A new solution to the one-group foil problem with comparison to Monte Carlo

The solution to the foil problem for monoenergetic neutrons in a physically thin foil embedded in an infinite moderating medium is considered. Both angular and scalar flux solutions are achieved for various values of the foil absorption optical thickness δ. The analytical solution is affected by the Laplace transform method, utilizing the method of Sobolev for the angular flux. The inversion of the Laplace transform is accomplished numerically to a high degree of accuracy. Comparisons of the analytical solutions with results from a Monte Carlo (MCNP) code show excellent agreement. These comparisons, which are free of any associated data or cross section dependencies, provide significant evidence of the capabilities of MCNP to evaluate the neutron transport behavior in such problems