A numerical analysis of antithetic variates in Monte Carlo radiation transport with geometrical surface splitting

A numerical study for effective implementation of the antithetic variates technique with geometric splitting/Russian roulette in Monte Carlo radiation transport calculations is presented. The study is based on the theory of Monte Carlo errors where a set of coupled integral equations are solved for the first and second moments of the score and for the expected number of flights per particle history. Numerical results are obtained for particle transmission through an infinite homogeneous slab shield composed of an isotropically scattering medium. Two types of antithetic transformations are considered. The results indicate that the antithetic transformations always lead to reduction in variance and increase in efficiency provided optimal antithetic parameters are chosen. A substantial gain in efficiency is obtained by incorporating antithetic transformations in rule of thumb splitting. The advantage gained for thick slabs (∼20 mfp) with low scattering probability (0.1-0.5) is attractively large . (author). 27 refs., 9 tabs