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 $[rY^{1}\vec{l}]^{\lambda=2}t_{+}$ where l is the orbital angular momentum. We also consider the $\lambda =1$ case. For $\lambda=0$, the operator vanishes. Whereas in a $\Delta N=0$ Nilsson model the summed strength is independent of the relative P$_{3/2}$ and P$_{1/2}$ occupancy when we allow for different frequencies $\omega_{i}$ in the x, y, and z directions there is a weak dependency on deformation.