Nilsson model and theU(612)symmetry scheme

The SU(3) limit of the $\mathrm{U}\left(\frac{6}{12}\right)$ boson-fermion symmetry has been studied in detail. By considering the single-particle structure of states, it has been possible to establish a one-to-one relation between bands in the symmetry scheme and those of the Nilsson model arising from the $2p_{\frac{1}{2}}$, $2p_{\frac{3}{2}}$, and $1f_{\frac{5}{2}}$ shell model states. The specific characteristics of the symmetry are shown to be evidenced empirically in the low lying bands of ${}_{}{}^{185}{}_{}{}^{}\mathrm{W}$. Moreover, it is shown that the $\mathrm{U}\left(\frac{6}{12}\right)$ SU(3) symmetry is able to account for the empirical fact of the fragmentation of single particle strength from the higher lying ½[501], $\frac{3}{2}\mathrm{}\left[501\right]\mathrm{}$, and $\frac{5}{2}\mathrm{}\left[503\right]\mathrm{}$ Nilsson bands. The results mentioned above, and also a comparison between the $B\left(E2\right)$ values predicted for the low lying bands in each model, confirm that the interacting boson-fermion approximation Hamiltonian employed incorporates the effects of Coriolis mixing in the Nilsson model. The question of supersymmetry is also discussed.