Structure of the mirror nucleiBe9andB9in a microscopic cluster model

The structure of the mirror nuclei ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ and ${}_{}{}^9{}_{}{}^{}\mathrm{B}$ is studied in a microscopic α+α+n and α+α+p three-cluster model using a fully antisymmetrized nine-nucleon wave function. The two-nucleon interaction includes central and spin-orbit components together with the Coulomb potential. The ground state of ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ is obtained accurately with the stochastic variational method, while several particle-unbound states of both ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ and ${}_{}{}^9{}_{}{}^{}\mathrm{B}$ are investigated with the complex scaling method. The calculation for ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ supports the recent identification for the existence of two broad states around 6.5 MeV, and predicts the 3/$2_2^{\mathrm{-}}$ and 5/$2_2^{\mathrm{-}}$ states at about 4.5 MeV and 8 MeV, respectively. The similarity of the calculated spectra of ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ and ${}_{}{}^9{}_{}{}^{}\mathrm{B}$ enables one to identify unknown spins and parities of the ${}_{}{}^9{}_{}{}^{}\mathrm{B}$ states. Available data on electromagnetic moments and elastic electron scatterings are reproduced very well. The enhancement of the E1 transition of the first excited state in ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ is well accounted for. The calculated density of ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ is found to reproduce the reaction cross section on a carbon target. The analysis of the beta decay of ${}_{}{}^9{}_{}{}^{}\mathrm{Li}$ to ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ clearly shows that the wave function of ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ must contain a small component that cannot be described by the simple α+α+n model. This small component can be well accounted for by extending a configuration space to include the distortion of the α particle to t+p and h+n partitions. © 1996 The American Physical Society.