

ld

L = 30 m5 µm

L = 12 m5 µm

Γn = ( 15.31 ± 0.12) meV

Γγ = (118.0 ± 1.4 ) meV

ρ(Γn, Γγ) = - 0.50

⇒

⇒

Γn = ( 15.26 ± 0.15) meV

Γγ = (118.9 ± 1.2 ) meV

ρ(Γn, Γγ) = - 0.63

VY,exp: only uncorrelated uncertainties due to counting statistics

ΔD ∼ 80 meV

ΔR ∼ 8 meV

ΔR ∼ 20 meV



Id-number Measurement Distance Angle

(flight path – moderator)

Target thickness

T1 Transmission 50 m 9o 10 μm

T2 Transmission 50 m 9o 50 μm

C1 Capture 30 m 0o 5 μm

C2 Capture 12 m 18o 5 μm

Measurements Γn / meV Γγ / meV ρ( Γn, Γγ )

VZ,exp: only uncorrelated uncertainties due to counting statistics

T1 15.06 ± 0.08 121.7 ± 1.3 0.55

T2 14.66 ± 0.30 124.8 ± 3.7 - 0.96

C1 15.31 ± 0.12 118.0 ± 1.4 - 0.50

C2 15.26 ± 0.15 118.9 ± 1.2 - 0.63

T1 + C1 15.14 ± 0.07 120.0 ± 1.0 0.06

T1 + C2 15.10 ± 0.07 120.2 ± 0.9 - 0.29

T1 + T2 + C1 + C2 15.14 ± 0.06 119.8 ± 0.7 - 0.47



Resonance parameters for natCd

Kopecky et al., NIMB 267 (2009) 2345 - 2350

Experiment ⇒ Data reduction with AGS ⇒ Resonance Shape Analysis

Thin – Thick transmission(1.3610-4 2.2410-4 at/b)

l = 0 J =1 χ2 = 0.98l = 0 J =0 χ2 = 1.30

0.1 0.2 0.3 0.4 0.5

-3

0

3

Res

idua

ls

Neutron Energy / eV

0.3

0.6

0.9

exp. data REFIT

Tran

smis

sion

Parameter p / meV ρ(pi,pj)

ΔD ∼ 20 meVΔR ∼ 0.2 meV ( L = 50 m)

ER 178.7 ± 0.1 1.00 0.53 0.28

Γγ 113.5 ± 0.2 1.00 0.26

Γn 0.640 ± 0.004 1.00


113Cd : impact of uncertainty components(only transmission)

Data reduction: dead time and background

Data reduction: uncorrelated uncertainties (counting statistics)


ER 178.7 ± 0.068 1.00 0.43 0.79

Γγ 113.5 ± 0.15 1.00 0.43

Γn 0.640 ± 0.0007 1.00


ER 178.7 ± 0.069 1.00 0.43 0.64

Γγ 113.5 ± 0.16 1.00 0.31

Γn 0.640 ± 0.0011 1.00


Data reduction: counting statistics, dead time, background

Parameter δpini p δp ρ(pi,pj)

ER Γγ Γn L n TD N

ER / meV - 178.7 ± 0.074 1.00 0.53 0.28 0.13 0.00 0.00 -0.34

Γγ / meV - 113.5 ± 0.22 1.00 0.26 0.20 0.02 -0.04 -0.70

Γn / meV - 0.640 ± 0.0036 1.00 0.11 -0.91 -0.00 -0.28

L / m 0.006 26.4439 ± 0.006 1.00 -0.00 0.01 -0.09

n / (at/b) 0.5 % ± 0.5 % 1.00 0.00 -0.00

TD / meV 0.5 % 25.46 ± 0.5 % 1.00 0.00

N (norm) 0.5 % 1.000 ± 0.0013 1.00


ER 178.7 ± 0.069 1.00 0.43 0.64

Γγ 113.5 ± 0.16 1.00 0.31

Γn 0.640 ± 0.0011 1.00

113Cd : impact of uncertainty components(only transmission)


GELINA (transmission + capture) + ORELA (transmission) RETROSPECTIVE Borella et al. PRC 76 (2007) 014605 and Horen et al. PRC 20 (1979) 478 Rochman and Koning

NIM A589 (2008) 85

ER gΓn / eV gΓγ / eV gΓnΓγ/(Γn+ Γγ) / eV ρ(Γn, Γγ) ρ(Γn, Γγ)

3.36 0.570 ± 0.004 0.146 ± 0.001 0.116 ± 0.001 - 0.15 - 0.16

66.00 82.210 ± 0.414 1.398 ± 0.018 1.375 ± 0.017 0.03 - 0.00

92.61 32.0 1.503 ± 0.017 1.436 ± 0.016

92.61 32.0 ± 16.0 ? 1.503 ± 0.017 1.436 ± 0.016 - 0.77

92.61 32.0 ± 4.0 1.503 ± 0.017 1.436 ± 0.016 - 0.10

Vθ from uncertainties in literature(retrospective ?)

