We investigate the Gamow-Teller (GT) transition strength distributions in the light carbon isotopes ${}^{12,14,16}\mathrm{C}$ within the framework of the deformed quasiparticle random-phase approximation (DQRPA). Nuclear deformation is explicitly incorporated through Skyrme-Hartree-Fock mean-field calculations combined with the QRPA formalism. The residual particle-hole $\left(\text{p-h}\right)$ and particle-particle $\left(\text{p-p}\right)$ interactions are derived from Brückner $G$-matrix calculations based on the CD-Bonn potential, and their impact on the low-lying GT strengths is systematically examined by varying the corresponding interaction strengths. We find that nuclear deformation, particularly that induced by a reduced spin-orbit strength, plays a significant role in interpreting the GT strength distribution of ${}^{12}\mathrm{C}$. In contrast, the calculated ${\mathrm{GT}}^{(-)}$ strength distribution of ${}^{14}\mathrm{C}$ in the spherical limit reproduces the essential features of the experimental $(p,n)$ charge-exchange data. The case of ${}^{16}\mathrm{C}$ reveals additional high-lying GT strength associated with deformation-induced configuration mixing.

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• Collective levels
• Nuclear structure & decays
• 6 ≤ A ≤ 19
• Nuclear density functional theory