Microscopic calculations of Λ single-particle energies

A binding energy data for total baryon number A ≤ 208 and for Λ angular momenta ℓΛ ≤ 3 are analyzed in terms of phenomenological (but generally consistent with meson-exchange) ΛN and ΛNN potentials. The Fermi hypernetted chain technique is used to calculate the expectation values for the Λ binding to nuclear matter. Accurate effective ΛN and ΛNN potentials are obtained which are folded with the core-nucleus nucleon densities to calculate the Λ single-particle potential UΛ (r). We use a dispersive ANN potential but also include an explicit ρ dependence to allow for reduced repulsion in the surface, and the best fits have a large ρ dependence giving consistency with the variational Monte Carlo calculations for 5ΛHe. The exchange fraction of the ΛN space-exchange potential is found to be 0.2-0.3 corresponding to m*Λ ≃ (0.74 - 0.82)mΛ. Charge-symmetry breaking is found to be significant for heavy hypernuclei with a large neutron excess, with a strength consistent with that obtained from the A = 4 hypernuclei

Λ single particle energies

The Λ single-particle energies BΛ 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 P≤ρ0 (ρ0 is normal nuclear density), and also the corresponding effective ΛN and ΛNN potentials. The Λ core-nucleus potential UΛ(r) is obtained by suitably folding these into the core density. The Schrödinger equation for UΛ and m*Λ is solved for BΛ. 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 5ΛHe, 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±1 MeV. The ΛN space-exchange fraction corresponds to m*Λ(ρ)≈0.75-0.80 and a ratio of ρ-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 = 4 HN. The fits without FF are excellent but inconsistent with the requirement for a FF, with 5ΛHe, and also with the CSB sign for A = 4