An Analytic Independent Particle Model for Atoms: I. Initial Studies

Abstract

Publisher Summary Properties such as ionization energy, excitation energy, transition probabilities, elastic, excitation, and ionization cross sections are needed in problems involving the deposition of charged particle energy in matter. A series of calculational studies have been undertaken that utilize a two-parameter analytic atomic independent particle model (IPM) potential that is close to the average Hartree–Fock potential acting on the electrons in an atom. An advantage of the analytic IPM approach is that one can directly use many techniques developed and exploited in extensive studies involving the nuclear independent particle models, e.g., the shell and optical models and distorted wave analyses of nuclear collisions. Among these techniques is the ability to adjust the parameters of the model in relationship to experimental data or data acquired from more rigorous calculations. In many instances, such an adjustment allows for small effects that are neglected at the present stage of applied atomic physics. The development of rapid numerical techniques for solving the radial Schrodinger equation permits to concentrate on the massive body of physics that can be encompassed by the use of realistic electron-atom potentials. In the work of Green, Sellin, and Zachor (GSZ) a simple analytic atomic IPM potential with a continuous first derivative was found that uses only two parameters. The adjustment of the two parameters of the GSZ-IPM model is quite sensitive to the data or weighting used in the adjustment.