Description and usage of experimental data for evaluation in the resolved resonance region SG - 36

Transcription

1 Description and usage of experimental data for evaluation in the resolved resonance region SG - 36

2 Objective Produce accurate cross section data together with reliable covariance information in the resonance region Reduce bias effects Produce reliable and realistic covariance data

3 SG36-contributions Problems with PPP Uncertainty components of experimental data Transmission Capture Evaluation models Case studies Reporting data Reporting experimental data Reporting response functions of TOF-spectrometers Reporting of RP in a new AGS-type format

4 Transmission PPP T exp B N C exp V Zexp ( C exp, B, N) 2 T 1 Z,exp ( ) (Texp Fm (x, )) V (Texp Fm (x, )) Exp. F m (x,) N N A x o 2 10% (5.2) B B ( ) ( ) 10% B P x / unit Solution : include N in adjustment procedure Zhao & Perey ORNL/TM D Agostini, NIM A346 (1994) 306 Fröhner, NSE 126 (1997) 1-18 A x o 2 only counting statistics 100 (0.61) ( ) ( )

5 Uncertainty components of experimental observables Transmission T m e n X tot Reaction cross section Y m r tot (1 e n x tot )... C F Y A r r r r r T exp N C in out C B B in out Y exp N r C C r B B r N N 0.5% B B out out 5% B B in in 5 10% N N 2% B B 5% B B r r 5 10% Ideal conditions + experimental verification of uncertainties (IRMM, INFN) Capture: Borella et al., NIMA 577 (2007) 626 Massimi et al., in preparation

6 (n,) E 1/2 ) / (barn ev 1/2 ) (n,) E 1/2 ) / (barn ev 1/2 ) GELINA : (n,) methodology 1.5% Borella et al., NIMA 577 (2007) 626 Total energy principle: C 6 D 6 with weighting functions Weighting functions which account for the threshold Verify experimentally the effect of WF and threshold Correction for -ray attenuation in the sample Use fixed background filters Perform background measurements with additional filters Perform additional background measurements with Pb Determine neutron flux with a double ionization chamber 2 thin layers of 10 B Normalization at a saturated resonance (account for gamma-ray attenuation) Neutron Energy / ev 0.5 mm (12 m) 1.0 mm (12 m) IAEA Evaluation HF + WF GELINA 12 m (1.0 mm) GELINA 30 m (1.0 mm) IAEA eval. HF + WF Neutron Energy / ev

7 Evaluation methods LSQ adjustment or Maximum Likelihood (Max. Entropy) 2 T 1 ( ) (zexp z m( )) V zexp (zexp z m( )) zm f( ) T 1 1 T 1 (G V z G ) (G V exp exp z z ) exp T 1 1 z V (G V G ) exp (linear model) : theoretical model parameters (, ) : exp erimental parameters Methods to account for all uncertainty components and avoid PPP Include all model parameters in adjustment procedure Fröhner, NSE 126 (1997) 1 18 Monte Carlo De Saint Jean et al., NSE 161 (2009) Marginalization Habert et al., NSE 166 (2010) Differ in the way the uncertainty of experimental parameters are taken into account At IRMM all tools available

8 Yield LSQ + GLUP (e.g. PUP) : 4.9 ev 197 Au(n,) Exp. (0.010 mm) REFIT Sample thickness : 0.01 mm 0.6 Peak uncertainty 0.1 % 1 % 10 % 0.4 (counting statistics) 0.2 Fit -all Fit -all Fit -all Neutron Energy / ev E = 4.9 ev = 122 mev n = 15 mev E n N (2%) Relative uncertainty in % Problem related to LSQ + GLUP

9 Yield Comparison 3 methods : 4.9 ev 197 Au(n,) Exp. (0.010 mm) REFIT Neutron Energy / ev E = 4.9 ev = 122 mev n = 15 mev Peak uncertainty (counting statistics) : 1% Sample thickness mm 0.01 mm Fit -all MC Marg. Fit -all MC Marg. E n N (2%) Relative uncertainty in %

10 Similar problem observed at CEA Transmission, PbI 2 sample : Least-squares fit of R with SAMMY and CONRAD. N T =1.163 ± (0.5%) SAMMY+GLUP CONRAC+GLUP CONRAD+Marginalization Direct perturbation R = 6.690±0.001 fm R = 6.697±0.001 fm R = 6.68 ± 0.16 fm R 0.14 fm

11 Case studies : experimental data base created Resonance parameters T exp = 0.1, 0.5 and 0.9 Y exp = 10-4, 0.3 and 0.9 counting statistics uncertainty 0.1, 1.0, 10% in peak (or baseline) Experimental parameters Data reduction (GELINA) Dead time Background Data analysis normalization n/n = 0.2% T eff = 5 K Response function E / ev / mev n / mev With: ( D + R ) < ( D + R ) > Recommendation : repeat study and verify the effect of self-shielding

12 Reporting of results + experimental conditions Facility/Neutron production (response function) Discuss with N. Otsuka Input from ntof, RPI, ORELA and IRMM, Contact POHANG, LANL Target characteristics areal density distribution, contact N. Otsuka Flux (recommend to provide the flux used for reaction data) Data Uncertainties Recommendation on dead time correction (< 1.2) Report TOF Report E + how it was deduced Ideally : AGS-concept In any case report separately Uncorrelated component (due to counting statistics) Normalization uncertainty

13 Probability desinsity Probability desinsity Response function R (L,E n ) ev ev ev ev ev ev ev ev ev ev ev ev ev cm Distance / cm Distance / cm

14 Time resolution of the facility Analytical description of response Order of magnitude of the parameters : 0 = 7 2 mm = 24 5 mm D c = 10 2 cm

15 Reporting of results + experimental conditions Facility/Neutron production (response function) Discuss with N. Otsuka Input from ntof, RPI and IRMM Target characteristics areal density distribution, contact N. Otsuka Flux (recommend to provide the flux used for reaction data) Data Uncertainties Recommendation on dead time correction (< 1.2) Ideally : AGS-concept In any case report separately Uncorrelated component (due to counting statistics) Normalization uncertainty

16 Data reduction process Reaction yield + Self-indication Transmission Y Y C B w w exp N r CB C dead time corrected counts B background contribution N normalization factor T exp N C in out C B B in out Histogram operations + Covariance information Y exp + covariance Y SI,exp + covariance T exp + covariance input Models

17 Data reduction : AGS concept Observable Z (dimension n) with k sources of correlated uncertainties V D S S T Z Z z z D Z : uncorrelated part n values S Z : correlated part dim. (n x k) X Z D z S z

18 Data reduction by AGS 235 U(n,f) measured at the GELINA facility*, L=10 m, 100Hz, 800Hz 100 Hz 800 Hz *Olivier Serot, Cyrille Wagemans

19 Implicit Data Covariance Matrix with AGS methodology

20 Reporting RP Link with AGS formalism M 11 x x G T G 1 12 ( x x) 22 = M T 1 T T T G G G G M G G G G 1 G x T x x G M x x x Cholesky decomposition of the positive-definite matrix M x into the product of a lower triangular matrix and its conjugate transpose lead to: 11 M x SS T If the contribution of the «statistical» uncertainties (from the fit) are negligible compared to the «systematic» uncertainties M x diag(var(x 1 ) var(x n )) Has to be verified : mathematics and also the impact of neglecting correlated terms in M x