Removal of forbidden states in a three-$\alpha$ system

Abstract

The ground and excited 0${}^{+}$ states of ${}^{12}$C are investigated in a 3$\alpha$ macroscopic model using the deep potential of Buck, Friedrich and Wheatley. The elimination of forbidden states is performed either by constructing the allowed state space explicitly or by using the orthogonalizing pseudopotential. The well-known enigmatic behavior of the latter approach is resolved. It is safe to define the forbidden states referring to the underlying microscopic model.

arXiv comment18pages, 2figures

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Cited by in corpus (6)

• Global-Vector Representation of the Angular Motion of Few-Particle Systems II
• Local versus nonlocal $\alpha \alpha$ interactions in $3\alpha$ description of ${}^{12}$C
• How the Pauli principle governs the decay of three-cluster systems
• 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