7Li elastic scattering cross section measurement using ... · 7Li elastic scattering cross section...

7Li elastic scattering cross section measurement using slowing-down spectrometer

G. Kessedjian, O. Méplan, A. Billebaud, A.Bidaud, R.Brissot, S. Chabod, V.Ghetta, D.Heuer,X.Doligez, E.Liatard,, E.Merle-Lucotte, A.Nuttin, H.E.Thyebault

LPSC, Université Joseph Fourier Grenoble 1, CNRS/IN2P3, Institut Polytechnique de Grenoble, Grenoble, France, 38000

[email protected]

EFNUDAT Paris mai 2010

motivations

• Molten Salt Reactor is one of the six concepts of GEN-IV reactor and it is based on liquid mixed fuel-coolant :

Ex : the Thorium Molten Salt Reactor use (7LiF+T hF4+UF4) as fuel and coolant

• To obtain the characteristics of breeder reactor, only 7Li have to be consider in the core to avoid 6Li(n,t ) reaction which decreases the number of neutron useful for the regeneration of fissile nuclei.

• The only coolant properties of LiF salt are interesting in reactor studies; then neutron reactions on these nuclei are needed for reactor physics

7Li total and elastic scattering cross section

GENEPI LPSC 500HzD (d,n)3He

En ~ 3.1 MeV

dBlanket of

Cgraphite

7LiF

Resonant target+

YAP Scintillator +

Photo-multiplicator

Experimental set-up (1): Graphite LiF slowing down spectrometer

• Measurement of slowing down time :

- Start : γ flash of GENEPI

- Stop : 197Au(n,γ) at (Er, tr)

• Time-Energy correlation :

Er = E0 . To

(Tr + To)2

Integral cross sectionmeasurement

<σ ( 7Li, 19F, natC )>on

[Er; 3.1] MeV

197Au(n,γ)

E0

Er

σ (n

,γ) (b

)

En (MeV)

7Li(n,el)

C (n,el)

• The slowing down time Tr is function <σ7Li(n,el)>; <σ19F(n,el)>; <σnatC(n,el)>, ρC ; ρLiF

• To determine <σ7Li(n,el)> , we use Monte Carlo simulations to extract the contribution of Li in the

mean slowing down time → We need a reference measurement on graphite with the same set-up

Neutron slowing down time measurement in the Graphite- LiF spectrometer

109Ag (Er=4.9eV)

107Ag (Er=16.5eV)197Au (Er=4.9eV)

natMo (Er=1.4 eV)

113,115In (Er=12eV)

Time (25ns/ch) Time (25ns/ch)

Time (25ns/ch) Time (25ns/ch)

Yiel

d (s

-1)

Yiel

d (s

-1)


En ~ 3.1 MeV

d

Cgraphite

Resonant target+

YAP Scintillator +

Photo-multiplicator

Experimental set-up (2): Graphite spectrometer

• reference slowing down time measurement : Graphite

197Au(n,γ)

E0

Er

σ (n

,γ) (b

)

En (MeV)

7Li(n,el)

C (n,el)

Integral cross sectionMeasurement of natC(n,el)

Tr= f(natC(n,el) ; ρC )


En ~ 3.1 MeV

d

Cgraphite

CF2

Resonant target+

YAP Scintillator +

Photo-multiplicator

Experimental set-up (3): Graphite-Teflon spectrometer

• slowing down time measurement of

Teflon (CF2)n

197Au(n,γ)

E0

Er

σ (n

,γ) (b

)

En (MeV)

7Li(n,el)

C (n,el)

Integral cross sectionMeasurement of 19F(n,el)

Tr= f( natC(n,el) ; ρC ; 19F(n,el) ; mTeflon ; VTeflon)

Time (25ns/ch)

Yiel

d (s

-1)

Time (25ns/ch)

Yiel

d (s

-1)

Data analysis : slowing down time measurement

Veto on γ flash

Data analysis : γ flash

σ1 = 0.46µs

σ2−3 =0.26 µs

γ flash gives : - the reference time- the time resolution of neutron pulse

Data analysis : 1) Integral cross section measurement of natC (n,el)

We measure the resonant time : Tr= f( σ (natC(n,el) ) ; ρC )

And we search σ (natC(n,el) ) = g(Tr ; ρC ) and the uncertainty on this measurement

For the low probability events, one method useful is the Bayesian approach

P(data | H) . P(H) = P(H | data) . P(data)

P(Hi | data) =

If Edata C EH then P(data) = Σi P(data | Hi) . P(Hi) = ∫EHP(data | H) . P(H) dH

Then, the probability of “data given Hi“ is determined by the likelihood function :

P(data | Hi) ∝ £ (Hi ; data) ∝ exp( - ) if the uncertainties follow a Gaussian distribution

χ² = Σ and (Tr)cal = MCNP Calculation (Hi)

P(data | Hi) . P(Hi)

P(data)

Hi Hi

χ²2

Edata

H1 H2 H3 … … … … …. Hn

EH

Statistical uncertainties σ(Ncal )

prior

Posterior

( Ncal (t) – Nexp (t) )²

σ²(Ncal) + σ² (Nexp)


Each point correspond to a MCNP calculation

which needs 24h on 20 CPU

P(∆C | data) ∝ £ (data ; ∆C) . Prior(∆C)


