Monday, March 04, 2013

George Gamow: 109th birthday

March 4th was the birthday or deathday of at least 15 famous enough physicists. For example, cosmologist Robert Henry Dicke (recall the Brans-Dicke scalar-tensor gravity and an amplifier) died in 1997. Ta-You Wu, the father of Chinese (not only nuclear) physics died in 2000. Particle experimenter Simon van der Meer died in 2011. Statistical mechanic Richard Tolman was born in 1881.

But I think that George Gamow is the most important character in this group. He was a very interesting and funny man of a sort and most of his cute stories may be found in My World Line, his autobiography published posthumously, but I will try to be a bit more serious and more technical now.

George Gamow was born on March 4th, 1904 (Old System), in Odessa, Russian Empire. Now it's the third largest town in Ukraine. His father was Russian and taught Russian, his mother was Ukrainian and taught geography and history for girls. He learned German (from a tutor) and French (from his mother) rather early on. His early papers were in Russian on German. Gamow later switched to English that he understood since the college years.

When he was 13, bolsheviks took over. He studied in Odessa and Leningrad (under Alexander Friedmann for a short time). George became a friend of Lev Landau, Dmitri Ivanenko, Matvey Bronshtein (executed by Stalin in 1938). These four men formed the group known as Three Musketeers who were meeting for a postdoc journal club of a sort. The brand was later hijacked by Gamow to describe the Alpher, Herman, and Gamow group.

As a young man, he was exposed to research at many powerful places including Göttingen, Copenhagen, and (briefly) Cambridge UK where he worked under Ernest Rutherford. In that era, he proposed the liquid drop model of the nucleus but he also worked on stellar physics.

When he was 28, he was elected to the Academy of Sciences of USSR – I assure you that he was an untypically young big shot in the socialist context where the seniority was/is measured almost exclusively by political opportunism and age. In the early 1930s, he worked at the Radium Institute in Leningrad where he was one of three bosses to develop Europe's first synchrotron.


He started to be pissed off by the bolsheviks when they disallowed him to attend a conference in 1931. Together with his wife, a physicist whom he nicknamed Rho so that she would not be the only strange person without a Greek letter, he tried to emigrate twice, paddling a kayak full of his wife, chocolate, and brandy for hundreds of kilometers. First, it was to Turkey, second it was to Norway. It was before global warming so the weather was poor at that time and both attempts were foiled. The silver lining was that no one politically important has learned about his excursions.

In 1933, he suddenly got a permission to attend the Solvay Conference in Brussels. His wife was finally allowed to go, too. With the help by Marie Curie etc., he could extend his vacations and work at the Curie Institute, University of London, and University of Michigan. In 1934, he moved to the U.S. to George Washington University. He quickly became important enough so that he was actually the guy who hired Edward Teller over there (moved him from London). They together published a paper on beta-decay selection rules. He was also publishing papers with Mario Schenberg and Ralph Alpher.

Despite his highly relevant knowledge, he wouldn't work on the Manhattan Project. Instead, he continued to study stellar and galactic evolution etc.

Alpha decay and tunneling

Now, let us return a little bit back to 1928. By that time, George Gamow would have formulated the theory of alpha decay involving tunneling of alpha-particles. Nikolai Kochin helped him with some maths. Gurney and Condon found similar but much less quantitative results. A fascinating idea based on quantum mechanics is behind this theory so let me spend a minute with it.

Alpha decay is a transformation of a nucleus \(N_i\) to a smaller nucleus \(N_f\) during which an alpha-particle i.e. the helium-4 nucleus is emitted:\[

N_i\to N_f +{}^4_2 {\rm He}

\] What's fascinating is that the rate of this process – or the lifetime of \(N_i\) – depends on which nucleus we are talking about. There is not just some dependence. The possible lifetimes hugely differ, by many and many orders of magnitude. For example, the half-life of uranium-238 is 4.5 billion years.

To compare, the medium-mass elements have some of the fastest alpha decays. We may say that it's because alpha-particles may easily form inside them. For example, \({}^{109}{\rm Xe}\) i.e. xenon-109 decays with the half-life of 13 millisecond which is 19 orders of magnitude shorter time than the half-life of uranium-238 above.

Now, if you don't know the right explanation, you should be shocked by this difference. Xenon-109 and uranium-238 are isotopes whose quantities are "of the same order" and we're talking about the decay of the same type, with the same particle emitted. So the two decays should have the same cause. Everything is "of the same order" in the two situations so you would expect the half-lives to be of the same order, too. But why would their rates differ by 19 orders of magnitude? Where does this ratio \(10^{-19}\) come from?

