Structure of Low-Lying2+States in Even-Even Nuclei and Beta-Gamma Angular Correlations

The ground states with spin $2^{-}$ of the odd-odd nuclei decay into those of the even-even nuclei through several channels, $2^{-}\stackrel{{\beta }_1}{\to }{0}^{+}$, $2^{-}\stackrel{{\beta }_2}{\to }{2}^{+}\stackrel{\gamma }{\to }{0}^{+}$, etc. In the $2^{-}\stackrel{{\beta }_2}{\to }{2}^{+}$ transition, all first forbidden matrix elements other than $B_{\mathrm{ij}}$ are reduced in magnitude from their normal values, if the $j$ selection rule of the $j-j$ coupling shell model or the $K$ selection rule of the rotational excitation in the collective model is realized in the main configurations of states $2^{-}$ and $2^{+}$. In such a case, the present theory distinguishes whether the ${\beta }_2$ decay obeys the $j$ selection rule or the $K$ selection rule. Furthermore, if the $j$ selection rule holds, the theory gives the configuration of the low-lying $2^{+}$ state. This is done by combining the data on ${\beta }_2-\gamma$ directional correlations and branching ratio of ${\beta }_1$ and ${\beta }_2$, with the calculated value for $\frac{{\left(\int B_{\mathrm{ij}}\right)}_1}{{\left(\int B_{\mathrm{ij}}\right)}_2}$ which is nuclear-model dependent. The first excited $2^{+}$ states in ${\mathrm{Se}}^{76}$, ${\mathrm{Sr}}^{86}$, ${\mathrm{Te}}^{122}$, and ${\mathrm{Xe}}^{126}$ are studied in comparison with available data on beta decays of ${\mathrm{As}}^{76}$, ${\mathrm{Rb}}^{86}$, ${\mathrm{Sb}}^{122}$, and