Nuclear spin–orbit interaction from chiral pion–nucleon dynamics Original Research Article

Using the two-loop approximation of chiral perturbation theory, we calculate the momentum and density dependent nuclear spin–orbit strength Uls(p,kf). This quantity is derived from the spin-dependent part of the interaction energy View the MathML source of a nucleon scattering off weakly inhomogeneous isospin symmetric nuclear matter. We find that iterated 1π-exchange generates at saturation density, kf0=272.7 MeV, a spin–orbit strength at p=0 of Uls(0,kf0)≃35 MeV fm2, 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 Vls underlying the empirical spin–orbit strength View the MathML source becomes a rather weak one, Vls≃17 MeV, after the identification rls=mπ−1 as suggested by the present calculation. We observe, however, a strong p-dependence of Uls(p,kf0) 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 2π-exchange for a finite nucleus. We also calculate the complex-valued isovector single-particle potential UI(p,kf)+iWI(p,kf) in isospin asymmetric nuclear matter proportional to τ3(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.