The exact solution of the time-dependent equation of radiative transfer in the interior of a semi-infinite atmosphere

Abstract

An exact solution to the time-dependent radiative transfer equation for the interior intensity in a semi-infinite atmosphere exhibiting temporal capture is obtained. The intensity is constructed from a solution found in neutron transport theory and can be expressed in terms of quadratures of elementary functions. The origin of the form of the emergent intensity found by Matsumoto is given, as well as a similarity relation and the relationship of the intensities in absorbing and nonabsorbing media.