Some remarks on Burkhardt's model for pressure broadening of spectral lines

Abstract

In order to understand the connection between impact and quasistatic approximation, Burkhardt treated a simple model: At one moment at most one particle interacts with the radiator and causes a constant line shift during its impact time. The subject of this paper is to give an exact treatment of this model including all the mixed terms neglected by Burkhardt. As in Burkhardt's treatment the line shape is a sum of two terms. For frequencies near the unperturbated line the first one behaves like the impact approximation, whereas the second one can be neglected. For frequencies far the unperturbated line (at least at one side of the spectre) the first one can be neglected and the second one behaves but a factor like the quasistatic approximation. The second term is the same as in Burkhardt's paper. The first term includes all the correlations neglected by Burkhardt and gives the impact approximation in its complete form.