Analysis of the Low-Lying Level Structure ofSi31

Abstract

The strong-coupling collective model has been applied to the low-lying level structure of ${\mathrm{Si}}^{31}$. Two rotational bands are identified corresponding to the Nilsson orbits 8 ($K=\frac{3}{2}$) and 9 ($K=\frac{1}{2}$), with the ground and first excited (760-keV) levels being the respective bandheads. Detailed comparisons are made concerning the properties of the low-lying levels, such as spectroscopic factors for neutron capture, $\ensuremath{\gamma}$-ray multipole mixing ratios, the $\ensuremath{\gamma}$-ray branching ratio for the 1.70-MeV level, and the $log\mathrm{ft}$ value for $\ensuremath{\beta}$ decay. The results indicate that ${\mathrm{Si}}^{31}$ is an oblate spheroid with a deformation on the order of $\ensuremath{\eta}\ensuremath{\approx}\ensuremath{-}2.0$. With the parameters $\ensuremath{\kappa}\ensuremath{\approx}0.10$, ${g}_{R}\ensuremath{\approx}0.32$, and $\ensuremath{\mu}\ensuremath{\approx}0.2$, the model is found to give reasonable results for many of the above properties. In particular, the model is found to predict the anomalously high $\frac{T(E2)}{T(M1)}$ multipole intensity ratio observed for the 1.70\ensuremath{\rightarrow}0-MeV $\ensuremath{\gamma}$-ray transition.