Λ single particle energies

The Λ single-particle energies B_Λ of hypernuclei (HN) are calculated microscopically using the Fermi hypernetted chain method to obtain for our ΛN and ΛNN potentials the Λ binding D(ρ) to nuclear matter, and the effective mass m_Λ^*(ρ) at densities ρ<~ρ₀ (ρ₀ is normal nuclear density), and also the corresponding effective ΛN and ΛNN potentials. The Λ core-nucleus potential U_Λ(r) is obtained by suitably folding these into the core density. The Schrödinger equation for U_Λ and m_Λ^* is solved for B_Λ. The fringing field (FF) due to the finite range of the effective potentials is theoretically required. We use a dispersive ΛNN potential but also include a phenomenological ρ dependence allowing for less repulsion for ρ<ρ₀, i.e., in the surface. The best fits to the data with a FF give a large ρ dependence, equivalent to an A dependent strength consistent with variational calculations of _Λ⁵He, indicating an effective ΛNN dispersive potential increasingly repulsive with A whose likely interpretation is in terms of dispersive plus two-pion-exchange ΛNN potentials. The well depth is 29±1MeV. The ΛN space-exchange fraction corresponds to m_Λ^*(ρ)≈0.75–0.80 and a ratio of p- to s-state potentials of ≈0.5±0.1. Charge symmetry breaking (CSB) is significant for heavy HN with a large neutron excess; with a FF the strength agrees with that obtained from the A=4HN. The fits without FF are excellent but inconsistent with the requirement for a FF, with _Λ⁵He, and also with the CSB sign for A=4.