Hoyle band and $α$ condensation in ${^{12}{\rm C}}$

The excited states in ${^{12}{\rm C}}$ are investigated by using an extended version of the so-called Tohsaki-Horiuchi- Schuck-Röpke (THSR) wave function, where both the $3α$ condensate and ${^{8}{\rm Be}} + α$ cluster asymptotic configurations are included. A new method is also used to resolve spurious continuum coupling with physical states. We focus on the structures of the "Hoyle band" states, $2_2^+$, and $4_2^+$ states, which are recently observed above the Hoyle state and of the $0_3^+$ and $0_4^+$ states, which are also quite recently identified in experiment. Their resonance parameters and decay properties are reasonably reproduced. All these states have gaslike configurations of the $3α$ clusters with larger root mean square radii than that of the Hoyle state. The Hoyle band is not simply considered to be the ${^{8}{\rm Be}}(0^+) +α$ rotation as suggested by previous cluster model calculations, nor to be a rotation of a rigid-body triangle-shaped object composed of the $3α$ particles. This is mainly due to the specificity of the Hoyle state, which has the $3α$ condensate structure and gives a rise to the $0_3^+$ state with a prominent ${^{8}{\rm Be}}(0^+)+α$ structure as a result of very strong monopole excitation from the Hoyle state.

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