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 nuclear spin-orbit strength $U_{ls}(p,k_f)$. This quantity is derived from the spin-dependent part of the interaction energy ${\Sigma }_{spin}=\frac{i}{2}\vec{\sigma }\cdot (\vec{q}\times \vec{p})U_{ls}(p,k_f)$ of a nucleon scattering off weakly inhomogeneous isospin symmetric nuclear matter. We find that iterated $1\pi$-exchange generates at saturation density, $k_{f0}=272.7$MeV, a spin-orbit strength at $p=0$ of $U_{ls}(0,k_{f0})\simeq 35$ MeVfm${}^2$ 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 ${\tilde{U}}_{ls}=V_{ls}{r}_{ls}^2$ becomes a rather weak one, $V_{ls}\simeq 17$ 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 $2\pi$-exchange for a finite nucleus. We also calculate the complex-valued isovector single-particle potential $U_I(p,k_f)+i{W}_I(p,k_f)$ 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 $p=k_f$.

20 pages, 10 Figures, Accepted for publication in Nuclear Physics A

Cited by in corpus (7)

• Modern Theory of Nuclear Forces
• Chiral approach to nuclear matter: Role of two-pion exchange with virtual delta-isobar excitation
• Nuclear energy density functional from chiral pion-nucleon dynamics
• Chiral SU(3) dynamics and $\Lambda$-hyperons in the nuclear medium
• Hypernuclear single particle spectra based on in-medium chiral SU(3) dynamics
• The baryon-decuplet in the chiral dynamics of Lambda-hyperons in nuclear matter
• Isovector nuclear spin-orbit interaction from chiral pion-nucleon dynamics