Kinetic Theory of Spectral Line Formation

Abstract

Spectral line formation is a non-Markovian process because the reemission spectrum of an atom depends on the frequency of the photon previously absorbed. We account for this effect by adopting a picture that ascribes finite widths to the atomic energy levels. History and success of this atomic model are discussed in some detail. In our semiclassical model, the state of an atom is characterized not only by its velocity and its excitation state, but also by the "substate" of the broadened atomic level it occupies. Accordingly, we define a generalized distribution function of the atoms in a given energy level which specifies their number density, their velocity distribution, and their distribution over the substates of the level. In this way, the formation of unpolarized spectral lines by multilevel atoms can be described by a set of kinetic equations for the generalized distribution functions of the atoms in the various energy levels and a set of transfer equations for the radiation intensities in the various spectral lines. The explicit form of these equations is derived taking into account all relevant radiative and collisional processes. The two-level atom is considered in detail, with special emphasis on the structure of the emission coefficient which is composed of three parts corresponding to complete redistribution in the laboratory frame, complete redistribution in the atomic rest frame, and coherent reemission in the atomic rest frame, respectively.