Three-Body Calculations forBe9Λwith Separable Potentials

Abstract

The ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{Be}_{}^9{}_{}{}^{}$ hypernucleus regarded as a three-body bound state is investigated with separable potentials between the $\alpha -\Lambda$ pair and the $\alpha -\alpha$ 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 $\alpha -\Lambda$ and $\alpha -\alpha$ data. As one of the applications of the exact three-body wave functions obtained by solving the three-body Schrödinger equation numerically, a perturbative calculation of the Coulomb energy of ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{Be}_{}^9{}_{}{}^{}$ gives a reasonable estimate of ∼ 3 MeV. The results of this three-body approach to the ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{Be}_{}^9{}_{}{}^{}$ system are discussed in relation to those of contemporary variational calculations.