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

Abstract

Using the two-loop approximation of chiral perturbation theory, we calculate the momentum and density dependent isovector nuclear spin-orbit strength $V_{ls}(p,k_f)$. This quantity is derived from the spin-dependent part of the interaction energy ${\Sigma }_{spin}=\frac{i}{2}\vec{\sigma }\cdot (\vec{q}\times \vec{p})[U_{ls}(p,k_f)-V_{ls}(p,k_f){\tau }_3\delta ]$ of a nucleon scattering off weakly inhomogeneous isospin-asymmetric nuclear matter. We find that iterated $1\pi$-exchange generates at saturation density, $k_{f0}=272.7$MeV, an isovector nuclear spin-orbit strength at $p=0$ of $V_{ls}(0,k_{f0})\simeq 50$ MeVfm${}^2$. This value is about 1.4 times the analogous isoscalar nuclear spin-orbit strength $U_{ls}(0,k_{f0})\simeq 35$ MeVfm${}^2$ 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 $U_{ls}(p,k_f)$. The effects of the three-body diagrams constructed from the Weinberg-Tomozawa $\pi \pi NN$-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.

Comments: 15 pages, 8 figures