Isovector nuclear spin-orbit interaction from chiral pion-nucleon dynamics

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Using the two-loop approximation of chiral perturbation theory, we calculate the momentum and density-dependent isovector nuclear spin-orbit strength Vls(p,kf). This quantity is derived from the spin-dependent part of the interaction energy Σspin=i/2σ→· (q→×p→)[Uls(p,kf)- Vls(p,kf3δ] of a nucleon scattering off weakly inhomogeneous isospin-asymmetric nuclear matter. We find that iterated 1π-exchange generates at saturation density, kf0=272.7 MeV, an isovector nuclear spin-orbit strength at p=0 of Vls(0,kf0)≃50 MeV fm2. This value is about 1.4 times the analogous isoscalar nuclear spin-orbit strength Uls(0,kf0)≃35 MeV fm2 generated by the same two-pion exchange diagrams. We also calculate several relativistic 1/M-corrections to the isoscalar nuclear spin-orbit strength. In particular, we evaluate the contributions from irreducible two-pion exchange to Uls(p,kf). The effects of the three-body diagrams constructed from the Weinberg-Tomozawa ππNN-contact vertex on the isoscalar nuclear spin-orbit strength are computed. We find that such relativistic 1/M-corrections are less than 20% of the isoscalar nuclear spin-orbit strength generated by iterated one-pion-exchange, in accordance with the expectation from chiral power counting.

Original languageEnglish
Pages (from-to)157-173
Number of pages17
JournalNuclear Physics, Section A
Issue number1-2
StatePublished - 2 Jun 2003


  • Effective field theory at finite density
  • Isoscalar and isovector nuclear spin-orbit interaction


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