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

Γ∂∂Γ∂

∂

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

σσ

σσ

⎥⎥⎦

⎤

⎢⎢⎣

⎡

Γ∂∂

Γ∂∂

=σ

γΓΓΓ

ΓΓΓ

γγγ

γ

K

K

)

)KK n2

,(

,(2

nK

n

nn

γ

γ

Γ+Γ

ΓΓ=

n

ngK

206Pb + n


1 10 100 1000100

101

102

103

104

5.19 eV18.83132.002850102710

C'ϕ

B'ϕ

Black Resonances

TOF

- spe

ctru

m /

(1/n

s)

Time-Of-Flight / μs

1 10 100100

101

102

103

B'γ

B'γ1

C'γ

B'γ

B'γ0

B'γ1

C'γ

B'γ =aoB'

γ0 + a1B'γ1

Time-Of-Flight / μs

B'γ0ϕϕ

γγϕγ

−

−

ε

σ=

BC

BCNY

'

'

rexp,

Borella et al., NSE 152 (2006) 1-14Borella et al., NIMA 577 (2007) 626

B’ϕ = b0 + b1 TOFb2

20 22 24 10000 10000010-4

10-3

10-2

10-1

100

Normalization URR

232Th(n,γ)t = 0.5 mm

Y

exp

Neutron Energy / eV

Internal normalization+ WF depending on σtot

Uncertainty 1.5%

232Th(n,γ) in URR


Borella et al. NSE 152 (2006) 1-14

Emin Emax σγ δσγ δσγ,u ρ

keV keV mb (%) (%)

4 6 1107.9 0.49 0.17 1.00 0.60 0.57 0.58 0.55 0.53 0.62 0.58 0.56 0.61 0.58 0.54 0.51

6 8 934.2 0.44 0.19 1.00 0.55 0.56 0.53 0.51 0.60 0.57 0.55 0.60 0.56 0.53 0.49

8 10 845.1 0.43 0.21 1.00 0.54 0.51 0.49 0.58 0.55 0.52 0.57 0.54 0.51 0.47

10 15 749.1 0.38 0.15 1.00 0.52 0.50 0.59 0.56 0.54 0.59 0.55 0.52 0.49

15 20 638.7 0.39 0.18 1.00 0.48 0.57 0.54 0.52 0.56 0.53 0.50 0.47

20 30 571.3 0.36 0.14 1.00 0.55 0.52 0.50 0.54 0.51 0.48 0.45

30 40 490.3 0.32 0.18 1.00 0.61 0.59 0.64 0.61 0.57 0.54

40 50 429.6 0.31 0.19 1.00 0.56 0.61 0.58 0.54 0.51

50 60 382.9 0.33 0.22 1.00 0.59 0.56 0.52 0.49

60 80 311.4 0.30 0.18 1.00 0.61 0.57 0.54

80 100 242.5 0.33 0.22 1.00 0.54 0.51

100 120 217.8 0.33 0.23 1.00 0.48

120 140 201.6 0.33 0.24 1.00

232Th(n,γ) in URR Uncertainty propagation AGS

Correlated: uncertainty dead time, background (capture)


Emin Emax σγ δσγ δσγ,u ρ

keV keV mb (%) (%)

4 6 1107.9 1.70 0.17 1.00 0.85 0.85 0.86 0.86 0.87 0.88 0.88 0.88 0.89 0.89 0.88 0.88

6 8 934.2 1.64 0.19 1.00 0.88 0.89 0.89 0.89 0.91 0.91 0.91 0.92 0.92 0.91 0.91

8 10 845.1 1.63 0.21 1.00 0.89 0.89 0.90 0.91 0.91 0.91 0.92 0.92 0.91 0.91

10 15 749.1 1.61 0.15 1.00 0.90 0.91 0.93 0.92 0.93 0.93 0.93 0.93 0.92

15 20 638.7 1.61 0.18 1.00 0.91 0.92 0.92 0.93 0.93 0.93 0.93 0.92

20 30 571.3 1.59 0.14 1.00 0.93 0.93 0.93 0.94 0.93 0.93 0.93

30 40 490.3 1.56 0.18 1.00 0.95 0.95 0.96 0.95 0.95 0.95

40 50 429.6 1.56 0.19 1.00 0.95 0.96 0.95 0.95 0.95

50 60 382.9 1.55 0.22 1.00 0.96 0.96 0.95 0.95

60 80 311.4 1.55 0.18 1.00 0.96 0.96 0.96

80 100 242.5 1.56 0.22 1.00 0.96 0.95

100 120 217.8 1.55 0.23 1.00 0.95

120 140 201.6 1.55 0.24 1.00

Borella et al. NSE 152 (2006) 1-14

232Th(n,γ) in URRUncertainty propagation AGS

Correlated: uncertainty dead time, background,+ normalization (1.5%)


232Th in URR Parameterization in URR by HF + WF

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.

