Abstract
The $\frac{M}{L}$ and $\frac{L}{K}$ orbital-electron-capture ratios in the decay of $^{55}\mathrm{Fe}$ have been determined by introducing the radioactive compound ferrocene-$^{55}\mathrm{Fe}$ into a multiwire, wall-less anticoincidence proportional counter as part of the counting gas mixture. The results are $\frac{{P}_{M}}{{P}_{L}=0.157\ifmmode\pm\else\textpm\fi{}0.003}$ and $\frac{{P}_{L}}{{P}_{K}}=0.117\ifmmode\pm\else\textpm\fi{}0.001$ at $Z=26$. These values are compared with various theoretical predictions and, together with previous experimental results on $\frac{M}{L}$ capture ratios at low $Z$, they demonstrate that of all the combinations of theoretical approaches, the Watson-Freeman wave functions with the exchange corrections of Vatai are the only ones which give good agreement with experiment at low $Z$. All other theoretical combinations lie considerably higher than experiment in the region below $Z=36$.
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