Abstract
Benchmark numerical results for one speed slab and sphere problems with isotropic scattering are reported by exploring the inverse problem in which the size of the system is specified and values of mean number of secondaries, c and neutron density are obtained. Two different techniques, the singular eigenfunctions with X-function, and solution of the integral transport equation with singularity subtraction method are investigated to yield precise results for c and the neutron density values. We report c values accurate up to 14 decimal places, and neutron density values up to nine figures. In several instances the results constitute an improvement over the previously reported benchmark results in the literature.
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