Formulas in the Fermi Theory of Beta Decay. II

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Abstract
Our previous work on beta spectrum, which has taken into account the finite charge distribution of the nucleus and the screening effect, is extended to the beta ray angular correlation. Formulas are given for the allowed and the first forbidden beta-gamma angular correlations including polarization of the gamma ray, and the second forbidden beta-gamma directional correlation, where we assume the mixed interaction of vector and axial vector types (VA) and the non-conservation of parity in beta decay. Since these formulas for the allowed and the first forbidden transitions have already been given by Morita (M.) and Morita (R. S.) for the case of the point unclear charge, we only rewrite them in this paper. If we use the effective radii theory again, our final formulas can be expressed in forms similar to the familiar expressions for light nuclei in the usual formulations. The deviations of the coefficients from the usual ones are graphically shown as functions of beta ray energies for Z=±10, ±30, ±50, ±70 and Z=±90 (for β\mp-decay), and significant deviations are found for heavy nuclei except for the allowed transition. Those are especially significant for the non-unique first forbidden, and the unique first and second forbidden transions (several ten percents for Z∼90). One of the important results is that our theory is again insensitive to the nuclear charge distributions.

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