Time‐Dependent One‐Speed Albedo Problem for a Semi‐Infinite Medium

A Laplace transformation technique is used to determine the neutron distribution in a semi‐infinite medium which has been irradiated by a neutron pulse. The result is given in terms of known solutions of Milne's problem and of the steady‐state albedo problem, which in turn are expressed by aid of Case's X‐function. Simple asymptotic approximations, valid for t ≫ 1, are deduced from the exact result.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71087/2/JMAPAQ-6-7-1125-1.pd

Invariant Imbedding and Case Eigenfunctions

A new approach to the solution of transport problems, based on the ideas introduced into transport theory by Ambarzumian, Chandrasekhar, and Case, is discussed. To simplify the discussion, the restriction to plane geometry and one‐speed isotropic scattering is made. However, the method can be applied in any geometry with any scattering model, so long as a complete set of infinite‐medium eigenfunctions is known. First, the solution for the surface distributions is sought. (In a number of applications this is all that is required.) By using the infinite‐medium eigenfunctions, a system of singular integral equations together with the uniqueness conditions is derived for the surface distributions in a simple and straight‐forward way. This system is the basis of the theory. It can be reduced to a system of Fredholm integral equations or to a system of nonlinear integral equations, suitable for numerical computations. Once the surface distributions are known, the complete solution can be found by quadrature by using the fullrange completeness and orthogonality properties of the infinite‐medium eigenfunctions. The method is compared with the standard methods of invariant imbedding, singular eigenfunctions, and a new procedure recently developed by Case.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70318/2/JMAPAQ-10-4-581-1.pd

Existence and Uniqueness Theorems for the Neutron Transport Equation

In an attempt to understand the conditions under which the neutron transport equation has solutions, and the properties of those solutions, a number of existence and uniqueness theorems are proved. One finds that the properties of the solution are closely related to the boundedness of the source as well as to certain velocity‐space integrals of the scattering kernel. Both time‐dependent and time‐independent equations are considered as are also the time‐dependent and time‐independent adjoint equations. Although only a very few of all possible existence and uniqueness theorems for these equations are considered here, the work may serve as a guide to the treatment of similar problems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70329/2/JMAPAQ-4-11-1376-1.pd

Relationships among Generalized Phase‐Space Distributions

The generalized phase‐space distributions, including the Wigner distribution, are presented in terms of expected values of generating operators. A generalization of the Weyl correspondence is obtained to provide expressions for generalized Wigner equivalents. Finally, rather simple relationships are obtained connecting the generalized phase‐space distributions to the Wigner distribution; and similar relationships are obtained for the generalized Wigner equivalents. In particular, it appears that, among the class considered, there is no reason to use any distribution other than the Wigner for performing any calculations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69967/2/JMAPAQ-10-2-233-1.pd

Recent Applications of Neutron Transport theory

Lectures presented at the University of Michigan Fast Reactor Physics Conference, June 8-12, 1964. Notes taken and prepared by N. J. McCormick.US AEC Contract No. AT-11-1-1372http://deepblue.lib.umich.edu/bitstream/2027.42/85789/1/MMPP-FRPC-64-1 PFZ.PDF2

The slowing down and thermalization of neutrons : by M. M. R. Williams. 582 pages, diagrams, 6 x 9 in. New York, John Wiley & Sons, Inc., 1966. Price, $19.50

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33346/1/0000743.pd

Quantum Statistics and Slow Neutron Scattering by Gases

A surprisingly simple expression in ``closed form'' for the cross section d2σ/dΩdϵ for the scattering of thermal neutrons (including polarized neutrons) from an ideal quantum gas is derived. This result extends the work of Van Hove on the quantum gas. An expansion is obtained for dσ/dϵ. The case of elastic scattering is treated separately. From these expressions is obtained a criterion for ignoring the statistics of the scatterer in favor of classical (Boltzmann) statistics. This criterion should have some validity for weakly interacting systems. It is shown that the effects of statistics on the neutron cross section for a helium‐4 gas range from 5% or less for the noninteracting gas up to as much as 40% for the interacting system.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70882/2/JCPSA6-47-12-4923-1.pd

Wigner Method in Quantum Statistical Mechanics

The Wigner method of transforming quantum‐mechanical operators into their phase‐space analogs is reviewed with applications to scattering theory, as well as to descriptions of the equilibrium and dynamical states of many‐particle systems. Inclusion of exchange effects is discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71122/2/JMAPAQ-8-5-1097-1.pd

Energy-dependent neutron transport theory in the fast domain : technical report

http://deepblue.lib.umich.edu/bitstream/2027.42/6822/5/bac9792.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/6822/4/bac9792.0001.001.tx