Comparison between experimental measurement and MCNP calculations

Prior ∆(JEFF-3.1) = constant→ integral measurement with slowing down Graphite spectrometer of σ(natC(n,el)) without « a priori » : Prior = constant→ experimental resolution of spectrometer : systematic error sc=1.7%

m1 = -0.13%σm1 = 1.66%

m2 = -0.65%σm2 = 1.82%

m3 = 2.28%σm3 = 2.25%

************************<mean> = 0.24%σ<mean> = 1.08%************************

1) Integral cross section measurement of natC (n,el)

Experimental dispersion of ±2%


Prior ∆JEFF-3.1 = G(m=0; σ = 2%)→ integral measurement with slowing down spectrometer of σ(natC(n,el)) using the knowledge of existing data

σc=,Vσ²(c(n,el) + σ² (ρ) = 1%


Weight (En) = importance of cross section at neutron energy Enin the integral measurement

Integral measurement of neutron induced elastic scattering cross section in the thermal region with a slowing down neutron spectrum


Prior ∆JEFF-3.1 sigma = constant

2) Integral cross section measurement of 19F (n,el)

y [ prior = cte ] = -4,712x + 16,36

y [prior=5%] = -2,0944x + 4,56

y [prior=5% ; σ(C(n,el))] = -0,672x + 2,67

-15

-10

-5

0

5

10

15

20

25

30

0 0,5 1 1,5 2 2,5 3 3,5 4∆ J

EFF-

3.1-

19F(

n,el

)

∆ JEFF-3.1-12C(n,el) (%)

correlation 12C(n,el) - 19F(n,el)

σ(12C(n,el)) = 1.7%

systematic dispersion on graphite explain the deviation of 19F(n,el) measurement

Correlation between natC(n,el) and 19F(n,el) (for only one measurement)

P(19F(n,el)| data; C(n,el)) Nuisance parameter

y [ prior = cte ] = -4,712x + 16,36

y [prior=5%] = -2,0944x + 4,56

y [prior=5% ; σ(C(n,el))] = -0,672x + 2,67

-15

-10

-5

0

5

10

15

20

25

30

0 0,5 1 1,5 2 2,5 3 3,5 4∆ J

EFF-

3.1-

19F(

n,el

)

∆ JEFF-3.1-12C(n,el) (%)


σ(12C(n,el)) = 1.7%

systematic dispersion on graphite explain the deviation of 19F(n,el) measurement

Correlation between natC(n,el) and 19F(n,el) (for only one measurement)

( (Ncal (t) – Nexp (t) )²χ² = Σt

σ²(Ncal) + σ² (Nexp) + ( )2. σ²(<Tr>)∂Ncal(t)

∂ twith = S<Tr>C . σc (%)

σ(<Tr>)<Tr>

Systematic errorStatistical errors systematic error on mean time

P(19F(n,el)| data; C(n,el)) Nuisance parameter

Error <Tr> = 0.136 µsS<Tr>c=0.61σc = 1.7 %

P(19F(n,el)| data; C(n,el))


Preliminary result

ρ natC(n,el) 19F(n,el) 7Li(n,el)natC(n,el) 1 -0.25 ?19F(n,el) -0.25 1 ?7Li(n,el) ? ? 1

∂ 19F(n,el) σF∂ natC(n,el) σC

= ρC;F


Mean value of 12C(n,el) elastic scattering Plateau ∆JEFF-3.1 = 0.1 ( 1) %

19F(n,el) elastic scattering Plateau ∆JEFF-3.1 = 3.1 ( 2.7) % / σJeff-3.1 = ~ 4%

Preliminary results

Correlation matrix of mean measurements on C and F

P(7Li(n,el)| data; C(n,el) ; 19F(n,el); ; ρ C ; mLiF; VLiF) = ?Nuisance parameterS

ρ 7Li; F = ? Because many cracks on LiF cristal

Perspective 3) absolute Integral cross section measurement of 7Li (n,el)

y = 1,58x - 1,7

-20

-15

-10

-5

0

5

10

15

20

25

-6 -4 -2 0 2 4 6 8 10 12

7Li

Nuisance parameterS

preliminary result

Perspective 3) absolute Integral cross section measurement of 7Li (n,el)

ρ 7Li; F = ? Because many cracks on LiF cristal

Relative 7Li(n,el) in reference to 19F(n,el)

P(7Li(n,el)| data; C(n,el) ; 19F(n,el); ; ρ C ; mLiF; VLiF) = ?

7Li total and elastic scattering cross sectionPerspective 3) absolute Integral cross section measurement of 7Li (n,el)

preliminary result : relative measurement

7Li(n,el) integral elastic scattering cross section - LPSC

Backup

x y [dy [dx]] 4.9 1.039 0.078 1000 1.039 0.078


Experimental dispersion of ±2%

x y [dy [dx]] 4.9 1.039 0.078 1000 1.039 0.078

44 gpes

We have to introduce the resolution of graphite spectrometer to analyze the Fluor cross section

y = -4,712x + 16,36R² = 0,9917

y-prior 5% = -2,0944x + 4,56R2 = 0,999

-10

-5

0

5

10

15

20

25

30

0 0,5 1 1,5 2 2,5 3 3,5 4

∆ J

EFF-

3.1-

19F(

n,el

)

∆ JEFF-3.1-12C(n,el) (%)


1 x σ(12C(n,el)) 2 x σ(12C(n,el)) 3 x σ(12C(n,el))

Interprétation géométrique : cas le plus simple

dak /dak’ = tan ϕ = ρk k’ σak/ σak’

ak

ak’σak

σak’

ρk k’ σak

ϕ

bk

bk’

Changementde base

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