Variational Calculations of the ${}^{12}C$ Nucleus Structure in a 3$\alpha$ Model Using a Deep Potential with Forbidden States

Abstract

The energy spectrum of the ${}^{12}C$ nucleus with $(J^{\pi },T)=(0^{+},0)$ and $(2^{+},0)$ is investigated in the framework of the multicluster dynamical model by using a deep $\alpha \alpha$-potential with forbidden states in the S and D waves. A very high sensitivity of the compact ground and first excited $2_1^{+}$ states energy levels to the description of the two-body forbidden states wave functions has been estabilished. It is shown also that the chosen method of orthogonalizing pseudopotentials yields convergent results for the energies of the excited $(0_2^{+},0)$ and $(0_3^{+},0)$ states of the ${}^{12}C$ nucleus with a well developed cluster like structure.