Structure of the mirror nuclei 9Be and 9B in a microscopic cluster model.

Abstract

The structure of the mirror nuclei $^{9}\mathrm{Be}$ and $^{9}\mathrm{B}$ is studied in a microscopic \ensuremath{\alpha}+\ensuremath{\alpha}+n and \ensuremath{\alpha}+\ensuremath{\alpha}+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/${2}_{2}^{\mathrm{\ensuremath{-}}}$ and 5/${2}_{2}^{\mathrm{\ensuremath{-}}}$ 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 \ensuremath{\alpha}+\ensuremath{\alpha}+n model. This small component can be well accounted for by extending a configuration space to include the distortion of the \ensuremath{\alpha} particle to t+p and h+n partitions. \textcopyright{} 1996 The American Physical Society.