Auxiliary Field Diffusion Monte Carlo (AFDMC) calculations have been employed to revise the interaction between $Lambda$-hyperons and nucleons in hypernuclei. The scheme used to describe the interaction, inspired by the phenomenological Argonne-Urbana forces, is the $Lambda N+Lambda NN$ potential firstly introduced by Bodmer, Usmani et al.. Within this framework, we performed calculations on light and medium mass hypernuclei in order to assess the extent of the repulsive contribution of the three-body part. By tuning this contribution in order to reproduce the $Lambda$ separation energy in $^5_Lambda$He and $^{17}_{~Lambda}$O, experimental findings are reproduced over a wide range of masses. Calculations have then been extended to $Lambda$-neutron matter in order to derive an analogous of the symmetry energy to be used in determining the equation of state of matter in the typical conditions found in the inner core of neutron stars.
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