density. In the following the input potential $U_\Lambda(\rho)$ is the one presented in fig.\[fig:ulambda\] for neutron matter.

The comparison of $\mu_\Lambda$ and $\mu_n$ is shown in fig.\[fig:chempot\]. The uncertainty band of the neutron chemical potential is related primarily to the range of possible values of the nuclear symmetry energy, $E_\text{{sym}} = (32\pm 3)$ MeV. We note that this uncertainty band also includes $\mu_n$ as given in Ref.[@APR1998] for their maximally repulsive interaction (AV18+$\delta v$ + UIX\*).

Fig.\[fig:chempot\] points out that the combined repulsion from two- and three-body hyperon-nuclear interactions is indeed potentially strong enough to avoid the appearance of $\Lambda$ hyperons in neutron stars: one finds $\mu_\Lambda > \mu_n$ throughout the neutron star density range, with a set of three-body parameters that is consistent with basic constraints from hypernuclei. However, two-body $\Lambda N$ interactions alone would not be sufficient to suppress the occurrence of $\Lambda$ hyperons. Their onset would appear at densities around $3\,\rho_0$. The resulting softening of the EoS would be prohibitive.

The Brueckner calculations underlying eq.(\[eq:mulambda\]) are based on the $YN$ potential taken from ref.[@Haidenbauer2013] (referred to as NLO13) which features a strong $\Lambda N\leftrightarrow\Sigma N$ coupling. This channel coupling is a major source of the $\Lambda N$ 