Abstract
The stationary version of the linear Boltzmann equation (the Lorentz model) is studied in the half-space x>0, x=0 being a grey surface of reflection coefficient κ (0≤κ≤1). The spherical harmonics method and Marshak-type boundary conditions are used to find expressions for n(K)(x), the particle density in the so-called PK approximation (K=1,3,5). The results given by the P5 approximation accord very well with recent numerical computations [R. G. Cole, T. Keyes, and V. Protopopescu, J. Chem. Phys. 81, 2771 (1984)]. The desideratum in this context, an accurate expression for the particle density, is produced by grafting the desirable features of n(5)(x) on an almost exact expression derived, for the special case of a black surface (κ=0), by J. LeCaine [Phys. Rev. 72, 564 (1947)].
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