Monopole excitation of the Hoyle state and linear-chain state in 12C

Background: Two new J(pi) = 0(+) states are recently observed a few MeV above the Hoyle state (the second 0(+) state in C-12). Their characteristics are only briefly discussed in theory and are still mysterious. Purpose: I give for the first time a comprehensive understanding of the structures of the 0(+) states by analyzing their wave functions and discuss relationship with the Hoyle state, similarities, and differences between the states. Method: I extend a microscopic alpha-cluster model called the Tohsaki-Horiuchi-Schuck-Ropke (THSR) wave function so as to incorporate the 2 alpha + alpha asymmetric configuration explicitly. The so-called r(2)-constraint method to effectively eliminate spurious continuum components is also used. Results: The 0(3)(+) state is shown to have a very large squared overlap with a single configuration of the extended THSR wave function in an orthogonal space to the Hoyle state as well as to the ground state. The 0(4)(+) state has a maximal squared overlap with a single extended THSR wave function with an extremely prolately deformed shape. Conclusions: The 0(3)(+) state appears as a family of the Hoyle state to have a higher nodal structure in the internal motions of the 3 alpha clusters, due to the orthogonalization to the Hoyle state. The 0(4)(+) state dominantly has a linear-chain structure, where the 3 alpha clusters move freely in a nonlocalized way, like a one-dimensional gas of the 3 alpha clusters.