Gauge dependence of atomic inner-shell transition rates from Dirac-Fock wave functions

Relativistic radiative and radiationless atomic inner-shell transition rates have been calculated with Dirac-Fock wave functions with the use of matrix elements that correspond to different gauges. Radiative rates computed in the length gauge are found to be larger than Coulomb-gauge results; for $K$-shell radiative widths, the difference is ∼20% at $Z=10\mathrm{}$ and falls to ∼4% at $Z=30\mathrm{}$; the difference for $L_2$ radiative widths is a factor of 2 at $Z=18\mathrm{}$ and ∼7% at $Z=48\mathrm{}$. Especially large discrepancies between length- and Coulomb-gauge results are found for $\Delta n=0\mathrm{}$ radiative transition rates. Auger transition rates calculated in the Lorentz and Coulomb gauges agree to better than 1% in all cases tested here; it is inferred that in first-order perturbation theory the Auger rate is practically gauge invariant. Certain general features of the effects of relativity on radiationless transitions are also discussed. These effects can arise from relativistic changes in the transition energies, relativistic orbital effects, and relativistic aspects of the pertinent operators. The relative importance of these factors is evaluated.