Dirac eigenvalues for screened Coulomb potentials

Abstract

Considers a single fermion moving in a screened Coulomb potential having the form V(r)=g(-1/r), where g is monotone increasing and concave. The method of potential envelopes is applied to this problem and it is shown that close approximations for the relativistic eigenvalues are given by the simple expression EnjP=minu in (0,1)(D(u)-uD'(u)+V(-1/D'(u))) where D(u)=DnjP(u) are the known exact eigenvalues for the hydrogenic atom with potential -u/r. Specific results for the first four eigenvalues of the atoms Z=14(5)84 are compared to corresponding accurate values found numerically by the use of Dirac spinor orbits.