High-spin torus isomers and their precession motions

Abstract

Background: In our previous study, we found that an exotic isomer with a torus shape may exist in the high-spin, highly excited states of $^{40}\mathrm{Ca}$. The $z$ component of the total angular momentum, ${J}_{z}=60\ensuremath{\hbar}$, of this torus isomer is constructed by totally aligning 12 single-particle angular momenta in the direction of the symmetry axis of the density distribution. The torus isomer executes precession motion with the rigid-body moments of inertia about an axis perpendicular to the symmetry axis. The investigation, however, has been focused only on $^{40}\mathrm{Ca}$.Purpose: We systematically investigate the existence of exotic torus isomers and their precession motions for a series of $N=Z$ even-even nuclei from $^{28}\mathrm{Si}$ to $^{56}\mathrm{Ni}$. We analyze the microscopic shell structure of the torus isomer and discuss why the torus shape is generated beyond the limit of large oblate deformation.Method: We use the cranked three-dimensional Hartree-Fock method with various Skyrme interactions in a systematic search for high-spin torus isomers. We use the three-dimensional time-dependent Hartree-Fock method for describing the precession motion of the torus isomer.Results: We obtain high-spin torus isomers in $^{36}\mathrm{Ar},^{40}\mathrm{Ca},^{44}\mathrm{Ti},^{48}\mathrm{Cr}$, and $^{52}\mathrm{Fe}$. The emergence of the torus isomers is associated with the alignments of single-particle angular momenta, which is the same mechanism as found in $^{40}\mathrm{Ca}$. It is found that all the obtained torus isomers execute the precession motion at least two rotational periods. The moment of inertia about a perpendicular axis, which characterizes the precession motion, is found to be close to the classical rigid-body value.Conclusions: The high-spin torus isomer of $^{40}\mathrm{Ca}$ is not an exceptional case. Similar torus isomers exist widely in nuclei from $^{36}\mathrm{Ar}$ to $^{52}\mathrm{Fe}$ and they execute the precession motion. The torus shape is generated beyond the limit of large oblate deformation by eliminating the $0s$ components from all the deformed single-particle wave functions to maximize their mutual overlaps.