$\frac{L}{K}$-Capture Ratio in ${\mathrm{Mn}}^{54}$, ${\mathrm{Fe}}^{55}$, ${\mathrm{Co}}^{57}$, and ${\mathrm{Co}}^{58}$ Decays

The multiwire proportional counter method has been applied to measurements of the $L$ and $K$ radiations arising from orbital electron-capture in gaseous sources of 290-day ${\mathrm{Mn}}^{54}$, 2.6-yr ${\mathrm{Fe}}^{55}$, 270-day ${\mathrm{Co}}^{57}$, and 72-day ${\mathrm{Co}}^{58}$. The presence of gamma transitions and positrons in the decay of ${\mathrm{Mn}}^{54}$, ${\mathrm{Co}}^{57}$, and ${\mathrm{Co}}^{58}$ is shown not to interfere with an accurate measurement of the $\frac{L}{K}$-capture ratio. The experimental values of the $\frac{L}{K}$-capture ratio are 0.098±0.006, 0.106±0.005, 0.099±0.011, and 0.108±0.004 for ${\mathrm{Mn}}^{54}$, ${\mathrm{Fe}}^{55}$, ${\mathrm{Co}}^{57}$, and ${\mathrm{Co}}^{58}$, respectively. The result for ${\mathrm{Fe}}^{55}$ is in excellent agreement with the earlier value measured by Scobie, Moler, and Fink, although the present value has been corrected for counter escape somewhat more exactly. These values lie above the theoretical results of Brysk and Rose by some 9% for ${\mathrm{Mn}}^{54}$, 9.3% for ${\mathrm{Fe}}^{55}$, 7% for ${\mathrm{Co}}^{57}$, and 17% for ${\mathrm{Co}}^{58}$. These discrepancies are reduced by application of the exchange correction pointed out by Bahcall to the theoretical results of Brysk and Rose. This correction for the effect of exchange among the various electrons participating in the electron capture process apparently explains the well-established general discrepancy between the precision experimental values and the theory of Brysk and Rose. Remaining slight discrepancies probably can be traced to systematic experimental errors.