$\mathrm{\Lambda }$ hypernuclear potentials beyond linear density dependence

In a recent paper [PLB 837 (2023) 137669] we showed that all measured ($1s_{\mathrm{\Lambda }}$, $1p_{\mathrm{\Lambda }}$) pairs of $\mathrm{\Lambda }$ binding energies in $\mathrm{\Lambda }$-hypernuclei across the periodic table, $12\le A\le 208$, can be obtained from a $\mathrm{\Lambda }$-nucleus optical potential with only two adjustable $\mathrm{\Lambda }N$ and $\mathrm{\Lambda }NN$ parameters, associated with leading linear and quadratic terms in the nuclear density, derived by fitting ${}_{\mathrm{\Lambda }}^{16}$N binding energies. Here we extend the previous analysis by performing least-squares fits to the full set of data points. Consequences of suppressing $\mathrm{\Lambda }NN$ interactions between core' nucleons and excess’ neutrons are studied and related predictions are made for ($1s_{\mathrm{\Lambda }}$, $1p_{\mathrm{\Lambda }}$) binding energies in ${}_{\mathrm{\Lambda }}^{40,48}$K, obtainable from upcoming ${}^{40,48}$Ca($e,e^{\mathrm{\prime }}{K}^{+}$) JLab experiments. We find $\mathrm{\Lambda }$-nucleus partial potential depths of $D_{\mathrm{\Lambda }}^{(2)}=-38.6\pm 0.8$~MeV ($\mathrm{\Lambda }N$) and $D_{\mathrm{\Lambda }}^{(3)}=11.3\pm 1.4$~MeV ($\mathrm{\Lambda }NN$), with a total depth $D_{\mathrm{\Lambda }}=-27.3\pm 0.6$~MeV at nuclear-matter density ${\rho }_0$=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.