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arXiv · 2001.08995

Peculiarity of the $^{12}$C$(0^+)$ and $^{12}$C$(2^+)$ energy spectrum in a 3$\alpha$ model

E. M. Tursunov·I. Mazumdar
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Abstract

Lowest energy spectrum of the $^{12}$C nucleus is analyzed in the 3$\alpha$ cluster model with a deep $\alpha\alpha$-potential of Buck, Friedrich and Wheatley with Pauli forbidden states in the $S$ and $D$ waves. The direct orthogonalization method is applied for the elimination of the 3$\alpha$-Pauli forbidden states. The effects of possible first order quantum phase transition are shown in the lowest $^{12}$C($0_1^+)$ and $^{12}$C($2_1^+)$ states from weakly bound phase to a deep phase. The ground and lowest $2^+$ states of the $^{12}$C nucleus in the deep phase are created by the critical eigen states of the Pauli projector for the $0^+$ and $2^+$ three-alpha functional spaces, respectively.

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E. M. Tursunov, I. Mazumdar. 2020-01-24. Peculiarity of the $^{12}$C$(0^+)$ and $^{12}$C$(2^+)$ energy spectrum in a 3$\alpha$ model. https://doi.org/10.1134/s1063778822020090

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