Abstract
This paper presents a consistent field-theoretic perturbative calculation of the Fermi function and the analytical model dependences of corrections to it. The screening, finite nuclear size, and radiative corrections are considered in a unified treatment. We are able to separate out the point-nucleus Fermi function from the corrections, and thus only treat the corrections in a power-series expansion. The proper way of incorporating the radiative correction into is discussed. Detailed analytical results for the model dependence of the finite-nuclear-size and radiative corrections are presented. The most realistic model chosen employs the nuclear charge distributions as given by Hofstadter and the single-particle harmonic-oscillator model for the nuclear matrix elements. The model-dependent results are used to calculate the values of the super-allowed decays of , , , , , , and . The values of the vector coupling constant are calculated for the above nuclei using the most realistic model, and the variation of the is discussed in the light of the predictions of the conserved-vector-current theory of weak interactions.
- Received 1 April 1968
DOI:https://doi.org/10.1103/PhysRev.175.1314
©1968 American Physical Society