Note on spin–orbit interactions in nuclei and hypernuclei

A detailed comparison is made between the spin–orbit interactions in Λ hypernuclei and ordinary nuclei. We argue that there are three major contributions to the spin–orbit interaction: (1) a short-range component involving scalar and vector mean fields; (2) a “wrong-sign” spin–orbit term generated by the pion exchange tensor force in second order; and (3) a three-body term induced by two-pion exchange with excitation of virtual Δ(1232)-isobars (à la Fujita–Miyazawa). For nucleons in nuclei the long-range pieces related to the pion-exchange dynamics tend to cancel, leaving room dominantly for spin–orbit mechanisms of short-range origin (parametrized, e.g., in terms of relativistic scalar and vector mean fields terms). In contrast, the absence of an analogous 2π-exchange three-body contribution for Λ hyperons in hypernuclei leads to an almost complete cancellation between the short-range (relativistic mean-field) component and the “wrong-sign” spin–orbit interaction generated by second order π-exchange with an intermediate Σ hyperon. These different balancing mechanisms between short- and long-range components are able to explain simultaneously the very strong spin–orbit interaction in ordinary nuclei and the remarkably weak spin–orbit splitting in Λ hypernuclei.