Ground-state properties and structure evolutions of odd-$A$ transuranium Bk isotopes from deformed relativistic Hartree-Bogoliubov theory in continuum

Abstract: The studies of transuranium nuclei are of vital significance in exploring the existence of the ``island of superheavy nuclei". This work presents the systematic investigations for the ground-state properties and structure evolutions of odd-$A$ transuranium Bk isotopes taking the deformed relativistic Hartree-Bogoliubov theory in continuum~(DRHBc) with PC-PK1 density functional, in comparison with those by spherical relativistic continuum Hartree-Bogoliubov~(RCHB) theory. The DRHBc calculations offer improved descriptions of the binding energies, closely aligning with the experimental data. The incorporation of deformation effects in DRHBc results in enhanced nuclear binding energies and a notable reduction in $\alpha$-decay energies. With the rotational corrections further incorporated, the theoretical deviation by DRHBc from the experimental data is further reduced. Based on the two-neutron gap $\delta_{\rm 2n}$ and the neutron pairing energy $E_{\rm pair}^n$, prominent shell closures at $N=184$ and $258$, as well as potential sub-shell structures at $N=142, 150, 162, 178, 218$, and $230$ are exhibited. A quasi-periodic variation among prolate, oblate, and spherical shapes as well as prolate deformation predominance have been shown in the evolutions of the quadrupole deformation. Possible shape coexistence is predicted in $^{331}$Bk with the oblate and prolate minima in close energies, which is further supported by the triaxial relativistic Hartree-Bogoliubov theory in continuum~(TRHBc) calculations. The neutron, proton, and charge radii predicted by DRHBc reveal pronounced kink structures at $N=184$ and $258$ in their evolutions with neutron number and compared to those by RCHB, deformation effect significantly enhances the radii of open-shell nuclei.