Analysis of the Low-Lying Level Structure ofSi31

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, $\gamma$-ray multipole mixing ratios, the $\gamma$-ray branching ratio for the 1.70-MeV level, and the $log\mathrm{ft}$ value for $\beta$ decay. The results indicate that ${\mathrm{Si}}^{31}$ is an oblate spheroid with a deformation on the order of $\eta \approx -2.0\mathrm{}$. With the parameters $\kappa \approx 0.10$, $g_R\approx 0.32$, and $\mu \approx 0.2$, 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 $\frac{T\left(E2\mathrm{}\right)\mathrm{}}{T\left(M1\mathrm{}\right)\mathrm{}}$ multipole intensity ratio observed for the 1.70→0-MeV $\gamma$-ray transition.