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

Abstract

The existence of the $0_3^{+}$ and $0_4^{+}$ states around 10 MeV excitation energy in ${}^{12}\mathrm{C}$ 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-Röpke) 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.

Comments: 9 pages, 5 figures. Submitted to PRC on July 7, 2016