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

TL;DR

This study uses advanced nuclear theory to explore how prolate and oblate shapes in Bk isotopes affect charge radii, revealing shape-dependent size differences linked to proton density structures.

Contribution

It provides a microscopic explanation for shape-dependent charge radii in Bk isotopes, highlighting the role of specific orbital occupations and density distributions.

Findings

Oblate shapes have larger charge radii than prolate shapes at similar deformation.

Charge radii are influenced by central proton density depressions ('bubbles').

The empirical formula for charge radii fails near mid-shell nuclei.

Abstract

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.