Li elastic scattering cross section measurement using slowing-down spectrometer

Transcription

1 7 Li 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, EFNUDAT Paris mai 2010

2 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 ( 7 LiF+T hf 4 +UF 4 ) as fuel and coolant To obtain the characteristics of breeder reactor, only 7 Li have to be consider in the core to avoid 6 Li(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

3 7 Li total and elastic scattering cross section

4 Experimental set-up (1): Graphite LiF slowing down spectrometer d GENEPI LPSC 500Hz D (d,n) 3 He En ~ 3.1 MeV Blanket of 7 LiF C graphite Resonant target + YAP Scintillator + Photo-multiplicator Measurement of slowing down time : 197 Au(n,γ) - Start : γ flash of GENEPI - Stop : 197 Au(n,γ) at (E r, t r ) Time-Energy correlation : σ (n,γ) (b) C (n,el) 7Li(n,el) E r = E 0. T o (T r + To) 2 Integral cross section measurement <σ ( 7 Li, 19 F, nat C )> on [E r ; 3.1] MeV E r E n (MeV) E 0

5 Neutron slowing down time measurement in the Graphite- LiF spectrometer Yield (s -1 ) 109 Ag (E r =4.9eV) 197 Au (E r =4.9eV) 107 Ag (E r =16.5eV) Time (25ns/ch) Time (25ns/ch) nat Mo (E r =1.4 ev) Yield (s -1 ) 113,115 In (E r =12eV) Time (25ns/ch) Time (25ns/ch) The slowing down time T r is function <σ7 Li(n,el)>; <σ19 F(n,el)>; <σnat C(n,el)>, ρ C ; ρ LiF To determine <σ7 Li(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

6 Experimental set-up (2): Graphite spectrometer d Resonant target + YAP Scintillator + Photo-multiplicator GENEPI LPSC 500Hz D (d,n) 3 He En ~ 3.1 MeV C graphite reference slowing down time measurement : Graphite Integral cross section Measurement of nat C(n,el) σ (n,γ) (b) C (n,el) 7Li(n,el) 197 Au(n,γ) T r = f( nat C(n,el) ; ρ C ) E n (MeV) E r E 0

7 Experimental set-up (3): Graphite-Teflon spectrometer d GENEPI LPSC 500Hz D (d,n) 3 He En ~ 3.1 MeV CF 2 C graphite Resonant target + YAP Scintillator + Photo-multiplicator slowing down time measurement of 197 Au(n,γ) Teflon (CF 2 ) n Integral cross section Measurement of 19 F(n,el) σ (n,γ) (b) C (n,el) 7Li(n,el) T r = f( nat C(n,el) ; ρ C ; 19 F(n,el) ; m Teflon ; V Teflon ) E n (MeV) E r E 0

8 Data analysis : slowing down time measurement Yield (s -1 ) Veto on γ flash Yield (s -1 ) Time (25ns/ch) Time (25ns/ch)

9 Data analysis : γ flash σ 2 3 =0.26 µs σ 1 = 0.46µs γ flash gives : - the reference time - the time resolution of neutron pulse

10 Data analysis : 1) Integral cross section measurement of nat C (n,el) We measure the resonant time : T r = f( σ ( nat C(n,el) ) ; ρ C ) And we search σ ( nat C(n,el) ) = g(t r ; ρ C ) and the uncertainty on this measurement For the low probability events, one method useful is the Bayesian approach E data P(data H). P(H) = P(H data). P(data) prior P(data H i ). P(H i ) P(H i data) = P(data) Posterior H i H i H 1 H 2 H 3. H n E H If E data C E H then P(data) = Σ i P(data H i ). P(H i ) = EH P(data H). P(H) dh Then, the probability of data given H i is determined by the likelihood function : χ² P(data H i ) (H i ; data) exp( - ) if the uncertainties follow a Gaussian distribution 2 ( N cal (t) N exp (t) ) ² χ² = Σ and (Tr) cal = MCNP Calculation (H i ) σ²(n cal ) + σ² (N exp ) Statistical uncertainties σ(n cal )

11 Data analysis : 1) Integral cross section measurement of nat C (n,el) Each point correspond to a MCNP calculation which needs 24h on 20 CPU P( C data) (data ; C). Prior( C)

12 Data analysis : 1) Integral cross section measurement of nat C (n,el) Comparison between experimental measurement and MCNP calculations

13 1) Integral cross section measurement of nat C (n,el) Prior (JEFF-3.1) = constant integral measurement with slowing down Graphite spectrometer of σ( nat C(n,el)) without «a priori» : Prior = constant experimental resolution of spectrometer : systematic error s c =1.7% m 1 = -0.13% σ m1 = 1.66% m2 = -0.65% σ m2 = 1.82% m 3 = 2.28% σ m3 = 2.25% ************************ <mean> = 0.24% σ <mean> = 1.08% ************************

