FULL RANGE SOLUTION OF HALF-SPACE NEUTRON-TRANSPORT PROBLEM

Based on the fact that the complete set of eigenfunctions of a half-range problem in [0, U] is also part of a larger set that is complete in the full-range [-U, U], a full-range boundary condition is introduced for solving the half-range problem. Specifically, this condition expresses the solution at the boundary valid for all u is an element of [ -U, U] as the sum of a given forward component in u is an element of[0, U] and the unknown backward component in u is an element of [-U, 0]. Thus the basically ill-posed nature of the half-range problem, viz., that is required to find the response in [-U, U] from given data in [0, U], is formulated over the entire domain at the boundary as compared to the usual approach that expresses the boundary condition only over [0, U]. This allows us, through a two-step process that considers the full-range properties of the eigenfunctions in [-U, U] only, to obtain numerically exact extrapolated end-point and Case X-function. This means, because of the relationship of these fundamental half-range data with standard half-range expansion coefficients a(0+) and A(v) [2], that the transient integral of the half-range solution has been reduced to mechanical quadratures.