A one parameter, semi-empirical formula for Λ-binding energy of heavy hypernuclei in the inverse powers of core mass number (A_c) has been developed in the framework of the folding model. Unlike similar calculations reported by other authors (Deloff 1971; Daskaloyanniset al 1985), we are able to take into account the effect arising from the difference in the number of protons and neutrons of the core nuclei having same mass number. The radius and diffuseness are parametrized using the experimentally known charge density data of a fairly large number of medium and heavy nuclei. The well depth parameter (i.e. Λ-binding energy in infinite nuclear matter) in the formula is obtained from a fit to theB_Λ data of_Λ²⁸Si,_Λ⁴⁰Ca,_Λ⁵¹V and_Λ³⁹Y. Using the original Λ-nucleus potential, theB_Λ of ground and the experimentally known excited states of these hypernuclei have also been calculated by solving numerically the two-body Schrödinger equation. The agreement with the experimental data is satisfactory.

Variational Monte Carlo calculations of the ground state separation energiesB_Λ of thes-shell hypernuclei and also of_Λ⁹Be have been made for an Urbana-type central space-exchange ΛN potential consistent with Λp scattering, and also including three-body ΛNN forces. Thes-shell hypernuclei are treated asA-body systems (A = baryon number), and_Λ⁹Be is analysed as a partially nine-body problem in the Λ — 2α model. The reduction ofB_Λ due to the space-exchange ΛN potential has been calculated for thes-shell hypernuclei for a range of interactions: both ΛN and ΛN + ΛNN forces. ForA = 3,4,5 the exchange energy is approximately, 0.04, 0.15 and 0.50 MeV, respectively. For_Λ⁹Be a much more limited study gives ≅ 1.3 MeV. These values are much larger than that for ‘soft’ ΛN +NN potentials when the correlations are weak.

The $\Lambda \Lambda$ binding energy ($B_{\Lambda \Lambda}$) of the s- and p-shell hypernuclei are calculated variationally in the cluster model and multidimensional integrations are performed using Monte Carlo. A variety of phenomenological 𝛬-core potentials consistent with the 𝛬-core energies and a wide range of simulated s-state $\Lambda \Lambda$ potentials are taken as input. The $B_{\Lambda \Lambda}$ of $_{\Lambda \Lambda}^{6}$He is explained and $_{\Lambda \Lambda}^{5}$He and $_{\Lambda \Lambda}^{5}$H are predicted to be particle stable in the $\Lambda \Lambda$-core model. The results for s-shell hypernuclei are in excellent agreement with those of non-VMC calculations. The $_{\Lambda\Lambda}^{10}$Be in $\Lambda \Lambda \alpha \alpha$ model is overbound for combinations of $\Lambda \Lambda$ and $\Lambda \alpha$ potentials. A phenomenological dispersive three-body force, $V_{\Lambda \alpha \alpha}$, consistent with the $B_{\Lambda}$ of $_{\Lambda}^{9}$Be in the $\Lambda \alpha \alpha$ model underbinds $_{\Lambda \Lambda}^{10}$Be. The incremental $\Delta B_{\Lambda \Lambda}$ values for the s- and p-shell cannot be reconciled, consistent with the finding of earlier analyses.