Resonance structures of excited states in ${}^9\mathrm{Be}$ and ${}^9\mathrm{B}$ are studied by means of a microscopic multicluster model. The two-body scattering of ${\{}^8\mathrm{Be}{(0\mathrm{}}^{+}{,2\mathrm{}}^{+}{,4\mathrm{}}^{+})+N;$ ${}^5\mathrm{He}$ or ${}^5\mathrm{Li}{(3/2\mathrm{}}^{-}{,1/2\mathrm{}}^{-})+\alpha \}$ is solved by the microscopic R-matrix method where two-cluster wave functions of ${}^8\mathrm{Be}$ and ${}^5\mathrm{He}$ are employed. These results are compared with the $\alpha +\alpha +N$ three-body complex scaling method to check the validity of neglecting three-body channels in the microscopic R-matrix method. The ${1/2}^{+}$ first excited state of ${}^9\mathrm{Be},$ which cannot be identified in the complex scaling method, is given as a ${}^8\mathrm{Be}{(0\mathrm{}}^{+})+n$ virtual state with a purely imaginary complex momentum, and this resonance lies on the second Riemann sheet only for the ${}^8\mathrm{Be}{(0\mathrm{}}^{+})+n$ channel. The ${1/2}^{+}$ resonance of the mirror nucleus ${}^9\mathrm{B}$ has a very large width, and its excitation energy as obtained from the analytic continuation of the S matrix to the complex energies shows a normal Thomas-Ehrman shift. The dimensionless reduced widths and the reduced width amplitudes are calculated for low-lying resonances, and the cluster structure of these states in ${}^9\mathrm{Be}$ is discussed.

• Received 4 February 2003

DOI:https://doi.org/10.1103/PhysRevC.68.014310