Thermalization of positronium in helium: A numerical study

In this paper we present a numerical study of positronium (Ps) thermalization in pure helium (He). Recent measurements of Ps thermalization yielded data that were analyzed to produce the scattering cross-sections in helium by using energy balance equations with an assumption of a Maxwell-Boltzmann distribution (MBD) function for Ps. We have applied a Monte Carlo code to test the cross-sections. As our code was developed without any approximations for the energy distribution function we have effectively also tested the assumptions and the validity of the simple theory based on Maxwellian distributions. We present the simulation results using the simulation technique that is limited only by the accuracy of the available cross-sections. We calculate thermalization profiles for several theoretical and measured cross-sections. Also, the temporal evolution of energy distributions has been shown along with diffusion coefficients and spatial ranges of penetration. Thermalization of the initial distribution is rapid and the data follow relatively closely, those calculated in recent experiment, which supports the choice of MBD and the obtained cross-section. However the distribution function most of the time deviates from the MBD due to strong scattering. Finally, we applied the same procedure to analyze Ps thermalization in water vapor.