Nuclear size effects and Coulomb corrections are included in the expression for the electron capture rate $R_{\epsilon }$ by using the "elementary-particle" approach of Armstrong and Kim. As an example, we use our result together with the corresponding expression for the positron emission rate $R_{{\beta }^{+}}$ to compute $\frac{R_{\epsilon }}{R_{{\beta }^{+}}}$ for certain ${\frac{1}{2}}^{+}\to {\frac{1}{2}}^{+}$ and ${\frac{1}{2}}^{+}\to {\frac{3}{2}}^{+}$ transitions in Gd. Our ratios are in good agreement with conventional impulse-approximation calculations and for a wide range of nuclear parameters, do not exhibit the anomalies seen experimentally.

RADIOACTIVITY Finite size and Coulomb corrections to electron capture and $\beta$-decay calculations.

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