K shell internal conversion coefficients at threshold

Abstract

Coulomb field effects on K shell internal conversion coefficients for threshold values of the gamma-ray energy are investigated using exact wave functions to describe both the bound and the continuum state electrons. Exact results for the internal conversion coefficients are obtained in terms of gamma functions and confluent hypergeometric functions. To facilitate numerical evaluation, the exact result is expanded in a series in αZ and the first three terms of this series are retained. The dominant terms are identical to the expressions obtained by Drell and by Dancoff and Morrison, in the non-relativistic approximation. Terms of order αZ times the dominant term are shown to be zero but the α 2 Z 2 corrections to the non-relativistic results are seen to bring the analytical results into closer agreement with the numerical results of Spinrad. The effects of finite nuclear size and screening are also considered.