Hoyle band andαcondensation inC12

The excited states in $^{12}\mathrm{C}$ are investigated by using an extended version of the so-called Tohsaki-Horiuchi-Schuck-R\"opke (THSR) wave function, where both the $3\ensuremath{\alpha}$ condensate and $^{8}\mathrm{Be}+\ensuremath{\alpha}$ cluster asymptotic configurations are included. A new method is also used to resolve spurious continuum coupling with physical states. I focus on the structures of the ``Hoyle band'' states (${0}_{2}^{+},\phantom{\rule{0.16em}{0ex}}{2}_{2}^{+}$, and ${4}_{2}^{+}$), which were recently observed above the Hoyle state, and of the ${0}_{3}^{+}$ and ${0}_{4}^{+}$ states, which were also quite recently identified in experiment. Their resonance parameters and decay properties are reasonably reproduced. All these states have dilute density structure of the $3\ensuremath{\alpha}$ or $^{8}\mathrm{Be}+\ensuremath{\alpha}$ clusters with larger root mean square radii than that of the Hoyle state. The Hoyle band is not simply considered to be the $^{8}\mathrm{Be}({0}^{+})+\ensuremath{\alpha}$ rotation as suggested by previous cluster model calculations, nor to be a rotation of a rigid-body triangle-shaped object composed of the $3\ensuremath{\alpha}$ particles. This is mainly due to the specificity of the Hoyle state, which has the $3\ensuremath{\alpha}$ condensate structure and gives rise to the ${0}_{3}^{+}$ state with a prominent $^{8}\mathrm{Be}({0}^{+})+\ensuremath{\alpha}$ structure as a result of very strong monopole excitation from the Hoyle state.