Breathing-like excited state of the Hoyle state in ${^{12}{\rm C}}$

TL;DR

This paper confirms the existence of two excited states in ${^{12}{ m C}}$ near 10 MeV, identifying one as a breathing-like excitation of the Hoyle state using microscopic cluster models and variational calculations.

Contribution

It introduces a fully microscopic 3$ ext{α}$ cluster model with GCM and variational methods to identify and analyze excited states around the Hoyle state in ${^{12}{ m C}}$, revealing a breathing-like nature of the $0_3^+$ state.

Findings

Confirmation of $0_3^+$ and $0_4^+$ states near 10 MeV in ${^{12}{ m C}}$

Identification of the $0_3^+$ state as a breathing-like excitation of the Hoyle state

Distinct structural differences between the $0_3^+$ and $0_4^+$ states

Abstract

The existence of the $0_3^+$ and $0_4^+$ states around 10 MeV excitation energy in ${^{12}{\rm C}}$ is confirmed by a fully microscopic 3$\alpha$ cluster model. Firstly, a GCM (generator coordinate method) calculation is performed by superposing optimized 2$\alpha$+$\alpha$ THSR (Tohsaki-Horiuchi-Schuck-R\"{o}pke) wave functions with the radius-constraint method. The obtained two excited $0^+$ states above the Hoyle state are consistent with the recently observed states by experiment. Secondly, a variational calculation using the single 2$\alpha$+$\alpha$ THSR wave function orthogonalized to the ground and Hoyle states is made and it also supports the existence of the $0_3^+$ state obtained by the GCM calculation. The analysis of the obtained $0_3^+$ state is made by studying its 2$\alpha$-$\alpha$ reduced width amplitude, its 2$\alpha$ correlation function, and the large monopole matrix element between this state and the Hoyle state, which shows that this $0_3^+$ state is a breathing-like excited state of the Hoyle state. This character of the $0_3^+$ state is very different from the $0_4^+$ state which seems to have a bent-arm 3$\alpha$ structure.