The Effect of Deformation on the Twist Mode

Using ${}^{12}$C as an example of a strongly deformed nucleus we calculate the strengths and energies in the asymptotic (oblate) deformed limit for the isovector twist mode operator $[r{Y}^1\vec{l}{]}^{\lambda =2}{t}_{+}$ where l is the orbital angular momentum. We also consider the $\lambda =1$ case. For $\lambda =0$, the operator vanishes. Whereas in a $\mathrm{\Delta }N=0$ Nilsson model the summed strength is independent of the relative P${}_{3\mathrm{/}2}$ and P${}_{1\mathrm{/}2}$ occupancy when we allow for different frequencies ${\omega }_i$ in the x, y, and z directions there is a weak dependency on deformation.