Hartree-Fock Calculation of Helium Hypernuclear Binding Energies

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