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The Effect of Randomness on Group Cross Sections, II

Charles N. Kelber and Philip H. Kier

Nuclear Science and Engineering

Volume 26 / Number 1 / September 1966 / Pages 67-72


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A model is developed for the estimation of the Doppler effect from the unresolved energy region for fissile nuclides. For energy intervals that contain enough resonances for the reaction rates to be statistically independent of neighboring intervals, many resonance structures, or ladders, are generated by a random process that preserves the average widths and strength function. For each ladder, the relative changes in the absorption and the fission rates with temperature are computed, including overlap effects. This procedure yields estimates of mean quantities and the dispersion of values about the mean when the reaction rates are regarded as random variables. The Doppler effect and its variance are obtained by incorporating these resonance integral calculations into a multigroup-perturbation theory formulation., This model has been used to estimate the Doppler effect for 239Pu in the Codd and Collins mixture. For a temperature change from 300 to 600°K, the contributions to Ak/k from the unresolved region (215 eV to 10 keV) and the resolved region ( < 215 eV) were calculated to be 290 X 10"6 and 440 X10-6, respectively. The probable error, or ^2/3 standard deviation in the Doppler effect, assumed to be solely from the unresolved region, was ± 290 X 10" 6.

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