Abstract
The boundary-value problem for determining the transmission function by means of the transport equation is solved using the invariant embedding method. The obtained solution makes it possible to find the angular distributions and energy spectra of atomic particles that have passed through a solid layer if the differential elastic and inelastic scattering cross sections are known. Exact numerical solutions to equations and analytical solutions to equations in the small-angle approximation are found. For problems of electron transport under conditions that are characteristic for the most actively used electron-spectroscopy procedures, the results obtained in the transport approximation are compared with the exact numerical solution and the solution in the small-angle approximation. It is shown that, within the framework of the transport approximation, it is impossible to describe a phenomenon such as “brightness-body rotation”. The calculation of various cases within the framework of the small-angle approximation is in good agreement with the exact solutions. The calculation error in the small-angle approximation does not exceed 10%. The results were approbated using DOM, MDOM, and DISORT codes applied in remote sensing of the Earth atmosphere.
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