Note on spin-orbit interactions in nuclei and hypernuclei

Abstract

A detailed comparison is made between the spin-orbit interactions in $\Lambda$ 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 $\Delta (1232)$-isobars (a 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 $2\pi$-exchange three-body contribution for $\Lambda$ 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 $\pi$-exchange with an intermediate $\Sigma$ 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 $\Lambda$ hypernuclei.

10 pages, 7 figures, to be published in Nuclear Physics A, Special Issue on "Strangeness Nuclear Physics (ed. A. Gal)

References in corpus (14)

• Recent Progress in Quantum Hadrodynamics
• Realistic models of pion-exchange three-nucleon interactions
• Peripheral Nucleon-Nucleon Phase Shifts and Chiral Symmetry
• In-medium nuclear interactions of low-energy hadrons
• Relativistic nuclear model with point-couplings constrained by QCD and chiral symmetry
• Relativistic nuclear energy density functional constrained by low-energy QCD
• Nuclear energy density functional from chiral pion-nucleon dynamics
• Nuclear Many-Body Dynamics constrained by QCD and Chiral Symmetry
• Chiral SU(3) dynamics and $\Lambda$-hyperons in the nuclear medium
• The relativistic self-energy in nuclear dynamics
• Three-body spin-orbit forces from chiral two-pion exchange
• In-medium chiral SU(3) dynamics and hypernuclear structure
• Spin-orbit coupling in nuclei and realistic nucleon-nucleon potentials
• $\Sigma$-nuclear spin-orbit coupling from two-pion exchange

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• Performance of the ATLAS muon trigger in pp collisions at $\sqrt{s}=8$ TeV
• A study of hyperons in nuclear matter based on chiral effective field theory
• Quasiparticle Random Phase Approximation with Interactions from the Similarity Renormalization Group
• Hypernuclear single particle spectra based on in-medium chiral SU(3) dynamics
• Structure of 55Ti from relativistic one-neutron knockout
• Nuclear energy density functional from chiral pion-nucleon dynamics revisited
• Addressing spectroscopic quality of covariant density functional theory
• Rolling Skyrmions and the Nuclear Spin-Orbit Force
• Overview of Strangeness Nuclear Physics
• Contribution of the rho meson and quark sub-structure to the nuclear spin-orbit potential
• Nuclear Matter and Finite Nuclei in the Effective Chiral Model
• From spin to pseudospin symmetry: The origin of magic numbers in nuclear structure
• Foundations of Strangeness Nuclear Physics derived from chiral Effective Field Theory