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

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 2 ~σ · (~q × ~ p )[Uls(p, kf ) − Vls(p, kf )τ3δ] of a nucleon scattering off weakly inhomogeneous isospinasymmetric nuclear matter. We find that iterated 1π-exchange generates at saturation density, kf0 = 272.7MeV, an isovector nuclear spin-orbit strength at p = 0 of Vls(0, kf0) ' 50 MeVfm2. This value is about 1.4 times the analogous isoscalar nuclear spin-orbit strength Uls(0, kf0) ' 35 MeVfm2 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 WeinbergTomozawa 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. PACS: 12.38.Bx, 21.65.+f, 24.10.Cn