Chapter 33 Particle Physics
33.1 The Yukawa Particle and the Heisenberg Uncertainty Principle Revisited
Summary
- Define Yukawa particle.
- State the Heisenberg uncertainty principle.
- Describe pion.
- Estimate the mass of a pion.
- Explain meson.
Particle physics as we know it today began with the ideas of Hideki Yukawa in 1935. Physicists had long been concerned with how forces are transmitted, finding the concept of fields, such as electric and magnetic fields to be very useful. A field surrounds an object and carries the force exerted by the object through space. Yukawa was interested in the strong nuclear force in particular and found an ingenious way to explain its short range. His idea is a blend of particles, forces, relativity, and quantum mechanics that is applicable to all forces. Yukawa proposed that force is transmitted by the exchange of particles (called carrier particles). The field consists of these carrier particles.

Specifically for the strong nuclear force, Yukawa proposed that a previously unknown particle, now called a pion, is exchanged between nucleons, transmitting the force between them. Figure 1 illustrates how a pion would carry a force between a proton and a neutron. The pion has mass and can only be created by violating the conservation of mass-energy. This is allowed by the Heisenberg uncertainty principle if it occurs for a sufficiently short period of time. As discussed in Chapter 29.7 Probability: The Heisenberg Uncertainty Principle the Heisenberg uncertainty principle relates the uncertainties
where
Example 1: Calculating the Mass of a Pion
Taking the range of the strong nuclear force to be about 1 fermi (
Strategy
The calculation is approximate because of the assumptions made about the range of the force and the speed of the pion, but also because a more accurate calculation would require the sophisticated mathematics of quantum mechanics. Here, we use the Heisenberg uncertainty principle in the simple form stated above, as developed in Chapter 29.7 Probability: The Heisenberg Uncertainty Principle. First, we must calculate the time
Solution
The distance the pion travels is
Now, solving the Heisenberg uncertainty principle for
Solving this and converting the energy to MeV gives
Mass is related to energy by
Discussion
This is about 200 times the mass of an electron and about one-tenth the mass of a nucleon. No such particles were known at the time Yukawa made his bold proposal.
Yukawa’s proposal of particle exchange as the method of force transfer is intriguing. But how can we verify his proposal if we cannot observe the virtual pion directly? If sufficient energy is in a nucleus, it would be possible to free the pion—that is, to create its mass from external energy input. This can be accomplished by collisions of energetic particles with nuclei, but energies greater than 100 MeV are required to conserve both energy and momentum. In 1947, pions were observed in cosmic-ray experiments, which were designed to supply a small flux of high-energy protons that may collide with nuclei. Soon afterward, accelerators of sufficient energy were creating pions in the laboratory under controlled conditions. Three pions were discovered, two with charge and one neutral, and given the symbols
The pions, or
Summary
- Yukawa’s idea of virtual particle exchange as the carrier of forces is crucial, with virtual particles being formed in temporary violation of the conservation of mass-energy as allowed by the Heisenberg uncertainty principle.
Problems & Exercises
1: A virtual particle having an approximate mass of
2: Calculate the mass in
3: Another component of the strong nuclear force is transmitted by the exchange of virtual K-mesons. Taking K-mesons to have an average mass of
Glossary
- pion
- particle exchanged between nucleons, transmitting the force between them
- virtual particles
- particles which cannot be directly observed but their effects can be directly observed
- meson
- particle whose mass is intermediate between the electron and nucleon masses
Solutions
Problems & Exercises
1:
3: