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Incoming links: Modern Theory of Nuclear Forces by Evgeny Epelbaum and others
Nuclear force Created 2026-10-06 Updated 2026-10-18
The residual strong interaction between nucleons. Its long-distance part involves pion exchange and depends on spin and isospin. It is distinct from directly exchanging gluons between color-singlet nucleons.
Why do protons and neutrons bind into an atomic nucleus, even though protons repel electrically? An attractive nuclear force can lower the total energy below that of separated nucleons, producing nuclear binding energy. The deuteron, containing one proton and one neutron, is the simplest such bound state.
In Quantum chromodynamics, nucleons are composite colour singlets built from quarks and gluons. Their residual nuclear force has a longest-range strong contribution from one-pion exchange, with additional interactions at shorter distances.[ref]
Modern Theory of Nuclear Forces by Evgeny Epelbaum and others. Modern Theory of Nuclear Forces, inspected preprint sections I and I.B
One-pion exchange 2026-10-18
Although the pion has spin zero, one-pion exchange depends on nucleon spin and isospin and includes a nuclear tensor force. Shorter-range and multiple-nucleon interactions also matter. The scalar Yukawa potential isolates a range mechanism rather than specifying the complete nuclear force.[ref]
Modern Theory of Nuclear Forces by Evgeny Epelbaum and others. Modern Theory of Nuclear Forces, inspected preprint sections I.B and II.B, especially equation (2.11) and Fig. 12