The recently observed resonance ( $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=32.5\mathrm{}$ MeV) in the $0_2^{+}-0_2^{+}$ channel of ${}_{}{}^{12}{}_{}{}^{}C+{}_{}{}^{12}{}_{}{}^{}C$ collisions is predicted to be a weakly coupled structure of two three- $\alpha$-particle states ( $0_2^{+}$ state of ${}^{12}$C). At the same time a well-known resonance ( $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=29\mathrm{}$ MeV) in the $0_1^{+}-0_2^{+}$ channel is explained as of three α particles plus ${}^{12}$C core structure. The band crossing model is shown to be valid also for inelastic scatterings to α-cluster states. A strong resonance is predicted in the $3_1^{-}-0_2^{+}$ channel in the same energy region. A relation to the linear chain configuration of six α particles is discussed.

• Received 1 September 1994

DOI:https://doi.org/10.1103/PhysRevLett.74.4141