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

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.