Charge radii of calcium isotopes within relativistic configuration-interaction density functional theory

The charge radii of calcium isotopes are investigated within the framework of relativistic configuration-interaction density functional (ReCD) theory. The ReCD theory microscopically incorporates beyond-mean-field correlations through rotational symmetry restoration and configuration mixing among quasiparticle excited states, and treats even-even and odd-$A$ isotopes on the same footing. It is found that beyond-mean-field correlations significantly soften the potential energy surfaces of calcium isotopes and shift the energy minima from nearly spherical mean-field solutions to deformed shapes. The quadrupole deformation parameters predicted by the ReCD theory show much better agreement with the available experimental data than the mean-field results, supporting the reliability of the calculated potential energy surfaces and highlighting the important role of beyond-mean-field correlations. Owing to the sensitive dependence of charge radii on nuclear deformation, the charge radii obtained within the ReCD framework are generally larger than the mean-field predictions. The nearly identical charge radii of $^{40}\mathrm{Ca}$ and $^{48}\mathrm{Ca}$, as well as the unexpectedly large charge radius of $^{52}\mathrm{Ca}$, are well reproduced. Compared with the mean-field calculations, the description of the odd-even staggering is improved, especially for the enhanced charge radii of $^{42}\mathrm{Ca}$ and $^{44}\mathrm{Ca}$. It is also worth noting that secondary local minima appear in the ReCD-based potential energy surfaces of the odd-$A$ calcium isotopes $^{41,43,47}\mathrm{Ca}$. The present results suggest that shape mixing between different local minima, which is not fully included in the present calculation, may further improve the description of the pronounced odd-even staggering observed in calcium isotopes.