Shell structure and shape transition in odd-$Z$ superheavy nuclei with proton numbers $Z=117$, 119: Insights from applying deformed relativistic Hartree-Bogoliubov theory in continuum

We present a systematic study on the structural properties of odd-$Z$ superheavy nuclei with proton numbers $Z=117,119$, and neutron numbers $N$ increasing from $N=170$ to the neutron dripline within the framework of axially deformed relativistic Hartree-Bogoliubov theory in continuum. The results are compared with those of even-even superheavy nuclei with proton numbers $Z=118$ and 120. We analyze various bulk properties of their ground states, including binding energies, quadrupole deformations, root-mean-square radii, nucleon separation energies, and $\alpha$-decay energies. The coexistence of competing prolate and oblate or spherical shapes leads to abrupt changes in both quadrupole deformations and charge radii as functions of neutron numbers. Compared to even-even nuclei, the odd-mass ones exhibit a more complicated transition picture, in which the quantum numbers of $K^{\pi }$ of the lowest-energy configuration may change with deformation. This may result in the change of angular momentum in the ground-state to ground-state $\alpha$ decay and thus quench the decay rate in odd-mass nuclei. Moreover, our results demonstrate a pronounced proton shell gap at $Z=120$, instead of $Z=114$, which is consistent with the predictions of most covariant density functional theories. Besides, large neutron shell gaps are found at $N=172$ and $N=258$ in the four isotopic chains, as well as at $N=184$ in the light two isotopic chains with $Z=117$ and $Z=118$, attributed to the nearly degenerate $3d$ and $4p$ spin-orbit doublet states due to the presence of bubble structure.