Direct Relativistic Formulation of Constant Magnetic and Electric Field Effects in Simple Atoms. II

Abstract

A previously developed method of obtaining approximate solutions to the Dirac equation for the electron is applied to the problem of constant electric and magnetic effects in simple atoms. This method makes the relativistic formulation of these problems straightforward. In all cases the standard expressions are reproduced, as one would expect, and hence illustrates the simplicity and utility of the method. The Zeeman effect is calculated to order α2, α being the usual fine structure constant, and it is seen that only the lowest order solutions are required. That is, one needs only the nonrelativistic solutions. The Stark effect and dipole transition matrix elements are calculated only to zero order in α as it is felt that that is all that is required for comparison with experiment. One concludes that the discrepancies between the theoretical values and experimental values of the oscillator strengths must be explained on the basis of nonrelativistic effects.