Beta-Gamma Correlations and Matrix Elements for Some First-Forbidden Nonunique Beta Transitions

Results of $\beta -\gamma$ directional-correlation measurements in the nonunique first-forbidden $\beta$ decay of the ground states of several odd-odd nuclei (${\mathrm{Sb}}^{124}$, ${\mathrm{Eu}}^{152}$, ${\mathrm{Re}}^{186}$, ${\mathrm{Tm}}^{170}$, ${\mathrm{Rb}}^{84}$) to the first $2^{+}$ levels in the even-even daughter nuclei are presented. These measurements were made as a function of the $\beta$-ray energy using a small shaped-field magnetic spectrometer. The results, in combination with all other available experimental data on each $\beta$ transition, have been analyzed to obtain the nuclear matrix element parameters. The analysis is based on the theoretical expressions given by Morita and Morita using exact electron radial wave functions which include finite nuclear size corrections. In addition, we have analyzed all available experimental data for the nonunique first-forbidden $\beta$ decay of ${\mathrm{Re}}^{188}$ and ${\mathrm{Rb}}^{86}$. A unique set of parameters was found for ${\mathrm{Re}}^{186}$, ${\mathrm{Re}}^{188}$, and ${\mathrm{Tm}}^{170}$ although the set for ${\mathrm{Tm}}^{170}$ suffers from a lack of adequate experimental information. For ${\mathrm{Rb}}^{86}$, the matrix element sets depend on whether the shape of the $\beta$ spectrum is statistical or not. For ${\mathrm{Rb}}^{84}$, five distinct sets of parameters were found which fit all available data equally well. For both ${\mathrm{Sb}}^{124}$ and ${\mathrm{Eu}}^{152}$, two sets of parameters were found that fit the data equally well; however, it is shown that a measurement of the $\beta$-circularly-polarized $\gamma$ correlation as a function of energy can eliminate one set in each case. Appropriate discussions based on nuclear models are given.