$\hat{I}›$ hypernuclear potentials beyond linear density dependence

Abstract

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

19 pages, 7 figures, 4 tables, minor changes, published in Nucl. Phys. A 1039 (2023) 122725; doi.org/10.1016/j.nuclphysa.2023.122725