M-Shell Electron Contribution to Orbital Electron Capture

The probability per unit time for capture of an electron from the $M$ shell is calculated by means of the method used by Brysk and Rose for capture from the $L$ and $K$ shells. In addition, the calculations for $L$ and $K$ shells are extended to give the results for third forbidden and third forbidden unique transitions. These calculations indicate that, at least in the case of unique forbidden transitions, the $\frac{M}{L}$ ratio exceeds 20% for all values of transition energy. The possibility of determining nuclear mass differences, order of forbiddenness of a transition, and numerical values for ratios of the nuclear matrix elements from experimental values of $\frac{M}{L}$ is discussed. This last procedure is applied to the determination of the nuclear matrix elements of ${}_{76}{}^{}{}_{}{}^{}\mathrm{Os}_{}^{185}{}_{}{}^{}$.