Binding Energies of Light Hypernuclei

Light hypernuclei play the role of a natural laboratory for the study of YN and NN interactions. The repulsive nature of the Lambda N interaction leads to the fact that possible bound states in hypernuclei arise due to the three-body nucleon-hyperon-nucleon interaction. The leading role in this interaction is assigned to the conversion Lambda N -> Sigma N of one type of hyperon to another. In this work, the binding energies of light hypernuclei are obtained by solving the homogeneous Faddeev integral equation for three particles with both realistic and phenomenological YN and NN potentials. The conversion of Lambda and Sigma hyperons is considered exactly. A numerical technique has been developed for the solution of the homogeneous integral Faddeev equation with three particles of different masses for the local form of pair potentials. A procedure generalized to local potentials for the approximate solution of integral equations by the Noyes-Kowalski method is presented. In order to speed up the numerical calculation, a procedure of four-dimensional spline interpolation of the obtained two-body T-matrices has been introduced and tested. Numerical calculations of binding energies are carried out both with charge-dependent separable potentials and with charge-dependent local potentials. The impact of higher partial waves of the NN potentials on the binding energy of light nuclei is discussed. The obtained values of the binding energies of the simplest nuclei H-3, He-3, are in good agreement with the available experimental values. In addition, four-body calculations with a partial-wave expansion of the pair potentials used have been carried out. It is shown that the approach developed can also be successfully applied when searching for the binding energies of four-body H-4(Lambda), He-4(Lambda) hypernuclei.