Effect of Exchange onMLElectron Capture Ratios

Abstract

Theoretical expressions that include the effect of electron exchange are given for $\frac{M}{L}$ electron-capture ratios; the results are presented in a form that makes clear the physical origin of the exchange corrections. Accurate values for $\frac{M}{L}$ ratios both with and without exchange corrections are tabulated for $Z$ between 13 and 37; these numerical results were calculated using the analytic Hartree-Fock wave functions of Watson and Freeman. The exchange correction for $Z$ greater than or equal to 38 has been estimated by a least squares extrapolation of the correction for lower $Z$ values. The effect of electron exchange on electron capture to positron-emission ratios is also discussed. The exchange-corrected theoretical $\frac{M}{L}$ ratio for ${}_{32}{}^{}{}_{}{}^{}\mathrm{Ge}_{}^{71}{}_{}{}^{}$ is 0.173, in disagreement with the recent measurement of Manduchi and Zannoni. It is suggested that some additional precision measurements of $\frac{M}{L}$ ratios be performed in order to clarify this discrepancy between theory and experiment.