Breathing-like excited state of the Hoyle state in 12C

The existence of the 0₃⁺ and 0₄⁺ states around 10 MeV excitation energy in ¹²C is confirmed by a fully microscopic 3 α cluster model. Firstly, a generator coordinate method (GCM) calculation is performed by superposing optimized 2 α +α Tohsaki-Horiuchi-Schuck-Röpke (THSR) 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 α +α THSR wave function orthogonalized to the ground and Hoyle states is made and it also supports the existence of the 0₃⁺ state obtained by the GCM calculation. The analysis of the obtained 0₃⁺ state is made by studying its 2 α -α reduced width amplitude, its 2 α correlation function, and the large monopole matrix element between this state and the Hoyle state, which shows that this 0₃⁺ state is a breathing-like excited state of the Hoyle state. This character of the 0₃⁺ state is very different from the 0₄⁺ state which seems to have a bent-arm 3 α structure.