The one-dimensional energy dependent linear neutron transport equation has been solved for the case of constant cross sections in an infinite absorbing medium with the approximation of isotropic scattering in the laboratory frame of reference. The method of solution was to apply a Fourier transform with respect to space and a Laplace transform with respect to lethargy. The Laplace inversion is performed analytically, while the Fourier inversion is accomplished by a highly accurate algorithm employing a Hurwitz-Zweifel expansion in combination with an Euler-Knopp transformation and a Romberg quadrature routine. This method results in solutions accurate to four places which are suitable for benchmarks.

No description available.

No description available.

Thesis (Ph. D.)--California Institute of Technology, 1968. / Also issued in print.

Thesis (M.S.)--University of Michigan, 1959.

Thesis (M.S.)--University of Michigan, 1965.

Thesis (M.S.)--University of Michigan, 1958. / eContent provider-neutral record in process. Description based on print version record.

Thesis (Ph. D.)--California Institute of Technology, 1968. / eContent provider-neutral record in process. Description based on print version record.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1984. / Typescript. Vita. Description based on print version record. Includes bibliographies.

Integral transport theory is used to compute transfer matrix elements for neutral particle streaming through r-z rectangular voids. The transfer matrix is utilized in a hybrid method; it interfaces with a conventional discrete ordinates calculation outside the void. Since the hybrid interface is accomplished within the inner iteration of an existing discrete ordinates code, standard sweeping schemes used in SN codes are not adversely affected. The resulting transfer matrix is independent of the multigroup energy structure used in a calculation. Further, the transfer matrix is not affected by changes in materials or cross sections outside the void. For these reasons, once a transfer matrix is calculated it can be used in a wide variety of problems containing a similar void. In this study, the transfer matrix hybrid, standard discrete ordinates, and Monte Carlo methods are applied to two sample problems to compare the accuracy of these methods. The Monte Carlo results are considered correct in order to compute errors in the deterministic calculations. The transfer matrix hybrid method is more accurate than conventional SN methods; the ray effect, persistent in discrete ordinates calculations, is substantially reduced. In addition, the transfer matrix hybrid executes faster than higher order SN calculations.