Electron polarization in beta decay and internal conversion
Young, Robert C.
Doctor of Philosophy
The general theory for beta decay is developed in section 2 using a consistent normalization and phase convention for the lepton wave functions; these phases are not consistent in the literature. The resulting general expression is specialized in section 3 to the case of beta polarization; that is, the nucleus is assumed randomly oriented before and after the transition, and no information is available on the direction of motion of the neutrino. In section 4, the functions needed to calculate the polarization are expanded in powers of the nuclear radius, without using the low-Z approximation. Formulas for these combinations of the electron wave functions are given (for the spectrum) more generally than they have previously appeared; those needed for the polarization have not been given accurately before. In terms of these combinations, expressions for the spectrum and polarization terms of the transition probability are presented, through second forbidden transitions. Somewhat simplified expressions, but retaining more accuracy than the usual low-Z formulas, are also given for the allowed and first forbidden transitions. The results of a numerical evaluation of the spectrum and polarization are compared in section 5 with the low-Z approximate values. These approximate values for the polarization are found to be extremely good, even when the results for the spectrum differ by a factor of two! The expression for the polarization is a ratio of similar terms, and the higher coulomb corrections cancel nearly completely. The effect of the coulomb field on the forbiddenness expansion is considered in section 6, and the application of polarization measurements to tests of time reversal is discussed.