title: 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.
authors.affiliation: Institute of Applied Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada.
authors.forename: Reinel
authors.initials: R
authors.lastname: Sospedra-Alfonso
authors.forename: Bernie D
authors.initials: BD
authors.lastname: Shizgal