Effect of the Finite Nuclear Size on Internal Conversion

It is shown that the finite nuclear size introduces additional nuclear matrix elements into the expression for the rate of internal-conversion-electron ejection which are distinctly different from that for gamma-ray emission of the same multipole order. To illustrate the effect of these new matrix elements, the correction to the $K$-conversion coefficient of magnetic-dipole transitions is calculated. It is shown that in cases where the gamma-ray matrix element is attenuated (e.g., $l$-forbidden $M1\mathrm{}$ transitions and the $M1\mathrm{}$ components in odd-$A$ rotational transitions), the new nuclear matrix elements may lead to appreciable deviations between the experimentally measured $K$-shell conversion coefficient and the theoretical calculations of Sliv. The conversion coefficients of other electric and magnetic transitions are also affected by the introduction of the new matrix elements, as well as angular-correlation measurements involving the conversion electrons.