Auxiliary Field Diffusion Monte Carlo study of the Hyperon-Nucleon interaction in $\Lambda$-hypernuclei

We investigate the role of two- and three-body $\Lambda$-nucleon forces by computing the ground state of a few $\Lambda$-hypernuclei with the Auxiliary Field Diffusion Monte Carlo algorithm. Calculations have been performed for masses up to A=41, including some open-shell hypernuclei. The results show that the use of a bare hyperon-nucleon force fitted on the available scattering data yields a consistent overestimate of the $\Lambda$-separation energy $B_\Lambda$. The inclusion of a hyperon-nucleon-nucleon interaction systematically reduces $B_\Lambda$, leading to a qualitatively good agreement with experimental data over the range of masses investigated.