Mutual Correlations of Pairing Correlations, Spin-Orbit Interaction, and Deformation Effects for the Ground State of 12C

Abstract

The intrinsic structure of C-12 remains a longstanding challenge in self-consistent mean-field approaches, as different density functional theory calculations predict either spherical or deformed ground-state configurations. In this work, we investigate the interplay between the spin-orbit interaction, pairing correlations, and quadrupole deformation in C-12 within the Skyrme-Hartree-Fock-Bogoliubov framework. By systematically varying the strengths of the spin-orbit interaction and the pairing interaction, we analyze the evolution of potential energy curves, single-particle shell structure, and occupation probabilities. For the normal spin-orbit strength, the spherical configuration remains remarkably robust against variations in the pairing strength. When the spin-orbit interaction is reduced, the shell structure around the Fermi surface becomes softened, allowing pairing correlations to play a decisive role in stabilizing an oblate intrinsic shape. These results demonstrate that, in C-12 , the spin-orbit interaction controls the onset of deformation, whereas pairing correlations determine whether deformation is realized. It means that Gamow-Teller transition strengths might be highly sensitive to these structural changes and thus provide a valuable probe of the underlying intrinsic configuration.