What is the residual strong nuclear force?

© 2026 Kieron Conway - All rights reserved.

Inside hadrons

As discussed in Part 1 of a Journey into Modern Physics, the strong-nuclear interaction is the force that keeps the quarks of protons confined to the tiny volume of the proton. The same applies to the neutron: in fact, it applies to the quarks in all hadrons, the proton being the only stable hadron when on its own.

Outside hadrons – the nucleus of an atom

So, how do all the protons and neutrons stay locked inside an atom's nucleus? All the protons are positively charged and should just break the nucleus apart with all that repulsive force at work. It's obvious that neutrons must play a part in stopping such a catastrophe but how?

The strong nuclear force leaks!

You can think of the strong nuclear force, leaking out of the protons and neutrons in a nucleus and creating a binding force for the components of a nucleus. This is known as the residual strong nuclear force, 'gluing' the nucleons together in a nucleus and preventing all the positively charged protons from breaking the nucleus apart.

The strong nuclear force is mediated by gluons inside the confines of the hadron, but what mediates the residual strong nuclear force?

The role of the mesons

In 1935, Hideki Yukawa proposed the existence of a previously unknown particle that could mediate the residual, strong-nuclear force between pairs of nucleons (protons and neutrons). He called this particle a meson, years before mesons were observed in particle accelerators or cosmic-ray experiments.

Yukawa was able to estimate the mass of this particle, and because it turned out to be similar to that of the muon (second generation electron), discovered around the same time, the mediator of the residual strong force was initially (and incorrectly) identified as the mu-meson.

In fact, the muon is a lepton, not a meson, and does not participate in the strong interaction at all. It was not until 1947 that the true mediators that Yukawa had predicted, were discovered: the pi mesons, also known as pions.

The pion family

The pion family consists of a triplet of pions:

• a positively charged pion (π⁺)

• a negatively charged pion (π⁻)

• a neutral pion (π⁰)

These particles turned out to be the key carriers of the long-range, attractive force that keeps nucleons tightly packed in a nucleus. They represent the mediators of the residual strong-nuclear interaction.

Neutral Pions & Long-range Attraction

As described in A Journey into Modern Physics, the residual strong interaction can be pictured, in a simplified way, as the strong force “leaking out” of a nucleon. One way to imagine this is that a gluon escapes from a nucleon and almost immediately becomes a neutral pion.

All mesons are composed of one quark and one antiquark. Ignoring quantum superposition for the moment, a neutral pion can be thought of as a mixture of quark-antiquark pairs, primarily:

• [UP + anti-UP]

• [DOWN + anti-DOWN]

Strange quark mesons (STRANGE + anti-STRANGE) exist but play no role in ordinary nuclear binding.

A simplified picture of attraction

A simplified way to imagine the attractive interaction of two nucleons is as follows:

1. An [UP-quark + anti-UP-quark] meson is released from a nucleon and enters either a neighbouring proton or a neutron, where the anti-quark annihilates the corresponding quark and the standard quark from the meson replaces the destroyed quark.

2. The same applies to a [DOWN-quark + anti-DOWN-quark] meson entering either a proton or a neutron.

3. This exchange transfers momentum and energy between nucleons without changing their identities.

Because both UP and DOWN quark combinations are possible, neutral pions can mediate attractive interactions between:

• two protons

• two neutrons

• a proton and a neutron

In all cases, the identities of the nucleons remain unchanged after the interaction, one acts as the source of the mediating pion and one acts as the recipient. This exchange of neutral pions provides a significant part of the long-range, binding force that holds nucleons together in nuclei.

Attraction mediated by neutral mesons

Here are some simplified Feyman diagrams representing neutral-pion mediated interactions between two nucleons.

The arrows in the above Feynman diagrams indicate which nucleon instigated the interaction and launched the mediator and which becomes the recipient. The LHS of each diagram indicates the state of the two particles before the interaction and the RHS shows the result after the interaction. The state of the particles is unchanged after the interaction.

It is this exchange of a neutral pion that can be considered to create the binding force between nucleons.

Charged pions also play a role

Charged pions can also mediate the long-range, interaction between nucleons, but they do so in a more intriguing way, by allowing the participating nucleons to temporarily swap identities.

In a simplified description:

• A proton can emit a positively charged pion (π⁺), briefly becoming a neutron.

• The π⁺ travels to a nearby neutron.

• When absorbed, the neutron briefly becomes a proton.

Alternatively:

• A neutron can emit a negatively charged pion (π⁻), briefly becoming a proton.

• The π⁻ travels to a nearby proton.

• When absorbed, the proton briefly becomes a neutron.

  
  

After the interaction, the nucleons rapidly return to their original identities.

Why this swapping of identities is allowed

Although the above process sounds strange, it does not violate any physical laws:

• Protons and neutrons are best understood as two states of the same particle, distinguished by a quantum property called isospin.

• The charged pion simply carries this isospin between nucleons.

• The interaction is brief and governed by quantum uncertainty.

• The end result is that the two participating nucleons regain their original identities.

  
  

Charged pion exchange is, in fact, stronger than neutral pion exchange, and plays a dominant role in long-range nuclear binding, emphasising the key role that neutrons play.

The Feynman diagrams for charged pion mediated interactions, up the point where the particles identities are swapped are as follows;

The LHS diagram shows a neutron launching a negatively-charged pion and this is captured by the neighbouring proton. Both particles swap identities temporarily. In the RHS diagram, the proton launches a positively-charged pion which then enters a neighbouring neutron and again, both nucleons temporarily swap identities.

The charged-pion, interaction is far stronger than the neutral-pion interaction.

More than just attraction

The residual strong nuclear force is not purely attractive.

At very short distances, nucleons experience a powerful repulsive interaction that prevents them from collapsing into one another. At these distances, the residual strong force becomes one of the strongest repulsive forces in nature.

This repulsion, together with the Pauli exclusion principle, ensures that nucleons maintain a stable separation inside the nucleus.

Short-range repulsion and heavier mesons

Heavier mesons contribute to this short-range behaviour. In particular, this involves a triplet of rho mesons and the lone omega meson.

Rho (ρ) mesons

• Rho mesons are more massive relatives of the pions.

• They come in positive, negative, and neutral forms.

• Their exchange becomes significant when nucleons are very close together.

• They contribute strongly to short-range repulsion and spin-dependent effects.

Omega (ω) mesons

• The neutral omega meson is even more massive that the rho mesons.

• It produces a very short-range, strongly repulsive interaction.

• This repulsive “core” becomes dominant when nucleons approach extremely closely.

In Summary - a self-regulating nuclear force

Taken together, these attractive and repulsive interactions make the residual strong nuclear force self-regulating, according to the separation of the two participating nucleons:

• Three Pions provide long-range attraction.

• Three Rho mesons (heavy versions of the pions) refine the interaction at shorter distances.

• One Omega meson generate a hard repulsive core.

This balance keeps nucleons tightly bound, yet prevents collapse. As a result, nuclei across the periodic table exhibit remarkably similar nucleon packing densities.

An intuitive outcome

These simplified descriptions represent an intuitive picture of underlying quantum-field interactions between the quarks in nucleons and the quarks in the mediating mesons, providing a delicate balance that allows atomic nuclei, and therefore matter itself, to exist.

Type 'rho and omega mesons' into Google and head for the Hyperphysics link titled 'Hadrons, Baryons and Mesons' where you can see details about their properties in a table.

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