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

Background: Two new J^π=0⁺ states are recently observed a few MeV above the Hoyle state (the second 0⁺ state in ¹²C). 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 α -cluster model called the Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave function so as to incorporate the 2 α +α asymmetric configuration explicitly. The so-called r²-constraint method to effectively eliminate spurious continuum components is also used.

Results: The 0₃⁺ 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 0₄⁺ state has a maximal squared overlap with a single extended THSR wave function with an extremely prolately deformed shape.

Conclusions: The 0₃⁺ state appears as a family of the Hoyle state to have a higher nodal structure in the internal motions of the 3 α clusters, due to the orthogonalization to the Hoyle state. The 0₄⁺ state dominantly has a linear-chain structure, where the 3 α clusters move freely in a nonlocalized way, like a one-dimensional gas of the 3 α clusters.