Publication Date


Document Type


First Advisor

Bushnell, David L.||Feeny, Harold F. (Harold Francis)

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Physics




The resonance escape probability, defined as the ratio of the number of neutrons which reach a given energy E in the resonance range to the number Which enter the resonance range from above, is calculated for a thorium-water moderator by use of the Narrow Resonance approximation, the Narrow Resonance with Infinite Mass Absorber approximation, and the Modified Narrow Resonance approximation. These methods are all based on the assumption that the width of the resonance peak is narrow compared to the average neutron loss in energy per collision with a nucleus. Since calculating the resonance escape probability by these methods can be both tedious and difficult for complicated mixtures, much of the results appearing in the literature are for simple hypothetical models such as a one to one ratio of fuel to a single moderator. An attempt here has been made to calculate the resonance escape probability for thorium under experimental conditions. The physical systems considered are five easily reproducible concentrations of TH(NO3)4 dissolved in water. The problem then becomes one of calculating the escape probability of thorium in a moderator of hydrogen, nitrogen, and oxygen. Only the first eight resonance peaks of thorium which contribute the major part of the total absorption are considered. The results are given for each of the eight peaks and for the combined effect of the eight peaks. Doppler-broadened Briet- Wlgner single level formulas are used for the energy dependent cross sections. The results show that for the five concentrations considered, the Modified Harrow Resonance approximation gives nearly exact values for the escape probability. The Narrow Resonance approximation gives good estimates, especially for the narrower resonance peaks of the more dilute mixtures. The Narrow Resonance with Infinite Mass Absorber approximation gives good results for the wider resonances of the more concentrated mixtures except for those resonance peaks that have large resonance scattering cross sections. Comparison with Monte Carlo calculations for the same mixtures, shows that the Monte Carlo method gives good enough results to make it useful for calculating the resonance escape probability.


Includes bibliographical references.||Includes illustrations.


vii, 59 pages




Northern Illinois University

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