Relativistic Corrections to the Dipole Sum Rule

The summed oscillator strength is calculated to order ${\left(\frac{v}{c}\right)}^2$ for a Dirac electron in a central force field. The result ${(1+T_{00})}^{-1\mathrm{}}$ 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.