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

The energy spectrum of the $^{12}C$ nucleus with $(J^π, T)=(0^+,0)$ and $(2^+,0)$ is investigated in the framework of the multicluster dynamical model by using a deep $αα$-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.

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