14 1) Integral cross section measurement of nat C (n,el) Experimental dispersion of ±2%

15 1) Integral cross section measurement of nat C (n,el) Prior JEFF-3.1 = G(m=0; σ = 2%) integral measurement with slowing down spectrometer of σ( nat C(n,el)) using the knowledge of existing data σ c =,Vσ²(c(n,el) + σ² (ρ) = 1%

16 1) Integral cross section measurement of nat C (n,el) Integral measurement of neutron induced elastic scattering cross section in the thermal region with a slowing down neutron spectrum Weight (En) = importance of cross section at neutron energy E n in the integral measurement

17 2) Integral cross section measurement of 19 F (n,el) Prior JEFF-3.1 sigma = constant

18 Correlation between nat C(n,el) and 19 F(n,el) (for only one measurement) 30 correlation 12C(n,el) - 19F(n,el) JEFF F(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 0 0,5 1 1,5 2 2,5 3 3,5 4 σ( 12 C(n,el)) = 1.7% JEFF C(n,el) (%) systematic dispersion on graphite explain the deviation of 19 F(n,el) measurement P( 19 F(n,el) data; C(n,el)) Nuisance parameter

19 Correlation between nat C(n,el) and 19 F(n,el) (for only one measurement) 30 correlation 12C(n,el) - 19F(n,el) JEFF F(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 0 0,5 1 1,5 2 2,5 3 3,5 4 σ( 12 C(n,el)) = 1.7% JEFF C(n,el) (%) systematic dispersion on graphite explain the deviation of 19 F(n,el) measurement P( 19 F(n,el) data; C(n,el)) Nuisance parameter ( (N cal (t) N exp (t) ) ² χ² = Σ t N σ²(n cal) + σ² (N exp) + ( cal (t)) 2. σ²(<tr>) t σ(<t r >) with <T = S <Tr>C. σ c (%) r > Statistical errors systematic error on mean time Systematic error

20 2) Integral cross section measurement of 19 F (n,el) Error <T r > = µs S <Tr>c =0.61 σ c = 1.7 % P( 19 F(n,el) data; C(n,el)) Preliminary result

21 2) Integral cross section measurement of 19 F (n,el) Mean value of 12 C(n,el) elastic scattering Plateau JEFF-3.1 = 0.1 ( 1) % 19 F(n,el) elastic scattering Plateau JEFF-3.1 = 3.1 ( 2.7) % / σjeff-3.1 = ~ 4% 19 F(n,el) nat C(n,el) = ρ C;F σ F σ C Correlation matrix of mean measurements on C and F ρ nat C(n,el) 19 F(n,el) 7 Li(n,el) nat C(n,el) ? 19 F(n,el) ? 7 Li(n,el)?? 1 Preliminary results

22 Perspective 3) absolute Integral cross section measurement of 7 Li (n,el) P( 7 Li(n,el) data; C(n,el) ; 19 F(n,el); ; ρ C ; m LiF ; V LiF ) =? Nuisance parameters ρ 7Li; F =? Because many cracks on LiF cristal

23 Perspective 3) absolute Integral cross section measurement of 7 Li (n,el) P( 7 Li(n,el) data; C(n,el) ; 19 F(n,el); ; ρ C ; m LiF ; V LiF ) =? Nuisance parameters ρ 7Li; F =? Because many cracks on LiF cristal 7Li Relative 7 Li(n,el) in reference to 19 F(n,el) y = 1,58x - 1, preliminary result

24 Perspective 3) absolute 7 Li total Integral and elastic cross scattering section measurement cross section of 7 Li (n,el) 7 Li(n,el) integral elastic scattering cross section - LPSC preliminary result : relative measurement

25 Backup

26 1) Integral cross section measurement of nat C (n,el) Experimental dispersion of ±2% x y [dy [dx]]

27 x y [dy [dx]]

28

29 44 gpes

30 44 gpes

31 44 gpes

32 correlation 12C(n,el) - 19F(n,el) 30 JEFF F(n,el) y-prior 5% = -2,0944x + 4,56 R 2 = 0,999 y = -4,712x + 16,36 R² = 0, ,5 1 1,5 2 2,5 3 3,5 4 1 x σ( 12 C(n,el)) 2 x σ( 12 C(n,el)) 3 x σ( 12 C(n,el)) JEFF C(n,el) (%) We have to introduce the resolution of graphite spectrometer to analyze the Fluor cross section

33 Interprétation géométrique : cas le plus simple a k σ ak ϕ ρ k k σ ak a k Changement de base b k σ ak da k /da k = tan ϕ = ρ k k σ ak / σ ak b k