The Searchlight Problem for Neutrons in a Semi-Infinite Medium

The solution to the searchlight problem for monoenergetic neutrons in a semi-infinite medium with isotropic scattering illuminated at the free surface is obtained through the numerical evaluation of an analytical expression for the scalar flux at various positions within the medium. The sources considered are normally incident pencil beam and isotropic point sources as well as a longitudinal uniformly distributed source. The analytic solution is effected by a recently developed numerical inversion technique applied to the Fourier-Bessel transform. The transform inversion results from the solution method of Rybicki, where the two-dimensional problem is solved by casting it as a variant of a one-dimensional problem. The numerical inversion results in a highly accurate solution. Comparisons of the analytic solution with results from Monte Carlo (MCNP) and discrete ordinates transport codes (DORT, TWODANT, and SMARTEPANTS) show excellent agreement. These comparisons, which are free from any associated data or cross-section set dependencies, provide significant evidence of the proper operation of the transport codes tested.