Why nuclei do not fall apart

Problem

Two protons close together inside a nucleus repel each other through Coulomb repulsion, and yet the nucleus stays bound and does not break apart. Explain, without using formulae, where the force that holds protons and neutrons together comes from, and why this force only acts at short range.

Solution

The force responsible is the strong nuclear interaction. It is an attractive force acting between all nucleons — both protons and neutrons — regardless of electric charge. At the distances typical inside a nucleus (of the order of a femtometre) it is roughly 100 times stronger than the Coulomb repulsion between protons: this is why it beats the electric repulsion and keeps the nucleus compact.

The decisive feature is the very short range: the strong force is practically zero beyond about $2\ \text{fm}$. Each nucleon therefore feels the attraction only of its immediate neighbours, not of every other nucleon in the nucleus. This property is called saturation: as the number of nucleons increases, the binding energy per nucleon does not keep growing indefinitely.

Saturation also explains why arbitrarily large stable nuclei do not exist: the strong force only binds neighbours, while the Coulomb repulsion acts between all protons and grows with size. Beyond a certain size the repulsion prevails and the nucleus becomes unstable.

$\ev{\text{strong force: attractive at short range (}<2\text{ fm), beats Coulomb inside the nucleus}}$

Connections

Topics: Nuclear physics Objects: Atomic nucleus