Exchange and Overlap Effects in Electron Capture and in Related Phenomena

Theoretical expressions are presented for $\frac{L}{K}$ electron capture ratios and electron capture-positron emission ratios that include the effects of electron exchange and imperfect atomic overlap. The role of electron exchange and imperfect atomic overlap in the determination of fluorescence yields is also discussed. In order to facilitate experimental comparisons, numerical values are presented for the exchange and overlap corrections to $\frac{L}{K}$ ratios and electrons capture-positron emission ratios; these correctiosn were calculated with the analytic Hartree-Fock wave functions of Watson and Freeman. The corrected $\frac{L}{K}$ ratios are in good agreement with the precisely measured $\frac{L}{K}$ ratios, showing that overlap and exchange corrections explain the systematic disagreement between the predictions of the usual electron capture theory and experiment.