Theory of Stark broadening—I soluble scalar model as a test

Abstract

The purpose of the present paper is to test, on an exactly soluble model, the validity of standard approximations used in the theory of Stark broadening of atomic lines. The mathematical treatment involves no approximation; in particular, overlapping and incomplete collisions are correctly taken into account. In setting up the model, standard physical approximations are made: the dipole approximation, and uncorrelated perturbers with classical paths. In addition, in order to permit exact solution, the problem is taken to be scalar. As the exact solution shows no divergences whatsoever, it is concluded that the usual divergences at small and large impact parameters, which would also be present in the scalar model, arise from inadequate mathematical procedures (non-uniform asymptotic expansions), and not from the neglect of particle correlations, or from full quantum-mechanical effects, as often stated. The quasi-static and impact approximations are recovered as leading terms of asymptotic expansions of the line correlation function. The dominant role played by the probability distribution and the covariance of the microfield in determining the profiles of Stark-broadening lines is stressed.