$\Lambda$ hypernuclear potentials beyond linear density dependence

Abstract

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

arXiv comment19 pages, 7 figures, 4 tables, minor changes, published in Nucl. Phys. A 1039 (2023) 122725; doi.org/10.1016/j.nuclphysa.2023.122725

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