Relativistic Corrections to the Dipole Sum Rule

Abstract

The summed oscillator strength is calculated to order ${(\frac{v}{c})}^{2}$ for a Dirac electron in a central force field. The result ${(1+{T}_{00})}^{\ensuremath{-}1}$ is interpreted in terms of the electron's increase of mass due to its kinetic energy. (${T}_{00}$ is the expectation value of the kinetic energy, in units of ${\mathit{mc}}^{2}$.) This analytical result is in fair agreement with our earlier numerical result, and those of Brown et al. for a $K$ electron of lead. We also calculate the bremsstrahlung-weighted cross section for a Dirac electron in a Coulomb field, and compare with our numerical result for lead.