Hartree-Fock Calculation of Helium Hypernuclear Binding Energies

Abstract

The binding energies of the $s$-shell hypernuclei ($_{\ensuremath{\Lambda}}\mathrm{H}^{4}$, $_{\ensuremath{\Lambda}}\mathrm{He}^{5}$, and $_{\ensuremath{\Lambda}\ensuremath{\Lambda}}\mathrm{He}^{6}$) have been calculated in the Hartree-Fock model, using Gaussian particle-particle potentials. Parameters of the $\ensuremath{\Lambda}\ensuremath{-}N$ interaction were determined from the experimental binding energies. These numerical results agree qualitatively with those of other calculations and also with the experimental $\ensuremath{\Lambda}\ensuremath{-}N$ scattering data, if short-range repulsions are included. Equality of the $\ensuremath{\Lambda}\ensuremath{-}N$ and $\ensuremath{\Lambda}\ensuremath{-}\ensuremath{\Lambda}$ potentials is consistent with these calculations.