---
title: "Why Yukawa expected a particle between the electron and proton"
description: "How can the short reach of the nuclear force suggest the mass of a new particle?"
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Particles · Experiments · Discovery

# Why Yukawa expected a particle between the electron and proton

How can the short reach of the nuclear force suggest the mass of a new particle?

Sandbox Physics · 2026-10-24

Nobel contribution: 1949-1

1. Start from a tightly bound nucleus
2. Ask why the force has a short reach
3. Introduce a massive exchanged field
4. Compare the prediction with mesons

Yukawa’s force-range argument was a theoretical prediction; the pion was identified later in cosmic-ray emulsions.

## The nucleus needed a force with a short reach

Two protons repel electrically, yet atomic nuclei hold protons close together. The force binding nuclei must overcome that repulsion at very short distances. Move far outside a nucleus and the special attraction quickly fades. In 1935, Hideki Yukawa asked whether this short reach was telling physicists something about a particle they had yet to find.

Electromagnetism already offered a way to organize the question. A field fills space and transfers energy and momentum between charges; quantum theory associates its disturbances with photons. Yukawa proposed a different field for the strong attraction between nuclear particles. Its quantum would carry mass, and that mass would set a natural distance beyond which the static attraction became weak.

Sources: [1]

## A massive field fades away more quickly

An electric charge produces a static field that spreads out gradually. Yukawa’s massive field has an additional suppression with distance. Close to the source, its attraction can be strong. Farther away, the field falls much more steeply. The larger the exchanged particle’s mass, the shorter the characteristic reach. Nuclear distances therefore pointed to a particle heavier than an electron but lighter than a proton.

The useful physical picture is a spatial response. Ask how far a disturbance in a field extends when the field’s quantum has a mass. Relativity and quantum mechanics supply the constants that turn that mass into a length. Two femtometres is twice a millionth of a billionth of a metre. That distance points toward an energy scale of order one hundred million electronvolts. Yukawa’s early estimate was about two hundred electron masses, close enough to identify a new range of masses worth searching for.

One often hears that particles briefly borrow energy and then repay it. That story is easy to remember but obscures the calculation. Energy and momentum are conserved in the interaction. The exchanged quantum inside a calculation need not obey the relation measured for a freely travelling particle. The finite spatial reach follows from the field equations.

The relation is useful even before an exact force law is known. If a proposed carrier were much lighter, its characteristic field would reach much farther; if it were much heavier, its effect would fade over a still smaller distance. The observed size of nuclei therefore restricted the proposal. A theory had to explain why the attraction mattered for neighbouring nucleons and quickly lost importance outside that scale.

Sources: [1]

## The first apparent candidate was the wrong particle

Cosmic rays soon supplied particles in the intermediate mass range. For a time, the particle now called the muon seemed a possible match. But mass alone was an incomplete identification. A particle carrying the nuclear attraction should interact strongly with nuclear matter. Muons passed through matter with behaviour characteristic of a heavy relative of the electron, and their nuclear interactions did not fit that task.

The important change came in 1947. Cecil Powell’s group, including César Lattes, Hugh Muirhead and Giuseppe Occhialini, studied photographic emulsions exposed to cosmic rays. The emulsion preserved short tracks in enough detail to follow a heavier meson stopping and producing a lighter secondary particle. The parent was the pion; the daughter was a muon. Distinguishing the two resolved the confusion created by placing both in one broad category of intermediate mass.

Sources: [2]

## The idea survived in a more detailed account of nuclear matter

Pions do play an important role in the longer-distance part of the force between nucleons, the collective name for protons and neutrons. Modern nuclear physics uses that connection in effective descriptions of nuclear forces. At shorter distances, the internal quarks and gluons require the more complete theory of strong interactions, quantum chromodynamics. The force holding quarks together and the residual force between nucleons are related levels of description.

Yukawa received the 1949 Nobel Prize for predicting mesons from nuclear-force theory. His achievement was to turn a measured feature of a force into a question about matter’s inventory. The nuclear force faded over a tiny distance; a new mass scale made that fade understandable. Experiment then had to find the right particle and check how it interacted.

Sources: [1] [2]

## Sources and reading notes

1. [Yukawa, On the Interaction of Elementary Particles I (1935)](https://doi.org/10.11429/ppmsj1919.17.0_48)

   Yukawa connects a finite force range with a massive exchanged quantum and estimates a mass between electron and proton masses.

2. [Lattes, Muirhead, Occhialini and Powell, Processes Involving Charged Mesons (1947)](https://doi.org/10.1038/159694a0)

   The emulsion observations distinguish the pion and its daughter muon; this is the experimental continuation of Yukawa’s proposal.

## Follow the next question

[The pion leaves a second track in photographic emulsion](https://sandboxphysics.com/stories/particle-evidence/powell-pion-emulsion/)

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