The model potential for positive ions

Abstract Some experience is reported of numerical calculations with atomic pseudo-potentials in the sense of Austin et al. (1962). The pseudo-potentials and/or the pseudo-wave-functions are not sufficiently smooth to give really good convergence to an expansion of the model wave-function in a crystal in terms of plane waves. The pseudo-potential of an ion is therefore replaced by a simple model potential with two parameters. These are adjusted to reproduce exactly the observed spectroscopic energy levels of an electron in the field of the ion. In this way a model potential is set up to represent the ion, useful for calculations in solids and liquids. Some numerical results are given and more extensive tables are available from the authors.