Onset of hyperon formation in neutron star matter from Brueckner theory

We determine fully self-consistent single-particle potentials and chemical potentials of nucleons and hyperons in asymmetric nuclear matter, using an extended Brueckner-Hartree-Fock formalism. We carefully analyze the onset of ${\ensuremath{\Sigma}}^{\ensuremath{-}}$ and $\ensuremath{\Lambda}$ formation in $\ensuremath{\beta}$ stable and charge neutral matter. The role played by the three-body nucleon interaction is widely discussed. The results indicate that formation of hyperons sets in at about (2--3) times normal nuclear matter density, for all the different nucleonic equations of state that are considered.