Variational calculations indicate that a reasonable description of .lambda.p scattering and of .lambda. separation energies can be obtained in terms of .lambda. N plus dispersive and TPE .lambda. NN forces. Results for the .lambda lambda. interaction and for 6/sub .lambda./He obtained from an analysis of 1°/sub .lambda lambda./Be are discussed. Coulomb and .lambda. N charge symmetry breaking effects in the A = 4 hypernuclei are discussed.

Variational Monte Carlo calculations have been made for the s-shell hypernuclei and also of /sub .lambda./9Be with a 2.cap alpha. + .lambda. model. The well depth is calculated variationally with the Fermi hypernetted chain method. A satisfactory description of all the relevant experimental .lambda. separation energies and also of the .lambda.p scattering can be obtained with reasonable TPE .lambda. N and .lambda. NN forces and strongly repulsive dispersive .lambda. NN forces which are preferred to be spin dependent. We discuss variational calculations for /sub .lambda lambda./6He and /sub .lambda lambda./1°Be with .cap alpha. + 2.lambda. and 2.cap alpha. + 2.lambda. models, and the results obtained for the .lambda lambda. interaction and for /sub .lambda lambda./6He from analysis of /sub .lambda lambda./1°Be. Coulomb effects and charge symmetry breaking in the A=4 hypernuclei are discussed. 28 refs.

The main objective is develop an extended Thomas-Fermi theory using a local density approach ("Thomas Fermi" model for short) to calculate binding energies, root mean square radii, density distributions for nuclei and hypernuclei and demonstrate that for "realistic" L-nuclear interactions, the core polarization effects are in general very small, both the polarizing energies as well as the change in rms radii.

The complexities of the s-shell .lambda.-hypernuclei (A less than or equal to 5) are explored. Difficulties associated with attempts to describe the hyperon-nucleon (YN) interaction in all such .lambda.-hypernuclei by simple, effective .lambda.p and .lambda.n potentials are examined. The explicit A dependence of the effective YN interaction due to .lambda. N-.sigma. N coupling and isospin differences among the nuclear core states is investigated. The necessity of using exact four-body theory to calculate small charge-symmetry-breaking effects (in the A = 4 system) using .lambda. N potentials fitted to free .lambda. N scattering data is emphasized. Possible use of s-shell hypernuclear binding energies to help distinguish among candidate YN potential parameterizations is discussed.