Semi-classical collisional functions in a strongly correlated plasma

Abstract

Collisions between atoms (or ions) and electrons play an important role in the interpretation of line spectra and for the modelling of stellar interiors. Plasma shielding effects due to electron and ion correlations are not negligible in the physical conditions of white dwarf atmospheres, owing to their high density. They also play a role in cool stars and for atomic transitions that are quasi-degenerate. In the standard formalism of Stark impact broadening of spectral lines and of cross sections, the electrostatic Coulomb potential is used to describe the interaction between the perturbing electrons and the emitting atom. Electronic correlations (screening effects) are usually taken into account by introducing a cut-off in the interaction when the electron-atom distance exceeds the Debye radius . A more consistent treatment to describe collective effects is the Debye-Hückel potential: the two-particle Coulomb field is shielded by the ensemble of the surrounding electrons. This is a good approximation only for high temperature and low density plasmas (weakly non-ideal plasmas), while for strongly non-ideal plasmas, the Coulomb cut-off potential or the ion sphere potential are more appropriate. These potentials, which can be written as the Coulomb potential with two correcting terms, are widely used in the literature. In this paper, we investigate the ion sphere model to describe the electron atom interaction in a strongly coupled plasma. New semi-classical collisional functions are derived for both the transition probability and the cross section, using the classical path approximation.