$Λ$ hypernuclear potentials beyond linear density dependence

In a recent paper [PLB 837 (2023) 137669] we showed that all measured ($1s_Λ$, $1p_Λ$) pairs of $Λ$ binding energies in $Λ$-hypernuclei across the periodic table, $12\leq A \leq 208$, can be obtained from a $Λ$-nucleus optical potential with only two adjustable $ΛN$ and $ΛNN$ parameters, associated with leading linear and quadratic terms in the nuclear density, derived by fitting $^{16}_{~Λ}$N binding energies. Here we extend the previous analysis by performing least-squares fits to the full set of data points. Consequences of suppressing $ΛNN$ interactions between `core' nucleons and `excess' neutrons are studied and related predictions are made for ($1s_Λ$, $1p_Λ$) binding energies in $^{40,48}_{~~~~Λ}$K, obtainable from upcoming $^{40,48}$Ca($e,e'K^+$) JLab experiments. We find $Λ$-nucleus partial potential depths of $D^{(2)}_Λ= -38.6\pm 0.8$~MeV ($ΛN$) and $D^{(3)}_Λ= 11.3\pm 1.4$~MeV ($ΛNN$), with a total depth $D_Λ= -27.3\pm 0.6$~MeV at nuclear-matter density $ρ_0$=0.17~fm$^{-3}$, consistently with our previous results. Extrapolation to higher nuclear densities and possible relevance to the `hyperon puzzle' in neutron-star matter are discussed.