Nuclear spin-orbit interaction from chiral pion-nucleon dynamics

摘要

Using the two-loop approximation of chiral perturbation theory, we calculate the momentum and density dependent nuclear spin-orbit strength U-ls (p, k(f)). This quantity is derived from the spin-dependent part of the interaction energy Sigma(spin) = (i)/(2)(σ) over right arrow (.) ((q) over right arrow x (q) over right arrow) U-ls (p, k(f)) of a nucleon scattering off weakly inhomogeneous isospin symmetric nuclear matter. We find that iterated 1pi-exchange generates at saturation density, k(f0) = 272.7 MeV, a spin-orbit strength at p = 0 of U-ls(0, k(f0)) similar or equal to 35 MeV fm(2), in perfect agreement with the empirical value used in the shell model. This novel spin-orbit strength is neither of relativistic nor of short range origin. The potential V-ls underlying the empirical spin-orbit strength (U) over tilde (ls) = V(ls)r(ls)(2) becomes a rather weak one, V-ls similar or equal to 17 MeV, after the identification r(ls) = m(pi)(-1) as suggested by the present calculation. We observe, however, a strong p-dependence of U-ls (p, k(f0)) leading even to a sign change above p = 200 MeV. This and other features of the emerging spin-orbit Hamiltonian which go beyond the usual shell model parametrization leave questions about the ultimate relevance of the spin-orbit interaction generated by 2pi-exchange for a finite nucleus. We also calculate the complex-valued isovector single-particle potential U-I(p, k(f)) + iW(I) (p, k(f)) in isospin asymmetric nuclear matter proportional to tau(3)(N - Z)/(N + Z). For the real part we find reasonable agreement with empirical values and the imaginary part vanishes at the Fermi-surface p = kf. (C) 2002 Elsevier Science B.V. All rights reserved. [References: 19]