We study the resonance spectroscopy of the proton-rich nucleus ${}^7$B in the ${}^4\mathrm{He}+p+p+p$ cluster model. Many-body resonances are treated under the correct boundary condition as Gamow states using the complex scaling method. We predict five resonances of ${}^7$B and evaluate the spectroscopic factors of the ${}^6$Be-$p$ components. The importance of the ${}^6$Be($2^{+}$)-$p$ component is shown in several states of ${}^7$B; this is a common feature of ${}^7$He, a mirror nucleus of ${}^7$B. For only the ground state of ${}^7$B, the mixing of the ${}^6$Be($2^{+}$) state is larger than that of ${}^6$He($2^{+}$) in ${}^7$He, which indicates a breaking of mirror symmetry. This is caused by the small energy difference between ${}^7$B and the excited ${}^6$Be($2^{+}$) state, the origin of which is Coulomb repulsion.

• Received 4 November 2011

DOI:https://doi.org/10.1103/PhysRevC.84.064306