We study the resonance spectroscopy of the proton-rich nucleus ${}^8$C in the $\alpha$+$p$+$p$+$p$+$p$ cluster model. Many-body resonances are treated on the correct boundary condition as the Gamow states using the complex scaling method. We obtain the ground state of ${}^8$C as a five-body resonance for the first time, which has dominantly the subclosed ${\left(p_{3/2}\right)}^4$ configuration and agrees with the recent experiment for energy and decay width. We predict the second $0^{+}$ state with the excitation energy of 5.6 MeV, which corresponds to the 2p2h state from the ground state. We evaluate the occupation numbers of four valence-protons in the ${}^8$C states and also the $J^{\pi }$ distribution of proton-pair numbers of the two $0^{+}$ states of ${}^8$C. The ground state involves a large amount of the $2^{+}$ proton-pair fraction, while the excited $0_2^{+}$ state almost consists of two of the $0^{+}$ proton pairs, which can be understood from the ${\left(p_{3/2}\right)}^2{\left(p_{1/2}\right)}^2$ configuration. We also discuss the mirror symmetry between ${}^8$C and ${}^8$He with an $\alpha$+four nucleon picture. It is found that the $0^{+}$ states retain the mirror symmetry well for the configuration properties of two nuclei.

• Received 22 December 2011

DOI:https://doi.org/10.1103/PhysRevC.85.034338