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Title: Density dependence of the $\Lambda$ potential in nuclear matter
Plain: Binding energies of $\Lambda$ hyperons in heavy hypernuclei show that a $\Lambda$ feels an attraction of about $30\,\mathrm{MeV}$ inside ordinary nuclear matter. Whether this attraction turns into repulsion at two to three times nuclear density decides whether Lambdas appear in neutron stars.
Precise: Determine the Lambda single-particle potential $U_{\Lambda}(n)$ in symmetric and pure neutron matter for n from $n_0\ \text{to}\ 3n_0$ ($n_0=0.16\ \mathrm{fm}^{-3}$), given $U_{\Lambda}(n_0)$ of about $-30\ \mathrm{MeV}$ from hypernuclear binding systematics. Answer: $U_{\Lambda}(n)$ with quantified uncertainty from $\Lambda N$ and $\Lambda NN$ interactions constrained by hypernuclear binding energies, femtoscopic correlations and lattice QCD, and the resulting Lambda threshold density in beta-equilibrated matter.
Settled by: A $\Lambda NN$ three-body force fixed by $p-p-\Lambda$ and $d-\Lambda$ femtoscopy and by binding energies of medium and heavy hypernuclei, used in quantum Monte Carlo or chiral many-body calculations of hyperonic matter.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
Status note: STAR reported the first deuteron-$\Lambda$ correlation measurement at RHIC in 2025 (arXiv 2511.15493), a new constraint on the three-body sector.
Posed since: (empty)