The scalar relativistic approximation

Abstract

A new method has recently been proposed for the approximate calculation of relativistic effects in atoms and solids. In this method, which is called the scalar relativistic approximation (SRA), the spin-orbit coupling term appearing in Dirac's equation is dropped; occasionally the minority component of the wave function is also neglected in defining the charge density. We propose here another derivation of the SRA that clarifies the approximations. A simple analytical treatment of the SRA for the hydrogen atom is given, and, as an example of the application of the SRA to the calculation of atomic states, results of self-consistent, local-density calculations for the ytterbium atom are given. The results show that, except for the spin-orbit splitting, relativistic effects (due to the Darwin and mass-velocity terms) are taken into account by the SRA very well.