Abstract
We generalize a three-dimensional Fourier transform method presented previously, to solve various forms of the linearized transport equation in planar geometry. Infinite-space problems are in general easily treated by our procedures. Half-space problems may also be solved analytically in, at least, the following cases: (i) separable scattering kernel (arbitrary particle speed); (ii) one-speed, anistropic scattering with rotation-invariant kernel; (iii) one-dimensional energy-dependent kernel of Kac; (iv) multigroup transport with down scattering only. The general importance of recursion relations to problems with nonseparable kernels is emphasized. A comparison is made between our methods and the two-dimensional singular eigenfunction approach, and a criterion is presented for the analytic solubility of any problem of the general form considered.
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