Skyrme-Hartree-Fock treatment of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Λ</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Λ</mml:mi><mml:mi>Λ</mml:mi></mml:math>hypernuclei with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>G</mml:mi></mml:math>-matrix motivated interactions

Skyrme-like hyperon-nucleon potentials are derived from $G$-matrix calculations and shown to reproduce well the $\ensuremath{\Lambda}$ single-particle spectra of hypernuclei measured at BNL and KEK. Previously known potentials are reexamined systematically. The fit of the spectra can restrict the radii of $\ensuremath{\Lambda}$ orbits in hypernuclear ground states, $\ensuremath{\Lambda}$ well depth and effective mass in nuclear matter, and polarization of nuclear cores caused by hyperon rather tightly. The implications of the $\ensuremath{\Lambda}N$ spin-orbit force to the spectra are considered. Hartree-Fock calculations of binding energies of ${}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}^{13}$B with density-dependent $G$-matrix $\ensuremath{\Lambda}\ensuremath{\Lambda}$ potentials are presented, taking note of the core-rearrangement effects induced by $\ensuremath{\Lambda}N$ interactions.