Ground-state properties and structure evolutions of odd-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>A</mml:mi></mml:math> transuranium Bk isotopes from deformed relativistic Hartree-Bogoliubov theory in continuum

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 $\mathrm{odd}\text{\ensuremath{-}}A$ 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 $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{decay}$ 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 ${\ensuremath{\delta}}_{2\mathrm{n}}$ and the neutron pairing energy ${E}_{\mathrm{pair}}^{n}$, prominent shell closures at $N=184$ and 258, as well as potential subshell structures at $N=142,150,162,178,218$, and 230 are exhibited. A quasiperiodic 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 $^{331}\mathrm{Bk}$ 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.