Constraints from $Λ$ hypernuclei on the $ΛNN$ content of the $Λ$-nucleus potential

A depth of $D_Λ\approx -28$ MeV for the $Λ$-nucleus potential was confirmed in 1988 by studying $Λ$ binding energies deduced from $(π^+,K^+)$ spectra measured across the periodic table. Modern two-body hyperon-nucleon interaction models require additional interaction terms, most likely $ΛNN$ three-body terms, to reproduce $D_Λ$. In this work we apply a suitably constructed $Λ$-nucleus density dependent optical potential to binding energy calculations of observed $1s_Λ$ and $1p_Λ$ states in the mass range $12\leq A\leq 208$. The resulting $ΛNN$ contribution to $D_Λ$, about 14 MeV repulsion at symmetric nuclear matter density $ρ_0=0.17$ fm$^{-3}$, makes $D_Λ$ increasingly repulsive at $ρ\gtrsim 3ρ_0$, leading possibly to little or no $Λ$ hyperon content of neutron-star matter. This suggests in some models a stiff equation of state that may support two solar-mass neutron stars.

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