Nuclear forces can be systematically derived using effective chiral Lagrangians consistent with the symmetries of QCD. I review the status of the calculations for two- and three-nucleon forces and their applications in few-nucleon systems. I also address issues like the quark mass dependence of the nuclear forces and resonance saturation for four-nucleon operators.

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Modern theory of nuclear forces

We review how nuclear forces emerge from low-energy QCD via chiral effective field theory. The presentation is accessible to the non-specialist. At the same time, we also provide considerable detailed information (mostly in appendices) for the benefit of researchers who wish to start working in this field.

Chiral effective field theory and nuclear forces

Few-nucleon forces and systems in chiral effective field theory

Nuclear forces from chiral Lagrangians using the method of unitary transformation II: The two-nucleon system

We evaluate, within one-loop chiral perturbation theory, the two-pion exchange diagrams with single and double delta-isobar excitation contributing to elastic NN-scattering. We find that virtual $\Delta$-excitation processes (in the static limit) produce the correct amount of isoscalar central attraction as needed in the peripheral partial waves with $L\geq 3$. Furthermore we compute the two-loop diagrams involving the $\pi\pi$-interaction (so-called correlated $2\pi$-exchange). Contrary to common believe these processes lead to negligibly small and repulsive corrections to the NN-potential. The exchange of vector mesons ($\rho, \omega$) turns out to be important for the F-wave phase shifts above $T_{lab}=150$ MeV. Without adjustable parameters we are able to reproduce the empirical NN phase shifts up to 350 MeV for $L\geq 3$ and up to about (50--80) MeV for the D-waves. This is therefore the characteristic window in which the NN-interaction is basically governed by chiral symmetry. Not surprisingly, the lower partial waves require non-perturbative methods and additional short-distance parametrizations of the NN-dynamics.

N. Kaiser

Papers

Peripheral NN-Scattering: Role of Delta-Excitation, Correlated Two-Pion and Vector Meson Exchange