The answer is that they're indeed qualitatively identical processes and the huge hierarchy arises because the natural formula for the half-life is the exponential of a reasonably large number (in certain units) and it's enough to change the exponent a little bit for the exponential to change dramatically.

In particular, we may approximately describe the initial nucleus \(N_i\) as a "bound state" of the final nucleus \(N_f\) and the alpha-particle. The alpha-particle is attracted to the rest of \(N_f\) inside \(N_i\). However, they may also exist independently of each other. If you draw the potential energy as a function of the distance between the centers of mass of \(N_f\) and the alpha-particle, you get a graph of the potential wall.

In quantum mechanics, the alpha-particle may sometimes tunnel through the barrier and the rate – think about the WKB approximation – goes like \(\exp(-{\rm Size})\) where \({\rm Size}\) is the appropriately calculated "size" of the barrier which grows both with its width and its height. More precisely,\[

\Gamma_\text{decay rate}&\sim |{\mathcal A}|^2,\\
\quad {\mathcal A}&\sim C\cdot \exp\zzav{-\int dx \sqrt{\frac{2m}{\hbar^2} \left( V(x) - E \right)}}

\] If you realize that \({\rm Size}\) is of order dozens or hundreds for typical nuclei (this number grows with \(Z\)), it's not hard to believe that the value of \({\rm Size}\) for xenon-109 and uranium-239 will differ by 44 and \(\exp(44)\) will produce those 19 orders of magnitude in the difference of the decay rates.

In popular presentations of quantum mechanics, you sometimes hear about a man who tries to walk through the wall many times and he ultimately succeeds. This is an unrealistic situation for humans but it is totally realistic for alpha-particles inside nuclei and the possibility to tunnel through the barrier (maybe we should say the probability to kayak through the sea) is the most important part of the explanation of the alpha-decay!

Big Bang Nucleosynthesis

I probably do think that Gamow deserved a Nobel prize for that explanation (recall that he has previously invented the liquid drop model of the nucleus); he has never received one. But there is another breakthrough that – in my opinion – has the importance of a Nobel Prize discovery. Gamow was an author of the Alpher-Bethe-Gamow that explained where the light nuclei in the Universe around us came from. (He was previously an early defender of Lemaitre's Big Bang Theory in the first place.)

Previously, I mentioned that Three Musketeers were actually four men. Here, you could generalize that insight and guess that Alpher-Bethe-Gamow had four authors, too. However, the right number is actually two. ;-) Hans Bethe was only added because the men had a sense of humor and they wanted the Greek alphabet to be more accurately reproduced on the title page.

OK, where and when were the light nuclei of hydrogen, helium, and lithium born? The answer to "where" is that they were born everywhere, in the whole Universe. The answer to "when" is during the first three minutes of the Universe, right after the Big Bang. At that time, the temperature was sufficient to allow the protons and neutrons to merge and to allow the nuclei to merge or split. You may calculate the equilibrium concentration of all the isotopes at every temperature (or every moment), given the known rates of all the relevant reactions.

Well, the required calculation is a bit more complicated because some reactions proceed too slowly relatively to the rate at which the temperature is changing. So there's not enough time to reach equilibrium for these reactions. But you may still calculate how many nuclei are transmuted etc.

The results are amazing: the calculation yields results for hydrogen, deuterium, tritium, helium-3, helium-4, and lithium-7, and the percentages remarkably accurately agree with the observations of the abundance of these isotopes in outer space.

Fred Hoyle added the theory how the heavier elements were born – inside stars, thermonuclear furnaces.


As soon as Watson and Crick discovered DNA in 1953, Gamow began to think about the problem how the four bases of DNA could code the twenty common amino acids in proteins. He sent a letter to Linus Pauling. Details of "Gamow's diamonds" were wrong – e.g. because his triplets were overlapping – but he accidentally managed to get the right answer, twenty, and he made Watson and Crick think along similar lines. They ultimately enumerated the right twenty omnipresent amino acids in proteins.

