232 Th EVALUATION IN THE RESOLVED RESONANCE RANGE FROM 0 to 4 keV Nuclear Data Group Nuclear Science...

232Th EVALUATION IN THE RESOLVED RESONANCE RANGE FROM 0 to 4 keV

Nuclear Data GroupNuclear Science and Technology DivisionOak Ridge National Laboratory

L.C. LEAL and H. DERRIEN

International Atomic Energy AgencySecond Research Coordination MeetingEvaluated Nuclear Data for Th-U Fuel CycleDecember 6-9, 2004IAEA Headquarters, Vienna, Austria

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OAK RIDGE NATIONAL LABORATORYU. S. DEPARTMENT OF ENERGY

Motivation for a new evaluation of 232Th 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

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Experimental database

Energy Range (eV)

References Measurements Type

Thickness (at/b)

Flight Path Length (m)

82.29 to 580 Garg et al. Columbia

Total Cross Section

- 200

212.32 to 4000

T=77 K

Ribon et al. CEA

Total Cross Section

- 103.7

0.008 to 15 Olsen et al. ORELA

Total Cross Section

- 22.532

15 to 4000 Olsen et al.

ORELA

Transmission 8 samples

0.0001608 to 0.19308

40.016

10 to 4000 GEEL Capture 1 sample

0.003176

58.386

10 to 100 NTOF Capture 1 sample

0.004109

185.2

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Code SAMMYReich-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

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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

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Starting with the 232Th 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

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Experimental Results

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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 <D> = 17.36 ± 0.71 eV for Jπ = 1/2+ (s-wave)

<D> = 26.71 ± 2.41 eV for Jπ = 1/2- (p-wave)

<D> = 67.54 ± 13.83 eV for Jπ = 3/2- (p-wave)

The Resonance Parameters (poor statistics)

434 resonances

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Wigner Distribution for l=0 and j=1/2+(The histogram represents the evaluated data)

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Wigner Distribution for l=1 and j=1/2-(The histogram represents the evaluated data)

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Thermal Values

Cross section Type

Experimental

(barns)

Calculated

(barns)

Capture 7.402 7.396

Total 20.377 20.319

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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 Δ3 theory together with the Wigner distribution law for determining small missing resonances.

New Resonance Parameters (Better Statistics)

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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 <D> = 16.57 ± 0.55 eV for Jπ = 1/2+ (s-wave) <D> = 16.94 ± 1.32 eV for Jπ = 1/2- (p-wave) <D> = 8.11 ± 0.02 eV for Jπ = 3/2- (p-wave)

The Resonance Parameters (better statistics)

946 resonances

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Wigner Distribution for l=0 and j=1/2+(The histogram represents the evaluated data)

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Delta3 Statistics for l=0 and j=1/2+(The histogram represents the evaluated data)

Δ3 Statistics Results

Theory: 0.549 ± 0.109

Measured: 0.488

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Conclusion The 232Th 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.

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232 Th EVALUATION IN THE RESOLVED RESONANCE RANGE FROM 0 to 4 keV Nuclear Data Group Nuclear Science...

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