Peculiarity of the C-12(0(+)) and C-12(2(+)) Energy Spectrum in a 3 alpha Model

摘要

Lowest energy spectrum of the C-12 nucleus is analyzed in the 3 alpha-cluster model with a deep as 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 3a Pauli forbidden states. The effects of possible first order quantum phase transition are shown in the lowest C-12(0(1)(+)) and C-12(2(1)(+)) states from weakly bound phase to a deep phase. The ground and lowest 2(+) states of the C-12 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.