Electron-Neutrino Angular Correlation

Angular correlation functions are calculated for allowed and first forbidden beta-decay transitions including the effect of the nuclear coulomb field. The process of beta-decay is viewed as a kind of scattering in which an incident negative energy neutrino is transformed by the Fermi interaction in to scattered electron in a positive energy state. The outgoing electronic wave function is calculated, and the angular correlation functions are determined from the angular dependent electron probability current through sections of a sphere at large distances from the nucleus. For allowed transitions, the angular correlation is found to be independent of atomic number and identical with the results of previous calculations which assumed $Z=0\mathrm{}$. The $Z=0\mathrm{}$ approximation is shown to be unreliable for first forbidden transitions in which correlation terms proportional to the first and second powers of the potential energy of an electron at the surface of the nucleus appear. This effect is important even for moderately heavy nuclei.