CI. The effect of a finite nucleus on beta-Decay

Abstract

Relativistic wave functions are derived for the electron in a potential field which is constant within the nucleus and Coulombian outside. The relative values of the cut-off wave-functions and the pure Coulomb wave-functions are calculated both for the discrete and continuous spectrum. The changes thereby produced in the probability of orbital electron-capture, in the continuous Beta-spectrum and in the ratio of probabilities of K-capture to positron emission are examined. It is concluded that for the heavier nuclei the probability of K-capture and the ratio of the probabilities of K-capture to positron emission are appreciably affected. The modifications produced in the continuous spectrum are greatest for spin change equal to n where n(n>1) is the degree of forbiddenness of the transition. In this case the coefficients of the squares and products of matrix elements given in the correction factors of Konopinski and Uhlenbeck are appreciably changed. Therefore for given values of the matrix elements the spectrum is modified.