Graduate Thesis Or Dissertation

 

A method for calculation of group-averaged resonance parameters Public Deposited

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/hh63sz85n

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  • A method of treating resonance captures for few energy group calculations is developed using the Narrow Resonance-Infinite Absorber approximation to the resonance integral. The application of this method is not restricted to this approximation, however, as other approximations to the resonance integral could also be used. The approach presented defines average parameters based on assuming that both the total dilute resonance integral and the total effective resonance integral are the sums over the individual resonances in the energy range under consideration. It is shown then that if the effective resonance integral equation for a single average resonance has the same functional form as the single resonances using the above definition for the total dilute resonance integral, then all parameters have been determined. The factor remaining to be calculated from these definitions is the averaged resonance peak height. This parameter, which is also in the form of a sum over the individual resonances, is then studied in some detail to see if any simpler form can be found. The first approach is to examine several simple cases representing basic types of resonance size combinations using only two resonances. These studies lead to considering several simplifications to the equation for the average resonance peak height, including a series form, a harmonic mean form, and several series corrections to harmonic mean. The range of applicability is examined and it is shown that none of these forms has universal applicability. Upon generalizing these approximations to include more resonances, several more forms based on correcting the mean value are postulated. Also based on this work, a functional form requiring curve fitting techniques is suggested. This curve fitting approach is not pursued here, however. These generalized equations for N resonances are applied to the resonances of several real isotopes. It is shown that the assumptions made in developing the approximations based on two resonances and then expanded to N resonances can be correlated with the results of applying these equations to the more complicated case of many resonances. This then forms a basis for predicting the behavior of group-averaged resonance parameters.
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