The Strong Nuclear Force — What Holds the Nucleus Together

Protons are positively charged. They repel each other via the electromagnetic force. Pack dozens of them into a space a few femtometres across and the repulsion is enormous. So what stops every nucleus heavier than hydrogen from flying apart? The strong nuclear force — the most powerful force in nature.

Two levels of the strong force

The strong force operates at two scales. At the deepest level, it binds quarks together inside protons and neutrons, mediated by particles called gluons. This is described by quantum chromodynamics (QCD) and involves "colour charge" rather than electric charge. A proton is made of two up quarks and one down quark held together by gluons.

At the nuclear level, what holds protons and neutrons together in a nucleus is actually the residual strong force — a spillover effect, analogous to how van der Waals forces between molecules are a residual effect of electromagnetic forces between their constituent charges. This residual force is mediated by virtual pion exchange between nucleons.

Key properties

The strong force is about 100 times stronger than electromagnetism at nuclear distances. But it has an extremely short range — roughly 1-3 femtometres. Beyond about 2.5 fm, the force drops to essentially zero. This short range has profound consequences for nuclear structure. Each nucleon only interacts with its nearest neighbours, not with every other nucleon in the nucleus. This is why the binding energy per nucleon saturates — adding more nucleons to a large nucleus doesn't increase the binding per nucleon because the new nucleons only "feel" their immediate neighbours.

Competition with Coulomb repulsion

The electromagnetic repulsion between protons has infinite range — every proton repels every other proton in the nucleus. The strong force only reaches nearest neighbours. As nuclei get larger, Coulomb repulsion grows faster than the strong force can compensate. This is why very heavy nuclei become unstable and undergo alpha decay or fission. It's also why the BE/A curve peaks at iron and declines for heavier elements.

The balance between the strong force and Coulomb repulsion determines which nuclei are stable, which are radioactive, and which can't exist at all. Our binding energy calculator uses the semi-empirical mass formula that encodes this competition in its volume and Coulomb energy terms.