HIGH-ORDER PERTURBATION THEORY FOR BOUND STATES OF AN ELECTRON IN A SCREENED COULOMB POTENTIAL

The solution to the nonrelativistic Schrödinger equation for a bound electron in an attractive screened Coulomb potential is investigated using the large-Z (Z is nuclear charge) asymptotic expansion theory. Both the basic asymptotic and perturbation solutions are found. The problem of finding the kth order perturbation wave function and energy for any state is reduced to solving, recursively, a set of k linear algebraic equations in k unknowns. The asymptotic expansions for the energy and wave functions are presented to the tenth order in perturbation theory for the 1S state and to fifth order for the general n, l=n-1 quantum state. Results for the 2S states are also given. Comparison of the perturbation-theory results with those of numerical integrations for the energy show excellent agreement. It is shown that a finite screening radius gives rise to a finite number of bound states, a result which contradicts some recently published work. Application of the screened Coulomb potential model to intensity cutoffs in the spectra of solar and laboratory hydrogen plasmas is discussed. © 1969 The American Physical Society.