A solution to the old puzzle of 0⁺ resonances above the 0⁺₂ Hoyle state in ¹²C — A new analysis with complex-scaled 3α OCM —

We have developed the complex-scaling method (CSM) by using the complex-range (or oscillating) Gaussian basis functions that are suited for describing highly oscillating few-body wave functions. The eigenvalue distribution of the complex scaled Hamiltonian becomes much more precise and the maximum scaling angle becomes drastically larger than those given by the use of real-range Gaussians. Owing to this advantage, we were able to isolate the S-matrix pole of the new broad 0⁺₃ resonance from the 3α continuum. This confirms the Kurokawa-Kato's prediction (2005) of the new 0⁺₃ resonance, which is considered to correspond to the newly observed 0⁺₃ resonance (E_x = 9.04 MeV, Γ = 1.45 MeV) by Itoh et al. (2013). As a result the long-standing puzzle for the 0⁺ and 2⁺ resonances above the 0⁺ Hoyle state in ¹²C was solved. In this paper, the negative parity resonances with J = 1⁻, 2⁻, 3⁻, 4⁻ and 5⁻ are newly calculated