Popular writings

During his later years, he would work at Berkeley and Boulder and I don't want to mention all the affiliations. More importantly, he started to teach a lot and popularize physics and he became a big achiever in this field, too. He wrote One, Two, Three... Infinity and the series of books about Mr Tompkins that won a prize from UNESCO. I do still believe they're very good books but I haven't read them for decades. :-)

He died on August 19th, 1968, one day after he wrote "The pain in the abdomen is unbearable and does not stop" to Ralph Alpher from Boulder. Two days after his death, the Soviet Union and allies occupied Czechoslovakia to stop our "socialism with a human face".


  1. i would assume he stopped being communist or socialist, right?

  2. I think the basic stories make it obvious that he has never been a socialist or communist in any sense. He wasn't excessively political, however.

    In the early Stalin years, he was allowed to travel to the West so he was never quite decoupled from it. Attempts to decouple him were a big problem for him. He wouldn't be interested in all the bad things that the commies were doing but he surely did care about science. In My World Line, you may learn that he considered the impact of the communists on biology - Lysenkoism in particular - to be the worst thing.

    If the authorities had learned that he attempted to emigrate on the kayak (twice), he would probably be arrested, to say the least. You don't expect "socialists" or "communists" to risk their lives while fleeing from the country of the ultimate communist paradise.

  3. there was a stupid Greek-American guy, i forgot his name that escaped the US with his friend's wife and scientific secrets to go to the USSR and later regretted it. he played an important role in computers and electronics in the country and later he ended up in Siberia.

  4. I completely agree with Gamov,

    that the bad habitude of socialist regimes of preventing scientists from travelling to international conferences really sucks and damages science :-(0).
    Seems they gave (and the still active socialist regimes are giving) a damn about science ...

  5. I still remember the lecture on alpha decay from more than 30 years ago in a modern physics course. And although I did not go on to become physicist, the sense of wonder at what some clear thinking, a few equations, and insight could accomplish has never left me. A very nostalgic moment.

  6. "Lemaitre's Big Big Theory" ? The one bangs ;-)

  7. LOL, good catch! You you! More precisely, thank you! ;-)

  8. Eleven years ago, a pretty black and white kitten wandered out of the woods behind our house, and we tool her in. Of course, she was pregnant, and she gave us four beautiful little male cats.

    Remembering the Alpher/Bethe/Gamow paper, we named them Alpher, Bethe, Gamow and Dirac, the latter for the delta function, of course.

  9. Nah, the "Big Big Theory" is really the theory that bangs and does everything else too :-P

    LOL :-D

  10. Well, there was an Italian-American guy, Bruno Pontekorvo, but he had everything in USSR and never regretted

  11. I remember reading and enjoying Gamow's playful science books when I was young.

  12. "...on the left side of average US physicists"

    right side would be the right word:)

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  14. Impressive after all these years ;-)

  15. It's at most a few months, not years, when Gordon was young. Imagine if your comment were a Gentleman's comment written about a Lady! ;-)

  16. Hmmm, it feels like Graham's number

    since I read them, thats "a few", right?

  17. Yeah right as if women never get these sorts teasing !... tsstss

  18. Gamow’s Berkeley years, 1954-6, coincided with my first two years there but I was blissfully unaware of the seminal 1948 paper and of Gamow himself.

  19. As a kid, back in the '50s, I kept copies of his popular works by my bedside. He was a major influence on my life, I think.

    I particularly remember in one of those little paperbacks reading his theory of the origin of the moon - via a collision between the earth and another body, with the Pacific Ocean as a remnant. (This was before continental drift was accepted.) I suppose you can still make the argument that there isn't enough light crust to cover the earth, because the moon "stole" it.

    In any case, there's a book, written in the past thirty years or so, which purports to establish the currently popular theory of a planetary collision being the origin of the moon. I was totally shocked that there was no mention of Gamow in that book!

    This is similar to Gamow's early prediction of the cosmic background radiation due to the big bang, which was completely ignored or "missed" by Dicke in the '60s when the latter "re-predicted" it, to Gamow's great annoyance.

    Well, at least Gamow's in your spell checker, and Dicke is not :-)

  20. Alexandre BagdonasOct 10, 2013, 9:32:00 PM

    As a Russian Immigrant in the US of course he would love to tell bad stories about USSR, specially during
    McCarthyism times. When Solzhenitsyn criticized the soviet life, Americans loved him. However when he started criticizing also the USA, then they started to be angry with a Russian criticizing their home country.

  21. They are always jealous at first but they adapt eventually Dilaton. It is much easier if the new cat is a kitten though. We've got 4 generations of well traveled cats here.. They even went to the Czech Republic and back 8)