High-spin torus isomers and their precession motions

Abstract

We systematically investigate the existence of exotic torus isomers and their precession motions for a series of $N=Z$ even-even nuclei from ${}^{28}$Si to ${}^{56}$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. We use the cranked three-dimensional Hartree-Fock (HF) method with various Skyrme interactions in a systematic search for high-spin torus isomers. We use the three-dimensional time-dependent Hartree-Fock (TDHF) method for describing the precession motion of the torus isomer. We obtain high-spin torus isomers in ${}^{36}$Ar, ${}^{40}$Ca, ${}^{44}$Ti, ${}^{48}$Cr, and ${}^{52}$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 ${}^{40}$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. The high-spin torus isomer of ${}^{40}$Ca is not an exceptional case. Similar torus isomers exist widely in nuclei from ${}^{36}$Ar to ${}^{52}$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.