σ(n,

tot)

/ b

Neutron Energy / keV0 50 100 150

60

70

80

90

100

σ(n,

γ) E

1/2 /

(b

eV1/

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

Code developed by I. Sirakov(IRMM - EFNUDAT project)


Sensitivity to average parameters(included in output)

0 50 1000

20

40

60

80

100


(<σ n,

γ > E

1/2 )

/ (b

arn

eV1/

2 )

σn,γ

s p d

0 50 10010-2

10-1

100

( δ<

σ n,γ>

/ <σ n,

γ >) /

(δθ

/ θ)

S0

S1

S2

Tγ,0

1/2+

Tγ,0

1/2-


Capture cross section dominated by l = 1and mainly determined by Tγ

-1/2 + impact of S1


232Th(n,γ) : Covariance matrix in URR

<σγ>Uncorrelated 1.0 %Correlated 1.5 %

<σγ> + < σtot>1.0 % 0.5 %1.5 % 1.0 %

+ S0 with uS0 = 0.5%

θ (uθ /θ) x 100

ρ x100 (uθ /θ) x 100

ρ x100

S0 16.3 100 - 81 - 18 32 23 0.5 100 - 16 38 - 13 28

T0+1/2 5.9 100 - 17 19 - 54 3.0 100 - 23 74 - 43

S1 4.7 100 - 65 79 2.0 100 - 21 52

T1-1/2 3.7 100 - 74 2.7 100 - 80

S2 20.0 100 11.2 100

En / keV (uσγ /σγ)

x 100 ρ x100 (uσγ /σγ)

x 100 ρ x100

5 1.54 100 96 96 90 1.49 100 99 96 93

10 1.53 100 97 92 1.42 100 98 91

50 1.51 100 93 1.43 100 94

100 1.63 100 1.48 100


Reliable model parameters from experiment

Requirements:

Well documented experimental observables in EXFOR

Including:

- experimental details ( RF, TD, n, …)

- all uncertainty components (correlated and uncorrelated)

⇒ Proposal IAEA / IRMM based on AGS


Uncertainty in literature (Phys. Rev. C)

Results only based on capture cross section measurements


[1] NSE 160 (2008) 200 - 206[2] NIM A 179 (1981), 13[3] NIM A 228 (1985), 217[4] NIM A 531 (2004), 392

Main Reference 1

Template for resonance cross section datain EXFOR

Facility GELINA 2,3 Neutron production 4

Primary neutron production target Uranium Time resolution primary beam (ns) 4 ns Moderator material H2O Surface Dimensions (mm x mm or diameter in mm)

2 containers 100 x 100 mm

Thickness (mm) 40 mm Experimental details

Measurement type Fission Flight path length (m) (moderator – target (detector): face to face distance)

(8.218 +/- 0.006) m

Angle (with respect to normal of moderator)

18 deg

Beam dimensions (mm x mm or diameter in mm)

Diameter 55 mm

Sample Type (metal, powder) Electrodeposition Chemical composition UO2 Atomic abundance of main element 99.9732 at% 236U Weight per unit area (g/cm2) (209.9 +/- 1.3) Uμg/cm2 Geometry

Surface dimensions (mm x mm or diameter in mm)

Diameter (50.0 +/- 0.1) mm

Thickness of main element (at/b) 5.354 10-6 at/b 236U Backing 20 μm aluminium

Containment description No container Temperature 25 meV

Proposal IRMM & NDS - IAEA


Template for resonance cross section data in EXFOR

AGSOutput

Detector Type Frisch gridded ionisation chamber Material CH4 (100%) Gas pressure Gas flow at 1 atm Geometry 2π

Flux normalization Reaction 10B(n,α) Cross section from ENDF/B-VI.8 Atomic abundance of main element 93.0 at% 10B Target thickness (8.05 +/- 0.10) 10B μg/cm2 Surface dimensions Diameter (50.0 +/- 0.1) mm

(236U- 10B : back to back) Normalization uncertainty (TOF-independent)

1.5 %

Data

Time-of-flight of first channel 3000 ns Time-of-fligth bin width / ns Column 1 Energy (relativistic formula, L = 8.238 m) eV Column 2 Yield in barn/at Column 3

Uncertainties (at 1 sigma level) Total (normalization not included) Column 4 Uncorrelated contribution (variance) Column 5 Other sources creating correlated uncertainty components

Dead time 10B [col 6] Background 10B [col.7, 8,9] Dead time 236U [col. 10] Background 236U [col.11,12,13]


Time-of-flight <-----> Energy

n

'n t

Lv =

L’m

R(L’m)

Detector

L0

L’ = L0 + Lm

En

e- beam

Analytical expressions in REFIT include storage term of Ikeda & Carpenter

10-2 100 102 1040

2

4

6

8

<Lm>

/ cm

Ikeda and Carpenter (analytical) MCNP

Neutron Energy / eV


Acknowledgementsupport through

• EFNUDAT– 197Au (C. Massimi)– Code for URR (HF + WF) (I. Sirakov)– REFIT : include new options (M. Moxon)

• NUDAME– Cadmium

• NDS – IAEA • JEFF project

covariance data of experimental observables in the ...€¦ · wonder 2009, cea cadarache, 29...

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