The binding energy of a Λ-particle in nuclear matter: A comparison of two formulations

Two approaches to the problem of calculating the binding energy B_Λ of a Λ-particle in nuclear matter are discussed. The first method is via the Bethe- Goldstone equation for the problem in the independent-pair approximation. The second method is a Green-function formulation which sums the ladder diagrams for the self-energy of the Λ-particle. Using an S-wave separable potential fitted to the ΛN scattering data, exact analytic expressions for B_Λ are found for both methods and compared. The relation between the two approaches is discussed and it is shown how to extend the Green-function formulation to include the effect of the higher-order cluster diagrams, contributing to the Λ-particle self-energy, in a consistent manner. It is pointed out that this approach provides a more systematic formulation than the usual extended Bethe-Goldstone approach. The model ΛN hard core problem is also investigated in the Green function approach in an appendix: the ground-state energy is rederived and expressions are found for the effective mass and damping of the Λ-quasi-particle up through terms of order (k_Fa)².