Λ single particle energies -: art. no. 055215

The Lambda single-particle energies B-Lambda of hypernuclei (HN) are calculated microscopically using the Fermi hypernetted chain method to obtain for our Lambda N and Lambda NN potentials the Lambda binding D(rho) to nuclear matter, and the effective mass m(Lambda)*(rho) at densities rho less than or equal to rho(o) (rho(o) is normal nuclear density), and also the corresponding effective Lambda N and Lambda NN potentials. The Lambda core-nucleus potential U-Lambda(r) is obtained by suitably folding these into the core density. The Schrodinger equation for U-Lambda and m(Lambda)* is solved for B-Lambda. The fringing held (FF) due to the finite range of the effective potentials is theoretically required. We use a dispersive Lambda NN potential but also include a phenomenological rho dependence allowing for less repulsion for rho<rho(0), i.e., in the surface. The best fits to the data with a FF give a large rho dependence, equivalent to an A dependent strength consistent with variational calculations of He-5(Lambda), indicating an effective Lambda NN dispersive potential increasingly repulsive with A whose likely interpretation is in terms of dispersive plus two-pion-exchange Lambda NN potentials. The well depth is 29 +/- 1 MeV. The Lambda N space-exchange fraction corresponds to m(Lambda)*(rho) approximate to 0.75-0.80 and a ratio of p- to s-state potentials of approximate to 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 EF are excellent but inconsistent with the requirement for a FF, with He-5(Lambda), and also with the CSB sign for A = 4. [S0556-2813(99)04811-6].