Prolate-oblate shape competition and impact on charge radii in Bk isotopes

The nuclear charge radius provides a fundamental probe of nuclear structure, yet experimental data remain rare in the actinide region. Using the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) with the PC-PK1 functional, we carry out a systematic investigation of prolate-oblate shape competition in odd-$A$ Bk isotopes. Deformation is found to play an important role in the description of charge radii $r_c$ by extending the density distribution. Notably, $r_c$ exhibits a distinct shape dependence: for a given absolute quadrupole deformation $|\beta_2|$, oblate shapes yield larger charge radii than their prolate counterparts in well-deformed nuclei near the mid-shell region, where the empirical formula $r_c(\beta_2) = \left(1 + \frac{5}{4\pi}|\beta_2|^2\right) r_c(0)$ fails to capture the observed behavior. This enhancement is attributed to a central depression (or ``bubble" structure) in the proton density, which microscopically originates from the non-occupation of the spherical $3s_{1/2}$($\Omega=1/2$) orbital in oblate minima. These findings establish a clear microscopic connection between nuclear shape, single-particle occupancy, and nuclear size.