Tuesday, January 23, 2007

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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  1. Dear Stefan,

    Thanks for this interesting post!

    Is there any chance some reader knows whether the name 'Hideki Yukawa' has a meaning? I couldn't find anything online, but it seems to me most Japanese names are quite pictorial.



  2. Interesting post! Thanks for reminding us!


    17. HIDEAKI: Japanese name meaning "shining excellence; splendid brightneess"

    18. HIDEKI: Japanese name meaning "splendid opportunity"

  3. Can't find a meaning for Yukawa, but for how it is written:


  4. Nice one. Looking at the plot in the Wilczek's article it is surprising how LITTLE of the nuclear force is properly captured by the pion exchange.

    Btw. \pi_0 mass 135 MeV :-)

  5. Hi Arun,

    Thanks! This is interesting. What a splendid man :-) Best,


  6. Nice celebration. Just one strange thing: is it normal in Germany to organize birthday parties for dead people? Or is it some new regulation of the European Commission? ;-)

  7. is it normal in Germany to organize birthday parties for dead people?

    Ah, we Germans just look for every possible occasion as a reason to party :-)

  8. Hi jester,

    thanks for the hint at the pion mass, I've fixed it. That's sort of embarassing, I always mix that up. But it wasn't the worst "typo" in the post ;-) ...

    Concerning the "modest" role of the pion for the nuclear forces: Just compare the Lagrangian of a scalar (or even spin 0 isovector) coupled to a Dirac fermion with the full-fledged Lagrangians used in relativistic mean-field theories of nuclear matter, as used e.g. in nucl-th/0209016, and you can see that there must be more than the pion to get the force right.

    Dear Lubos,

    hm, no fault of Brussel overregulation - I will have to think about a better title for future similar posts ;-) But thanks that you liked it anyway ...

  9. Hi Bee, I didn't know that Germans were the #1 party animals. At any rate, they're not #1 beer drinkers. It's the Czechs, followed by the Irish who only drink 1/2 of beer per year per capita than Czechs. :-)

    Stefan, you wrote that spin 1 messengers are "modern" physics. I think it's unfair to Oscar Klein, a pre-war string theory-like genius, who has really constructed a near-standard model with the nucleon doublet and SU(2) spin 1 messengers, without realizing the non-Abelian symmetry fully.

    See http://arxiv.org/abs/hep-th/9411233

    I hope as Germans, you agree that Gross has the authority to talk about Klein. ;-)

  10. Hi Lubos,

    jah... German brewers have been constantly complaining over the the last years that the per captia consumption of beer is in steady decline... No chance of "Weltmeister im Biertrinken" ;-)...

    Concerning "modern", what I wanted to say is that these kinds of meson-exchange models, in more sophisticated versions than concieved originally by Yukawa, are still the state of the art in nuclear structure theory.

    I can imagine that you may not call that "modern" ;-)

    Thank you very much for the Gross reference about Klein! That's funny indeed - the more so since both are not German!

    More seriously, I've heard once somthing that Klein had already some kind of Yang-Mills theory, but didn't know any details - so I really appreciate the reference. Klein is indeed also a very interesting physicist, and not so well-known as he probably deserves.

    Best, stefan


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