Monopole transition strength function of ${}^{12}$C in three-$\alpha$ model

Abstract

The energy level structure of ${}^{12}$C nucleus at a few MeV above the three-$\alpha$ threshold is still unsatisfactory known. For instance, most microscopic calculations predicted that there exist one $0^{+}$-state in this energy region besides the well known Hoyle state, while some experimental and theoretical studies show the existing of two $0^{+}$-states. In this paper, I will take a three-$\alpha$-boson (3$\alpha$) model for bound and continuum states in ${}^{12}$C, and study a transition process from the ${}^{12}$C($0_1^{+}$) ground state to 3$\alpha$ $0^{+}$ continuum states by the electric monopole ($E0$) operator. The strength distribution of the process will be calculated as a function of $3\alpha$ energy using the Faddeev three-body theory. The Hamiltonian for the $3\alpha$ system consists of two- and three-$\alpha$ potentials, and some three-$\alpha$ potentials with different range parameters will be examined. Results of the strength function show a double-peaked bump at low energy region, which can be considered as two $0^{+}$-states. The peak at higher energy may originate from a 3$\alpha$ resonant state. However, it is unlikely that the peak at the lower energy is related to a resonant state, which suggests that it may be due to so called "ghost anomaly". Distributions of decaying particles are also calculated.

arXiv comment5 pages, 4 figures

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Cited by in corpus (1)

• Low-energy ${}^{12}$C continuum states in three-$\alpha$ model