Energy and shape relaxation in binary atomic systems with realistic quantum cross sections

Abstract

We use the spatially homogeneous linear Boltzmann equation to study the time evolution of an initial non-equilibrium distribution function of an ensemble of test particles dilutely dispersed in a background gas at thermal equilibrium. The systems considered are energetic N in He and Xe in He. We employ the quantum mechanical differential cross section to define the collision operator in the Boltzmann equation. The Boltzmann equation is solved with a moment method based on the expansion of the distribution function in the Sonine (Laguerre) polynomials as well as with a direct simulation Monte Carlo method. The moment method provides the approximate eigenvalues and eigenfunctions of the linear Boltzmann collision operator. The reciprocal of the eigenvalues is a measure of the relaxation times to equilibrium. For hard sphere cross sections, the relaxation of the average energy and the shape of the distribution function can be characterized by a single time scale determined by the momentum transfer cross section. We show that this is also the case for realistic quantum cross sections with dominant small angle scattering contributions.