Abstract
A set of functions spanning the solution space of the integral transport equation near a boundary in semi-infinite plane geometry is obtained and used to reduce the problem to that of a system of linear algebraic equations. Expressions for the boundary angular flux are obtained by matrix multiplication, and the theory is extended to adjacent half-space problems by matching the angular flux at the boundary. Thus a unified theory is obtained for well-behaved arbitrary sources in semi-infinite plane geometry. Numerical results are given for both Milne's problem and the problem of constant production in adjacent half-spaces, and albedo problems in semi-infinite geometry. The solutions for the flux density are best near the boundary, and for the angular flux are best for angles near the plane of the boundary; it is conjectured that the theory will prove most useful when extended to arrays of finite slabs.
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