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

TL;DR

This study investigates the monopole transition strength function of ${}^{12}$C using a three-alpha model and Faddeev theory, revealing two low-energy $0^+$ states and a possible resonance at higher energy.

Contribution

It introduces a three-alpha boson model combined with Faddeev theory to analyze ${}^{12}$C's continuum states and monopole transitions, providing new insights into its low-energy structure.

Findings

Double-peaked strength distribution indicating two $0^+$ states

Identification of a high-energy resonance possibly related to a 3$oldsymbol{eta}$ state

Low-energy peak likely due to ghost anomaly rather than a resonant state

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.