The memorandum presents an exact and efficient method of computing a well-defined resolvent, or Green's function, for one-velocity neutron transport or radiative transfer in a one-dimensional slab or sphere with isotropic scattering. It is shown that the resolvent for the slab may be simply expressed in terms of a 'complex-valued' solution to the transport equation, using the Laplace transform and contour deformation. (The procedure for computing this solution by means of simple quadratures and rapidly convergent Fredholm equations is given.) The result for the sphere resolvent, which is closely related to that for the slab, is also presented, with particular attention to the flux resulting from a point source in the center of a sphere. (Author)
This report is part of the RAND Corporation External publication series. Many RAND studies are published in peer-reviewed scholarly journals, as chapters in commercial books, or as documents published by other organizations.
Our mission to help improve policy and decisionmaking through research and analysis is enabled through our core values of quality and objectivity and our unwavering commitment to the highest level of integrity and ethical behavior. To help ensure our research and analysis are rigorous, objective, and nonpartisan, we subject our research publications to a robust and exacting quality-assurance process; avoid both the appearance and reality of financial and other conflicts of interest through staff training, project screening, and a policy of mandatory disclosure; and pursue transparency in our research engagements through our commitment to the open publication of our research findings and recommendations, disclosure of the source of funding of published research, and policies to ensure intellectual independence. For more information, visit www.rand.org/about/principles.
The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.