Internal Conversion Coefficients: General Formulation for all Shells and Application to Low-Energy Transitions

Exact analytical results (in the case of a point nucleus with no screening) for the internal conversion coefficients for any shell are presented. These results simplify considerably at threshold values of the gammaray energy. Numerical results, at threshold, are obtained for the $K$, $L(L_{\mathrm{I}},L_{\mathrm{II}},L_{\mathrm{III}})$ and $M(M_{\mathrm{I}},M_{\mathrm{II}},M_{\mathrm{III}},M_{\mathrm{IV}},M_{\mathrm{V}})$ shells, for 19 values of $Z$ in the range $5<~Z<~95$, and for the first five electric and magnetic multipoles. The results for the $K$ shell agree with those obtained by Spinrad. It is shown that the theshold results are actually correct to order $P$ (momentum of electron in units of its mass). The effects of finite nuclear size are also considered.