Effect of Atomic Electron Screening on the Shape of Forbidden Beta Spectra

In Fermi's theory of beta decay the influence of the atomic electrons on the shape of the spectra is often disregarded since the influence is small except at low energies. However, there is some interest in knowing exactly how small it is. This paper gives an approximate calculation of the screening effect, both for allowed and for forbidden spectra. The Thomas-Fermi model for the atomic electrons and WKB approximations for the wave functions of the emitted particles are used. The results for the allowed spectra agree with those of Rose and of Longmire and Brown. The calculations for the forbidden spectra lead to a simple rule for finding the screening effect in any specific case.