Consistency between the monopole strength of the Hoyle state determined by structural calculation and that extracted from reaction observables

TL;DR

This study confirms that the monopole strength of the Hoyle state, derived from structural models, aligns with values obtained from reaction data, indicating no missing strength in the state.

Contribution

The paper demonstrates the consistency between structural and reaction-based monopole strength measurements for the Hoyle state using a fully microscopic approach.

Findings

Microscopic reaction calculations reproduce inelastic cross sections accurately.

Monopole transition strength from structure matches that from reaction observables.

No missing monopole strength is found for the Hoyle state.

Abstract

We analyze the $\alpha$-$^{12}$C inelastic scattering to the $0^+_2$ state of $^{12}$C, the Hoyle state, in a fully microscopic framework. With no free adjustable parameter, the inelastic cross sections at forward angles are well reproduced by the microscopic reaction calculation using the transition density of $^{12}$C obtained by the resonating group method and the nucleon-nucleon $g$ matrix interaction developed by the Melbourne group. It is thus shown that the monopole transition strength obtained by the structural calculation is consistent with that extracted from the reaction observable, suggesting no missing monopole strength of the Hoyle state.