Binding energies of Λ particles and the Λ-N interaction

Abstract

The implications of Λ-binding energies for the Λ-nucleon interaction have been considered when three-body forces are included in addition to two-body Yukawa forces. In part I the light hypernuclei with baryon number ≦ 5 are considered. For ΛH 3 the effect of three-body forces is small and may be obtained by a perturbation procedure; the binding energy of ΛH 3 being almost entirely determined by the two-body forces. For ΛH 5 the He 4 core is assumed to be undistorted by the Λ. The binding energies of ΛH 4, ΛHe 4 do not seem capable of yielding significant information about the interaction strenghts. The two-body system ΛH 2 is not bound unless the three-body forces are very strongly attractive. In part II the potential felt by a Λ in nuclear matter, this being considered as a Fermi gas, is calculated using perturbation theory. Both direct and exchange two-body forces are considered. The second order contributions, the effect of nuclear pair correlations and the velocity dependence are all small. The nucleon exchange factor used for the three-body forces strongly suppresses their effect in nuclear matter. The implications of ‘empirical’ values of the Λ-potential depth are considered. In particular if the pion-baryon couplings predominate then strongly attractive three-body forces of not too large a range are favoured, corresponding to a larger singlet than triplet two-body volume integral.