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Incoming links: One-pion exchange
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
Yukawa meson theory of nuclear forces 2026-10-18
In 1935, Hideki Yukawa proposed a new massive exchange quantum to explain nucleon binding. His paper began with the inadequacy of an Electron–neutrino exchange description of the binding strength. It then required a potential energy falling faster with distance than a Coulomb potential, introduced an exponentially decaying field, and related its inverse range to the exchange particle's rest mass. This was a theoretical proposal, not a detection with an apparatus of his own.[ref]
On the Interaction of Elementary Particles. I by Hideki Yukawa. On the Interaction of Elementary Particles. I, opening motivation, equations (1)–(3) and (12); text inspected in a retypeset mirror
The crucial idea is that a finite rest mass supplies a length scale even in empty space. In a scalar model, the static limit of a Klein-Gordon equation produces the modified Helmholtz equation. Its decaying Green's function gives the Yukawa potential. The derivation below isolates this range mechanism; one-pion exchange also carries spin and isospin structure.
The nuclear emulsion track experiment used developed photographic emulsions exposed to cosmic rays and inspected microscopically. Stopping pions gave daughter muon tracks with closely grouped ranges. Comparing penetrating muons with pion-induced nuclear breakup distinguished their interactions; this was not a direct static force measurement. The muon is a lepton, not Yukawa's strongly interacting meson.[ref]
The Cosmic Radiation by Cecil Frank Powell. The Cosmic Radiation, printed pp. 144–145 and 151–152, especially Fig. 5; inspected in the Columbia-hosted Nobel volume