Hyperon-nucleus potentials

Abstract

We review models for the interaction of baryons ( N, Λ, Σ and Ξ) with nuclei, emphasizing the underlying meson exchange picture. Starting from a phenomenological one boson exchange model (the Nijmegen potential, as an example) which accounts for the available NN, ΛN and ΣN two-body scattering data, we show how to construct the effective baryon-nucleon interaction ( G-matrix). Employing the folding model, we then obtain the many-body potentials for bound states in terms of the nuclear density and the appropriate spin-isospin weighted G-matrices. The models we emphasize most impose SU(3) constraints on baryon-baryon coupling constants SU(3) is broken through the use of physical masses), although we also compare with rough estimates based on quark model relations between coupling constants. We stress the essential unity and economy of such models, in which nucleon and hyperon-nucleus potentials are intimately related via SU(3), and the connection between the two-body and many-body potentials is preserved. We decompose the nuclear potentials into central and spin-orbit parts, each of which is isospin dependent. For nucleons, the microscopic origin of the isospin dependent Lane potential V 1 N is clarified. For Λ and Σ hyperons, the one boson exchange model with SU(3) constraints leads to one-body spin-orbit strengths V LS B which are relatively weak ( V LS Λ ≈ 1.5−2 MeV, V LS Σ ≈ 2.5−;3 MeV, compared to V LS N ≈ 7−9 MeV). We demonstrate the interplay between symmetric and antisymmetric two-body spin-orbit forces which give rise to these results, as well as the special role of K and K ∗ exchange for hyperons. We contrast these results with predictions based on the naive quark model. From S and P-wave two-body interactions, a Lane potential for the Σ of depth V 1 Σ ≈ 50−60 MeV is predicted although this result is somewhat uncertain. For the Ξ, the nuclear potential is very different in various models for the two-body interaction based on SU(3) or the quark model: the predicted depth varies from V 0 Ξ ≈ 25 MeV (attraction) to V 0 Ξ ≈ −30 MeV (repulsion), so even the sign of the Ξ potential is uncertain. Our discussion of the real part of hyperon-nucleus potentials is extended to treat the absorptive potentials for Σ and Ξ. We point out the role of Pauli blocking, binding corrections, spin-isospin selectivity of ΣN → ΛN conversion, and isospin mixing in determining the Σ width.