Quasi-doublets in the 3α Spectrum of ¹²C

Within the three-α cluster model of ¹²C, we perform configuration-space Faddeev calculations of the low-lying 0⁺ and 2⁺ states. Resonance states are treated using a variant of the analytic continuation in the coupling constant (ACCC) method. The phenomenological Hamiltonian includes both two-body and three-body interactions. The recently proposed effective-field-theory-motivated leading-order (LO) αα interaction is approximated by a Gaussian-type (LO-simulating) potential to reproduce the experimental α--α scattering phase shifts. The parameters (V,β) of the three-body force, V3bf(ρ) = V exp\![ -1/2 (ρ/β)² ], are determined by fitting the experimental spectrum of ¹²C. We investigate the possibility of a universal set of two- and three-body interactions capable of simultaneously reproducing the energies of lowest 0⁺ or 2⁺ states. For the 2⁺ levels, we find that the condition β > 3 fm must be satisfied for such universality. The ACCC method, combined with the effective-mass approach, reveals level anticrossing and demonstrates coupling between the 0₁⁺ and 0₂⁺ states, as well as between the 2₁⁺ and 2₂⁺ states, which can be interpreted as quasidoublet structures in the 3α spectrum. The calculated results are compared with those obtained using the Ali--Bodmer potentials and the next-to-next-to-leading-order (NNLO) interaction. We find that the LO-simulating potential reduces the strength of the three-body force required to reproduce the low-lying spectrum.