The long-range parts of the Λ-N and Λ-λ potentials

The two-pion exchange contributions to the Λ-N and Λ-Λ potentials areobtained on the basis of the Mandelstam representation of the scattering amplitude. Formulae for V0, Vs and VT in the expression V = V0+Vs(σ1·σ2)+VTS12+… are given in terms of the parameters related to the π-N and π-Λ scattering amplitudes. The quantity V0 involves the S-wave π-λ scattering amplitude which is as yet experimentally unknown; VS and VT depend only on the P-wave gp-N and π-λ interactions, which are assumed to be dominated by the 3-3 resonance N∗ and Y1∗ resonance (1385 MeV), respectively. Higher partial waves are ignored. Only VS and VT are evaluated numerically. It is found that VS and VT are extremely small. This implies that the strongspin-independence of the phenomenological Λ-N force is characteristic of the short-range part of the potential.