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.

Cited by in corpus (9)

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• Local versus nonlocal $\alpha \alpha$ interactions in $3\alpha$ description of ${}^{12}$C
• Comparative variational studies of $0^{+}$ states in three-$\alpha$ models
• Breaking and restoration of rotational symmetry on the lattice for bound state multiplets
• Removal of forbidden states in a three-$\alpha$ system
• The role of the Pauli principle in three-cluster systems composed of identical clusters
• Peculiarity of the ${}^{12}$C$(0^{+})$ and ${}^{12}$C$(2^{+})$ energy spectrum in a 3$\alpha$ model
• Spatial Structure of the ${}^{12}$C Nucleus in a 3$\alpha$ Model with Deep Potentials Containing Forbidden States
• On the Spectrum of the Many-Body Pauli Projector