RESONANCE ABSORPTION OF NEUTRONS IN NUCLEAR REACTORS. (thesis)

Abstract

7 5 : of resonance absorption of neutrons in nuclear reactors is considered. Formulas for the effective resonance integral of single resonances are given in the "narrow resonance" approximation in homogeneous media and in the "narrow resonance" and "infinite mass absorber" approximation in heterogeneous media. It is shown that the Doppler effect in homogeneous media can be expressed through a certain function of two variables, J( xi , beta ). The properties of this function are studied in detail, and a tabulation given. The effect of interference between resonance and potential scattering on the effective resonance integral is studied. In heterogeneous media in the "narrow resonance" case it is shown that the Doppler effect can again be expressed through the same function, J( xi , beta ), as in the homogeneous case if a rational approximation for the average escape probabilities due to Wigner is introduced. Furthermore, it is shown that then a formal identity exists between the homogeneous and heterogeneous cases for "narrow" resonances. The error caused by Wigner's rational approximation is studied in detail, and in the case of no Doppler broadening and no interference scattering an improved formula is suggested. In heterogeneous media in the "infinite mass absorber" case an approximate expression for the albedo of an absorber lump is suggested on the basis of heuristic arguments. Precise calculations of the albedo based on a variational method of solving the monoenergetic transport equation are compared with this approximation, and show it to be quite accurate. Use of the approximate albedo again permits expression of the Doppler effect through the function J( xi , beta ). The effect of interference between potential and resonance scattering is also studied in the "infinite mass absorber" approximation. These results are applicable to calculating the absorption in low energy resolved resonances for which the widths and energy are known. In the region beyond the experimental limit of resolution statistical considerations are employed. The formulas for single resonances are averaged over the probability distributions of the partial widths. The theory is then applied to the calculation or the effective resonance integrals of uranium and thorium rods, and good agreement is obtained for uranium and fair agreement for thorium. At high energies resonance absorption cross sections fall sufficiently low to permit neglect of flux depression effects, and attention is focussed on average reaction cross sections. A study of the effect of fluctuations in the partial widths on average reaction cross sections is given. Some general theorems are derived independent of the probability distributions of the widths. If the widths are distributed in member distributions of the chi- squared family, it is shown that the multiple integrals over these distributions which ex press the averages can be reduced to a single infinite integral. This integral is evaluated in the eighteen simplest cases of interest. A Monte Carlo program for the electronic computer ORACLE for evaluating these averages is described. It is shown that enough experimental data on neutron reactions in U/ sup 238/ exists below 500 kev to overdetermine the s-, p-, d-, and f-wave strength functions. Analysis of the data including the important effects of fluctuations in the widths yields consistent values for the strength functions, in support of the theory. Finally, the statistical formalism of Hauser and Feshbach is transformed from the channel spin representation to another which is more convenient in the presence of spin-orbit coupling. The effect of small amounts of spin-orbit coupling in the analysis of the U/sup 238/ reaction data is found to be unimportant. Finally, it is proven that the total, the compound nucleus formation,