Happy Birthday, Hideki Yukawa!

Do we have a clue how the protons and neutrons in the atomic nucleus stick together? A Japanese guy born 100 years ago gave us the first hint how this may happen:

Hideki Yukawa made the proposal, in 1935, that the nuclear force with its characteristic short range and saturation properties could be mediated by a massive exchange particle with roughly 1/10 the mass of the proton. When after some initial confusion about the nature of the mesotron - now better known as the muon - the pion, discovered in 1947, was recognized as Yukawa's exchange particle, he was awarded the Nobel prize in physics for 1949.

Yukawa, born on January 23, 1907 in Tokyo and grown up in Kyoto, was, by curious coincidence, a classmate in high school of another Japanese Nobel Prize winner, Sin-Itiro Tomonaga.


Hideki Yukawa (1907-1981) in 1949. (Source: Yukawa Institute for Theoretical Physics)

Yukawa was an Assistant Professor at Osaka University when he published his paper "On the Interaction of Elementary Particles. I." in Proc. Phys.-Math. Soc. Japan 17, 48 (1935). In quantum field theory, still very new at that time, forces are described by the exchange of virtual particles. I am not so sure about how and when this concept has emerged. It shows up in a paper by Dirac in Proc. R. Soc. London. Series A 136, 453-464 (1932) for the electromagnetic interaction between two charges, and it seems that it was expanded in a series of papers by Dirac, Fock, and Podolsky in 1932.

Anyway, electromagnetism with its 1/r potential is a long-range force, and as such very different from the force between nucleons. Because the energy of a nucleus is proportional to the volume of a nucleus, or to number of nucleons, as expressed in the Bethe-Weizsäcker mass formula for nuclei, it was clear that the range of the nuclear force should be very short, of the order of femtometer (10^-15 m), the scale of the diameter of the nucleus.

Following the ideas of quantum field theory, Yukawa had the insight that this can be achieved if the force between nuclei is mediated by particles which have a mass. In this case, the Coulomb form of the electromagnetic potential is damped by an exponential factor, with a damping length inversly proportional to mass of the exchange particle. This is the Yukawa potential. For the nuclear force with a range of 2 femtometer, Yukawa predicted a mass of the exchange particle of 100 MeV (remember 200 MeV · 1 fm = 1) - today we know that the pion has a mass of 135 MeV. Extracts from his paper and outlooks on the current understanding of nuclear forces can be found in the first pages of a presentation by Wolfram Weise.

In Yukawa's theory, the exchange particle is a boson with spin 0 - as in the equation written on the blackboard. The interation of this spin 0, or scalar, boson to fermions is the Yukawa coupling. In the standard model of particle physics, the Yukawa coupling of fermions to the Higgs field gives the fermions their mass.

Interaction by scalar particles is always attractive - as recognized by a puzzled Dirac, who discovered that in his calculation of the one-dimensional Coulomb problem "this interaction energy agrees numerically with what we should expect from a one-dimensional electrostatic theory. There is, however, a mistake in sign, as it gives an attractive force between like charges." The nuclear potential must also have repulsive components. These must be mediated by spin 1, or vector particles, as in modern relativistic meson theories of the nuclear forces. How these theories can be understood in terms of quarks and gluons is a topic of current reseach - there is a nice overview by Frank Wilczek in a recent issue of Nature (subscription required, a plot of the potential can be seen for free).

So, maybe soon there will be a much deeper understanding of the forces between protons and neutrons - and this interesting physiscs goes back to your initial ideas, Mr. Yukawa - Happy Birthday!

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TAGS: PHYSICS, PHYSICISTS, YUKAWA