Abstract
An analytical description of X-ray photoemission spectra is constructed on the basis of solution of the boundary-value problem for the transport equation taking internal sources into account by invariant embedding methods. Solutions in the small-angle approximation and exact solutions obtained as a result of the numerical procedure. The photoelectron path lengths distributions in a target and coefficients of expansion of the photoemission flux density in a series of inelastic scattering multiplicities are determined. The invalidity of approaches neglecting processes of multiple elastic scattering when describing energy X-ray photoemission spectra is shown. Errors appearing in the case where approximations are used are estimated.
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