232 Th EVALUATION IN THE RESOLVED RESONANCE RANGE FROM 0 to 4 keV Nuclear Data Group Nuclear Science and Technology Division Oak Ridge National Laboratory.

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Presentation transcript:

232 Th EVALUATION IN THE RESOLVED RESONANCE RANGE FROM 0 to 4 keV Nuclear Data Group Nuclear Science and Technology Division Oak Ridge National Laboratory L.C. LEAL and H. DERRIEN International Atomic Energy Agency Second Research Coordination Meeting Evaluated Nuclear Data for Th-U Fuel Cycle December 6-9, 2004 IAEA Headquarters, Vienna, Austria

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 2 Motivation for a new evaluation of 232 Th resonances ● Include transmission measurements from ORELA (Olsen et al.) ● Include capture cross sections from GEEL ● Include capture cross sections from NTOF ● Improve the statistical spin distribution for s- wave (l=0 j=1/2+) and p-wave (l=1 for j=1/2- and j=3/2-) ● Include new thermal cross section values

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 3 Experimental database Energy Range (eV) ReferencesMeasurements Type Thickness (at/b) Flight Path Length (m) to 580Garg et al. Columbia Total Cross Section to 4000 T=77 K Ribon et al. CEA Total Cross Section to 15Olsen et al. ORELA Total Cross Section to 4000Olsen et al. ORELA Transmission8 samples to to 4000GEELCapture1 sample to 100NTOFCapture1 sample

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 4 Code SAMMY  Reich-Moore R-Matrix formalism;  Baye’s method of fit;  Free gas model for Doppler broadening of the resonances;  Gaussian experimental resolution plus exponential tail;  Experimental effect corrections (background, normalization);  Self-shielding and multiplescattering correction for the capture cross section (recently improved version of SAMMY). Method of analysis

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 5  Determination of external resonance parameters leading to consistent values of the effective radius R’ and of the normalization correction parameters;  Effective radius obtained: R’ = 9.72 ± 0.02 fm External Resonance Parameters Determination

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 6  Starting with the 232 Th ENDF/B-VI resonance evaluation (There is only l=0 with j=1/2+ and l=1 with j=1/2- resonances in the ENDF evaluation);  Include resonances for l=1 with j=3/2-;  Sequential analysis of several experimental data sets, using the parameter covariance matrix from one sequence to the next;  Fitting of the transmission data;  Fitting of the capture data;  Fitting of the thermal cross section data (total and capture); Method of analysis

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 7 Experimental Results

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 8 Experimental Results

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 9 Experimental Results

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 10 Experimental Results

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 11 Experimental Results

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 12 Experimental Results

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 13 Energy range 0 to 4 keV  228 s-wave resonances for Jπ = 1/2+  147 p-wave resonances for Jπ = 1/2-  59 p-wave resonances for Jπ = 3/2- Average Resonance Parameter  = ± 0.71 eV for Jπ = 1/2+ ( s-wave)  = ± 2.41 eV for Jπ = 1/2- (p -wave)  = ± eV for Jπ = 3/2- (p -wave) The Resonance Parameters (poor statistics) 434 resonances

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 14 Wigner Distribution for l=0 and j=1/2+ (The histogram represents the evaluated data)

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 15 Wigner Distribution for l=1 and j=1/2- (The histogram represents the evaluated data)

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 16 Wigner Distribution for l=1 and j=3/2- (The histogram represents the evaluated data)

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 17 Thermal Values Cross section Type Experimental (barns) Calculated (barns) Capture Total

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 18  Use of Computer Code SUGGEL; Statistical assignment of orbital angular momentum l for each resonance;  Use of known distribution law of R-matrix resonances parameters; Porter-Thomas distribution, Wigner distribution  Use of the Δ 3 theory together with the Wigner distribution law for determining small missing resonances. New Resonance Parameters (Better Statistics)

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 19 Energy range 0 to 4 keV (number of resonances proportional to 2j+1)  240 s-wave resonances for Jπ = 1/2+  233 p-wave resonances for Jπ = 1/2-  473 p-wave resonances for Jπ = 3/2- Average Resonance Energy Spacing  = ± 0.55 eV for Jπ = 1/2+ ( s-wave)  = ± 1.32 eV for Jπ = 1/2- (p -wave)  = 8.11 ± 0.02 eV for Jπ = 3/2- (p -wave) The Resonance Parameters (better statistics) 946 resonances

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 20 Wigner Distribution for l=0 and j=1/2+ (The histogram represents the evaluated data)

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 21 Wigner Distribution for l=1 and j=1/2- (The histogram represents the evaluated data)

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 22 Wigner Distribution for l=1 and j=3/2- (The histogram represents the evaluated data)

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 23 Delta3 Statistics for l=0 and j=1/2+ (The histogram represents the evaluated data) Δ 3 Statistics Results Theory: ± Measured: 0.488

O AK R IDGE N ATIONAL L ABORATORY U. S. D EPARTMENT OF E NERGY 24 Conclusion  The 232 Th resonance parameters in the energy range 0 to 4 keV were obtained from the analysis of high resolution transmission data and capture cross section data;  Good prediction of the thermal cross section values; Improved Resonance Parameters  The statistical distribution of the s- and p-wave resonances agree relatively well with theoretical predictions;  Most of the p-wave resonances were identified leading to a better representation of the capture cross sections mainly at higher energies.