Higher Order Effects inβ−γCorrelations Involving AllowedβTransitions

Higher order effects in allowed $\beta$ transitions may be generated by the interference of the allowed Gamow-Teller components with second-forbidden components. In strongly hindered $\beta$ transitions, this interference effect is expected to give rise to $\beta -\gamma$ directional correlations with measurable anisotropies. The $\beta -\gamma$ directional correlations of the hindered allowed $\beta$ transition ($log\mathrm{ft}>\mathrm{}8\mathrm{}$) in the deformed nuclei ${\mathrm{Eu}}^{152}$, ${\mathrm{Eu}}^{154}$, and ${\mathrm{Tb}}^{160}$ were studied. The $\beta$-correlation factor $A_2^{}{}_{}{}^{\beta }$, which characterizes the $\beta$ transition in the expression for the $\beta -\gamma$ directional correlation $W\left(\theta \right)=1+A_2^{}{}_{}{}^{\beta }A_2^{}{}_{}{}^{\gamma }{P}_2\left(cos\theta \right)$, was found to be vanishingly small in all cases, except that of ${\mathrm{Tb}}^{160}$. The results are: $A_2^{}{}_{}{}^{\beta }=-0.017\mathrm{}\pm 0.012$ for the 0.70-MeV $\beta$ transition of ${\mathrm{Eu}}^{152}(logft=10.6)$; $A_2^{}{}_{}{}^{\beta }=+0.016\mathrm{}\pm 0.020$ for the 0.20-MeV $\beta$ transition of ${\mathrm{Eu}}^{152}(logft=9.6)$; $A_2^{}{}_{}{}^{\beta }=0.007\mathrm{}\pm 0.006$ for the 0.58-MeV $\beta$ transition of ${\mathrm{Eu}}^{154}(logft=10.0)$; and $A_2^{}{}_{}{}^{\beta }=+0.041\mathrm{}\pm 0.015$ for the 0.566-MeV $\beta$ transition of ${\mathrm{Tb}}^{160}(logft=8.1)$. A summary of $\beta -\gamma$ directional correlation measurements on allowed $\beta$ transitions is presented and the implications of the results are discussed. In most cases the experimental results suggest that the effects that cause the reduction of the allowed matrix elements are also operative in reducing the second-forbidden matrix elements.