Resonance states ofC12in a microscopic cluster model

Abstract

Excited states in $^{12}\mathrm{C}$ were theoretically investigated by means of the $\ensuremath{\alpha}+\ensuremath{\alpha}+\ensuremath{\alpha}$ microscopic cluster model where the complex scaling method was applied to localize the three-body resonance states. We extended the model space with respect to that by R. Pichler et al. [Nucl. Phys. A618, 55 (1997)] by taking into account all partial waves up to the $G$ wave in the two Jacobi coordinates and found that the ${2}^{+}$ resonance excited states are significantly affected by this extension whereas the ${0}^{+}$ states are insignificantly affected. The present model localizes the third ${0}^{+}$ state around 4--5 MeV with respect to the three-body threshold but cannot localize the ${0}^{+}$ state, which could correspond to the experimentally assumed ${0}^{+}$ state at 3.0 MeV (${E}_{x}=10.3$ MeV). Moreover, the second ${2}^{+}$ state is localized around 2--3 MeV, which might correspond to the ${2}^{+}$ state measured by M. Itoh et al. [Nucl. Phys. A738, 268c (2004)], and the third ${2}^{+}$ state is localized around 4--5 MeV, which is overlapping with the third ${0}^{+}$ and the second ${4}^{+}$ states.