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The strong interaction is the color interaction described by quantum chromodynamics. Quarks carry color charge, gluons mediate the interaction and also carry color themselves, and physical low-energy states organize into color-singlet hadrons.
At short distances, asymptotic freedom makes a perturbative treatment useful. At hadronic distances, confinement and strong collective dynamics require other methods. The binding of quarks into a proton and the residual interaction between nucleons in an atomic nucleus are related effects at different descriptive levels. The latter can be modeled using hadrons rather than pretending that a free gluon simply travels between two structureless nucleons. Scattering resolves the short-distance constituents, while hadron and nuclear spectra constrain their low-energy collective behavior.