First-Forbidden Transitions in Parity-Nonconserving Beta Decay

Abstract

Our previous work on beta-gamma directional correlations is extended to phenomena of nonconservation of parity in beta decay. The parameters, ${{b}_{L{L}^{\ensuremath{'}}}}^{(n)}$, which express the beta-ray angular distributions, are given for first-forbidden transitions of a general interaction, $\mathrm{STPVA}$, where we assume no interferences between $\mathrm{STP}$ and $\mathrm{VA}$. All of the possible interferences among the six nuclear matrix elements, $\mathfrak{M}(\ensuremath{\beta}\ensuremath{\sigma}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{r})$, $\mathfrak{M}(\ensuremath{\beta}{\ensuremath{\gamma}}_{5})$, $\mathfrak{M}(\ensuremath{\beta}\mathrm{r})$, $\mathfrak{M}(\ensuremath{\beta}\ensuremath{\alpha})$, $\mathfrak{M}(\ensuremath{\beta}\ensuremath{\sigma}\ifmmode\times\else\texttimes\fi{}\mathrm{r})$, and $\mathfrak{M}({{B}_{\mathrm{ij}}}^{\ensuremath{\beta}})$ for $\mathrm{STP}$ (and the corresponding matrix elements for $\mathrm{VA}$) are taken into account. By using these ${{b}_{L{L}^{\ensuremath{'}}}}^{(n)}'\mathrm{s}$, it is easy to express the correction factor of beta spectra, the beta-ray angular distributions from oriented nuclei, and the angular correlations between beta rays and circularly polarized gamma rays from unoriented nuclei in double and triple cascade transitions. The experimental data on the beta decays of ${\mathrm{Sb}}^{124}$ and ${\mathrm{Au}}^{198}$ are analyzed.