A simple potential model for estimates of exchange effects in electron capture decay

Abstract

In a central field description the use of hydrogen wavefunctions for computation of exchange and overlap integrals can be justified as long as relative potential changes are small. The simple procedure leads to linear and quadratic forms, respectively, in the relative potential changes Delta Z/Z from the initial to the final state of the orbitals. Bahcall factors Bn are derived which only contain potential ratios of the nth orbital to the 1s orbital in first order and the relative potential alteration of the nth orbital during the electron capture (EC) process. Their contribution to the variation of the EC decay constant lambda epsilon leads to mod ( Delta lambda epsilon / lambda epsilon )Delta B mod approximately=0.2/Z2 for a single charge ionisation of an element (or ion) of atomic number Z. As far as it is justified to model chemical variations in a single-centre consideration by statistical occupation number changes in the valence shell, this allows an estimate of possible disturbances in the interpretation of lambda epsilon variations in terms of electron density variations near the nucleus and thus of contributions to Mossbauer isomer shift calibration from this method.