Semiphenomenological studies of the ground state binding energies of hypernuclei.

Abstract

We show that the binding energies of $_{\mathrm{\ensuremath{\Lambda}}}^{5}\mathrm{He}$ and p-shell hypernuclei can be satisfactorily explained in the folding model approach using a density dependent effective \ensuremath{\Lambda}N interaction. Our analysis predicts a very reasonable value of the range of the \ensuremath{\Lambda}N interaction. The calculated value of ${B}_{\ensuremath{\Lambda}}$ of $_{\mathrm{\ensuremath{\Lambda}}}^{7}\mathrm{Li}$ using the cluster model density for $^{6}\mathrm{Li}$ and the best fit parameters of this potential supports the view that $^{6}\mathrm{Li}$ possesses an \ensuremath{\alpha}-d cluster structure. Using this potential we also determine the average size parameter (${a}_{0}$) of the oscillator shell model density of nucleons in N\ensuremath{\ne}Z core nuclei from fitting the ${B}_{\ensuremath{\Lambda}}$ values of the corresponding hypernuclei. The effect of different forms of density distribution of core nuclei on the values of potential parameters is investigated and is found to be very small. As regards the form of density dependence, a ${\ensuremath{\rho}}^{2/3}$ form is found to be the most appropriate for this purpose and is used throughout this work. Other forms do not give a satisfactory account of the data.