Effect of deformation on the twist and other dipole modes

Abstract

The dependence on deformation of the isovector twist mode $([{\mathrm{rY}}^{1}\stackrel{\ensuremath{\rightarrow}}{l}{]}^{\ensuremath{\lambda}=2}{t}_{+})$ is investigated. We calculate the strengths and energies in the asymptotic (oblate) limit using ${}^{12}\mathrm{C}$ as an example of a strongly deformed nucleus. We also consider the $\ensuremath{\lambda}=1$ case. In a $\ensuremath{\Delta}N=0$ Nilsson model the summed strength is independent of the relative ${P}_{3/2}$ and ${P}_{1/2}$ occupancy but when we allow for different frequencies ${\ensuremath{\omega}}_{i}$ in the x, y, and z directions there is an enhancement of this strength due to deformation. This dependence is stronger than that for the ordinary dipole mode but much weaker than that for the scissors mode. At the same time, it is observed that there are considerable changes in the spectrum and that the strength is strongly fragmented amongst these disparate levels. We further show that in this model the associated spin mode $[{\mathrm{rY}}^{1}\stackrel{\ensuremath{\rightarrow}}{s}{]}^{\ensuremath{\lambda}}{t}_{+}$ has a weaker dependence on deformation and is less fragmented than the twist mode.