We investigate the properties of the single Λ hypernuclei within a Skyrme-Hartree-Fock (SHF) model. The parameters of the Skyrme type effective lambda-nucleon (ΛN) interaction are obtained by fitting to the experimental Λ binding energies of hypernuclei with masses spanning a wide range of the periodic table. Alternative parameter sets are also obtained by omitting nuclei below mass number 16 from the fitting procedure. The SHF calculations are performed for the binding energies of the Λ single-particle states over a full mass range using the best fit parameter sets obtained in these fitting procedures and the results are compared with the available experimental data. The data show some sensitivity to the parameter sets obtained with or without including the nuclei below mass 16. The radii of the Λ orbits in the hypernuclear ground states and the Λ effective mass in nuclear matter show some dependence on different parameter sets. We present results for the total binding energy per baryon of the hypernuclei over a large mass region to elucidate their stability as a function of the baryon number. We have also employed the our best fit ΛN parameter sets to investigate the role of hyperons in some key properties of neutron stars.

We extend our Skyrme-Hartree-Fock (SHF) approach, which was used earlier to describe successfully the single-Λ hypernuclei, to investigate the binding and the ΛΛ bond energies of the double-Λ hypernuclei. The nucleon-nucleon (NN) and Λ-nucleon (ΛN ) interactions are taken from our previous study. For the ΛΛ force, several Skyrme-like potentials available in the literature have been used. We discuss the sensitivity of the calculated ΛΛ binding and bond energies to the ΛΛ and ΛN force parameters. It is found that the existing ΛΛ hypernuclear data do not allow to distinguish between various ΛΛ force parameter sets used by us. However, they show some selectivity for a particular set of the ΛN potential determined in our previous work. Keywords: Study of double-Λ hypernuclei; Skyrme-Hartree-Fock model; Lambda-Lambda interaction. PACS Number(s): 21.10.Dr, 21.30.Fe, 21.60.J 1450026-1 Int. J. Mod. Phys. E 2014.23. Downloaded from www.worldscientific.com by FLINDERS UNIVERSITY LIBRARY on 02/06/15. For personal use only. 1450026-2 Int. J. Mod. Phys. E 2014.23. Downloaded from www.worldscientific.com by FLINDERS UNIVERSITY LIBRARY on 02/06/15. For personal use only.