Physics 1935

On the Interaction of Elementary Particles

Hideki Yukawa

The nuclear force is short because its carrier is heavy — a new particle, the meson.

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In depth · the introduction

What holds an atom's nucleus together is a force so strong it crushes the protons' mutual repulsion — yet it vanishes a hair's breadth away. Yukawa explained both facts with one bold guess: the force is carried by a brand-new particle, and that particle is heavy.

The big idea

By 1935 physicists knew the nucleus was packed with protons and neutrons, but were stuck on a paradox. The force gluing them must be enormous — far stronger than the electric repulsion that should blow a nucleus apart. Yet it reaches no farther than the nucleus itself; an inch away, it's simply gone. What kind of force is mighty up close and absent just beyond?

Yukawa's answer borrowed a picture from electromagnetism. There, two charges 'feel' each other by exchanging photons — particles of light. Maybe, he said, two nucleons feel the nuclear force by exchanging a new particle of their own. Here is the twist: a photon has no mass, which is exactly why electric and magnetic forces reach across the universe. If the new particle had mass, the force it carries would die off after a tiny distance. From the known size of the nucleus, Yukawa could even predict the mass — about 200 times the electron's. He had conjured a particle no one had ever seen, just from how far a force could reach.

How it came about

Hideki Yukawa was a young theorist at Osaka, working in a Japanese physics community that was only beginning to be heard abroad. Europe's giants — Heisenberg, Fermi — had tried to explain nuclear binding by having particles swap electrons and neutrinos, but the numbers came out far too weak. Yukawa spent restless months on the problem, and his leap was to stop reusing the known particles and invent the right one.

He published in 1935, in a Japanese journal, in English, and for years almost nobody noticed. Then in 1936 a particle of roughly the right mass turned up in cosmic rays, and excitement flared — only to curdle when that particle turned out to barely touch nuclei, so it couldn't be the glue. The real one, the pion, was finally caught in 1947. Two years later Yukawa won the Nobel Prize, the first ever awarded to a Japanese scientist.

Why it mattered

Yukawa changed what a 'force' even means. After him, every fundamental force in nature is understood as the trading of particles — and a simple rule connects the carrier's weight to the force's reach: heavier carrier, shorter range. That single insight organizes the whole modern catalogue of forces, from the massless photon that lets light cross galaxies to the heavy particles behind radioactivity. He also showed that a careful theorist, armed only with a paradox and a wave equation, can predict a new piece of the universe before any instrument finds it.

A way to picture it

Imagine two boats on a lake tossing a heavy medicine ball back and forth. Each throw shoves the thrower backward and the catcher onward — the exchange itself acts like a force between the boats. Now notice: because the ball is heavy, you can only heave it a short way before it splashes down. The boats must be close for the game to work at all. Swap in a feather-light beach ball and you could toss it clear across the lake — a long-range force. Yukawa's nuclear force is the heavy-ball game; electromagnetism is the beach ball. The weight of what's thrown sets how far the force can reach.

Where it sits

Yukawa stands midway in a long relay. Maxwell had cast electromagnetism as a field; quantum theory made that field's quantum the photon; Yukawa generalized the move to a force that needed a heavy quantum, and so opened the era of particle exchange. From his idea runs a straight line to the W and Z particles of the weak force, to quarks and gluons, and to the Higgs boson — whose 'Yukawa couplings' (his name, attached for good) are how the other particles get their mass. The nuclear glue he was after is now seen as a leftover of deeper forces, but the way of thinking he founded is the language all of particle physics still speaks.

The original document

Original source text

Introduction — the problem of the nuclear force

H. Yukawa · On the Interaction of Elementary Particles · Proc. Phys.-Math. Soc. Japan, 3rd ser., 17 (1935) 48–57 · Received 1935

At the present stage of the quantum theory little is known about the nature of interaction of elementary particles. Heisenberg considered the interaction of “Platzwechsel” between the neutron and the proton to be of importance to the nuclear structure.

Recently Fermi treated the problem of β-disintegration on the hypothesis of “neutrino”. According to this theory, the neutron and the proton can interact by emitting and absorbing a pair of neutrino and electron. Unfortunately the interaction energy calculated on such assumption is much too small to account for the binding energies of neutrons and protons in the nucleus.

To remove this defect, it seems natural to modify the theory of Heisenberg and Fermi in the following way. The transition of a heavy particle from neutron state to proton state is not always accompanied by the emission of light particles, i.e., a neutrino and an electron, but the energy liberated by the transition is taken up sometimes by another heavy particle, which in turn will be transformed from proton state into neutron state.

Now such interaction between the elementary particles can be described by means of a field of force, just as the interaction between the charged particles is described by the electromagnetic field. … In the quantum theory this field should be accompanied by a new sort of quantum, just as the electromagnetic field is accompanied by the photon.

The field describing the interaction

Field Describing the Interaction

In analogy with the scalar potential of the electromagnetic field, a function U(x, y, z, t) is introduced to describe the field between the neutron and the proton. This function will satisfy an equation similar to the wave equation for the electromagnetic potential.

The potential of force between the neutron and proton should, however, not be of Coulomb type, but decrease more rapidly with distance. It can [be] expressed, for example by ±g² · e^(−λr)/r, where g is a constant with the dimension of electric charge … and λ with the dimension cm.⁻¹

Since this function is a static [solution] with central symmetry of the wave equation (∆ − (1/c²)∂²/∂t² − λ²) U = 0, let this equation be assumed to be the correct equation for U in vacuum. In the presence of the heavy particles, the U–field interacts with them and causes the transition from neutron state to proton state.

Rough estimation shows that the calculated values agree with the experimental results, if we take for λ the value between 10¹² cm⁻¹ and 10¹³ cm⁻¹ and for g a few times of the elementary charge e, although no direct relation between g and e was suggested in the above considerations.

The quantum that carries the field

Nature of the Quanta Accompanying the Field

The U–field above considered should be quantized according to the general method of the quantum theory. Since the neutron and the proton both obey Fermi's statistics, the quanta accompanying the U–field should obey Bose's statistics. … The law of conservation of the electric charge demands that the quantum should have charge either +e or −e.

[Writing the free-space wave equation in the form (px² + py² + pz² − W²/c² + mU²c²) U = 0,] the quantum accompanying the field has the proper mass mU = λh/c.

Assuming λ = 5 × 10¹² cm⁻¹., we obtain for mU a value 2 × 10² times as large as the electron mass. As such a quantum with large mass and positive or negative charge has never been found by the experiment, the above theory seems to be on a wrong line. We can show, however, that, in the ordinary nuclear transformation, such a quantum can not be emitted into outer space.

Summary & a cosmic-ray guess

Summary

The interactions of elementary particles are described by considering a hypothetical quantum which has the elementary charge and the proper mass and which obeys Bose's statistics. The interaction of such a quantum with the heavy particle should be far greater than that with the light particle in order to account for the large interaction of the neutron and the proton as well as the small probability of β-disintegration.

The massive quanta may also have some bearing on the shower produced by cosmic rays.

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Department of Physics, Osaka Imperial University · 1935