Abstract
Strongly deformed oblate superheavy nuclei form an intriguing region
where the toroidal nuclear structures may bifurcate from the oblate
spheroidal shape. The bifurcation may be facilitated when the nucleus
is endowed with a large angular moment about the symmetry axis with
$I=I_{z}$. The toroidal high-$K$ isomeric states at their local
energy minima can be theoretically predicted using the cranked
self-consistent Skyrme-Hartree-Fock method. We use the cranked
Skyrme-Hartree-Fock method to predict the properties of the toroidal
high-spin isomers in the superheavy nucleus $^{304}{120}_{184}$. Our
method consists of three steps: first, we use the
deformation-constrained Skyrme-Hartree-Fock-Bogoliubov approach to
search for the nuclear density distributions with toroidal
shapes. Next, using these toroidal distributions as starting
configurations we apply an additional cranking constraint of a large
angular momentum $I=I_{z}$ about the symmetry $z$-axis and search for
the energy minima of the system as a function of the deformation. In
the last step, if a local energy minimum with $I=I_{z}$ is found, we
perform at this point the cranked symmetry- and
deformation-unconstrained Skyrme-Hartree-Fock calculations to locate a
stable toroidal high-spin isomeric state in free convergence. We have
theoretically located two toroidal high-spin isomeric states of
$^{304}{120}_{184}$ with an angular momentum $I$=$I_z$=81$\hbar$
(proton 2p-2h, neutron 4p-4h excitation) and $I$=$I_z$=208$\hbar$
(proton 5p-5h, neutron 8p-8h) at the quadrupole moment deformations
$Q_{20}=-297.7$~b and $Q_{20}=-300.8$~b with energies 79.2 MeV and
101.6 MeV above the spherical ground state, respectively. The nuclear
density distributions of the toroidal high-spin isomers
$^{304}{120}_{184}(I_z$=81$\hbar$ and 208$\hbar$) have the maximum
density close to the nuclear matter density, 0.16 fm$^{-3}$, and a
torus major to minor radius aspect ratio $R/d=3.25$. We demonstrate
that aligned angular momenta of $I_z$=81$\hbar$ and 208$\hbar$ arising
from multi-particle-multi-hole excitations in the toroidal system of
$^{304}{120}_{184}$ can lead to high-spin isomeric states, even though
the toroidal shape of $^{304}120_{184}$ without spin is unstable.
Toroidal energy minima without spin may be possible for superheavy
nuclei with higher atomic numbers, $Z\gtrsim$122, as reported
previously [A. Staszczak and C. Y. Wong,Acta Phys. Pol. B 40 , 753
(2008)].
