In the last years auxiliary field diffusion Monte Carlo has been used to assess the properties of hypernuclear systems, from light- to medium-heavy hypernuclei and hyper-neutron matter. One of the main findings is the key role played by the three-bod
y hyperon-nucleon-nucleon interaction in the determination of the hyperon separation energy of hypernuclei and as a possible solution to the hyperon puzzle. However, there are still aspects of the employed hypernuclear potential that remain to be carefully investigated. In this paper we show that the isospin dependence of the Lambda-NN force, which is crucial in determining the NS structure, is poorly constrained by the available experimental data.
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-Urban
a 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.
The onset of hyperons in the core of neutron stars and the consequent softening of the equation of state have been questioned for a long time. Controversial theoretical predictions and recent astrophysical observations of neutron stars are the ground
s for the so-called hyperon puzzle. We calculate the equation of state and the neutron star mass-radius relation of an infinite systems of neutrons and $Lambda$ particles by using the auxiliary field diffusion Monte Carlo algorithm. We find that the three-body hyperon-nucleon interaction plays a fundamental role in the softening of the equation of state and for the consequent reduction of the predicted maximum mass. We have considered two different models of three-body force that successfully describe the binding energy of medium mass hypernuclei. Our results indicate that they give dramatically different results on the maximum mass of neutron stars, not necessarily incompatible with the recent observation of very massive neutron stars. We conclude that stronger constraints on the hyperon-neutron force are necessary in order to properly assess the role of hyperons in neutron stars.
