On a quasi-optimal exponential transform energy-dependent parameter for biasing gamma deep-penetration monte Carlo transport

New biasing schemes or improvement of existing ones is still an outstanding work. In fact, even though the calculation speed of modern computers increases greatly, it is not sufficient to compensate for the inclusion of more realistic physics (e.g. continuous energy) and more complex geometry description inside Monte Carlo codes. This article aims to present a new energy-dependent parameter for exponential transform suited for deep penetration gamma transport in various specified materials. The gamma transport equation dedicated to deep penetration leads, for an assigned asymptotic form, to a characteristic equation whose solution gives the exponential transform parameters as a function of material and transport data for a given initial energy. The exponential transform energy-dependent parameters are tested on a simplified but heavy configuration (2 MeV source inside a double shell made of 40 cm of stainless steel and 40, 50 or 60 cm of lead) with French Monte Carlo code TRIPOLI 4.3, one of the few codes allowing for energy dependence in the exponential transform parameters. The numerical results are such that the deeper penetration conditions are fulfilled, the higher factor of merit of our results compared to the one based upon a gamma removal cross-section concept as a correction to isotropic scattering. The asymptotic gamma angular distribution is also derived. (authors)