Abstract
The $_{\ensuremath{\Lambda}}\mathrm{Be}^{9}$ hypernucleus regarded as a three-body bound state is investigated with separable potentials between the $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\Lambda}$ pair and the $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ pair (without the Coulomb interaction). The energy eigenvalue is found to be consistent with the magnitudes of the force parameters obtained by fits to the $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\Lambda}$ and $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ data. As one of the applications of the exact three-body wave functions obtained by solving the three-body Schr\"odinger equation numerically, a perturbative calculation of the Coulomb energy of $_{\ensuremath{\Lambda}}\mathrm{Be}^{9}$ gives a reasonable estimate of \ensuremath{\sim} 3 MeV. The results of this three-body approach to the $_{\ensuremath{\Lambda}}\mathrm{Be}^{9}$ system are discussed in relation to those of contemporary variational calculations.
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