Энергии связи легких гиперядер

Abstract

Light hypernuclei play the role of a natural laboratory for the study of Y N and NN interactions. The repulsive nature of the ΛN interaction leads to the fact that possible bound states in hypernuclei arise due to the threebody nucleon–hyperon–nucleon interaction. The leading role in this interaction is assigned to the conversion ΛN → ΣN of one type of hyperons 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 Y N and NN potentials. The conversion of Λ and Σ hyperons is exactly taken into account. A technology has been developed for the numerical solution of the homogeneous integral Faddeev equation with three particles of different masses for pair potentials in a local form. A procedure generalized to local potentials for the approximate solution of integral equations by the Noyes–Kowalski method is presented. To speed up the numerical calculation, a procedure for fourdimensional spline interpolation of the found two-body T -matrices was introduced and tested. Numerical calculations of binding energies were carried out both with charge-dependent separable potentials and with charge-dependent local potentials. The influence of higher partial waves of NN potentials on the binding energy of light nuclei is discussed. The obtained values of the binding energies of the simplest nuclei ³H, ³He, ³_ΛH, ³_ΛHe are in good agreement with the available experimental values. In addition, four-body calculations with a partial-wave expansion of the used pair potentials were carried out. It is shown that the developed approach can also be successfully applied to search for the binding energies of four-body ⁴_ΛH, ⁴_ΛHe hypernuclei.