Nuclear force

Electrons in atoms move under the Coulomb force. Nuclei of average mass have roughly 8 MeV of binding for every nucleon, much more than any atomic binding energy, so something other than electric attraction must hold a nucleus together: a strong attraction of an entirely new kind.

It has to beat the repulsion between the protons and hold protons and neutrons inside the tiny nuclear volume. Its properties were worked out from many experiments between 1930 and 1950.

(i) It is far stronger than the electric repulsion among the protons, which it has to overpower to keep the nucleus together. Gravity is weaker again than the electric force.

(ii) Between two nucleons the force drops rapidly to zero once they are more than a few femtometres apart. This short range gives saturation in medium and large nuclei, and so the near-constant binding energy per nucleon.

Fig. 13.2 roughly plots the potential energy of two nucleons against separation. It is lowest at r₀ ≈ 0.8 fm: beyond 0.8 fm the force is attractive, and closer than 0.8 fm it is strongly repulsive.

(iii) The force between neutron and neutron, proton and neutron, and proton and proton is roughly the same: the nuclear force does not depend on electric charge.

Unlike Coulomb's law or Newton's law of gravitation, the nuclear force has no simple mathematical formula.