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We systematically investigate the existence of exotic torus isomers and theirprecession 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 anddiscuss why the torus shape is generated beyond the limit of large oblatedeformation. We use the cranked three-dimensional Hartree-Fock (HF) method withvarious Skyrme interactions in a systematic search for high-spin torus isomers.We use the three-dimensional time-dependent Hartree-Fock (TDHF) method fordescribing the precession motion of the torus isomer. We obtain high-spin torusisomers in $^{36}$Ar, $^{40}$Ca, $^{44}$Ti, $^{48}$Cr, and $^{52}$Fe. Theemergence of the torus isomers is associated with the alignments ofsingle-particle angular momenta, which is the same mechanism as found in$^{40}$Ca. It is found that all the obtained torus isomers execute theprecession motion at least two rotational periods. The moment of inertia abouta perpendicular axis, which characterizes the precession motion, is found to beclose to the classical rigid-body value. The high-spin torus isomer of$^{40}$Ca is not an exceptional case. Similar torus isomers exist widely innuclei from $^{36}$Ar to $^{52}$Fe and they execute the precession motion. Thetorus shape is generated beyond the limit of large oblate deformation byeliminating the $0s$ components from all the deformed single-particle wavefunctions to maximize their mutual overlaps.

High-spin torus isomers and their precession motions