Relativistic Corrections in the Theory ofK-Electron Ejection DuringKCapture

Abstract

The momentum spectrum of the $K$ electrons ejected during allowed $K$-capture decay is calculated for the case in which there is no competing positron emission. It is shown that certain relativistic effects, associated with the spin of the electron, are important in determining the ejected-electron spectrum, even at low energies. To take these effects into account, the electronic states are described by the solutions of an approximate Dirac Hamiltonian developed by Biedenharn and Swamy. Preliminary to the calculation, both the eigenfunctions and Green's function of this Hamiltonian are discussed. The results of the calculation differ appreciably from previous nonrelativistic calculations. Contrary to these previous theories, the theory presented here is shown to be in good agreement with recent experimental observations.