Abstract
The relaxation of a nonequilibrium test particle population of mass m1 in contact with a background gas of particles of mass m2 at temperature Tb is studied with the spatially homogeneous Boltzmann equation. A pseudospectral method of solution is employed which is based on the discretization of the distribution function at a nonuniform grid that coincides with a quadrature. In order to implement this approach, the integral collision operator of the Boltzmann equation is expressed explicitly in terms of a kernel which is also discretized. This procedure fails if the classical differential collision cross section is used as it diverges for small scattering angles and the kernel is no longer well defined. In the present paper, we choose the interaction potential between the test particles and the background particles to be the Maxwell molecule interaction, that is, V(r) = V0(d/r)4 for which the eigenvalues and eigenfunctions are well known. We employ the quantum mechanical differential cross section for this...
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