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Rudolf Peierls

Rudolf Peierls

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Rudolph Peierls, the son of a Jewish businessman, was born in Berlin, Germany, on 5th June, 1907. He studied nuclear physics under Werner Heisenberg and in 1929 he conceived the theory of positive carriers to explain the thermal and electrical conductiveness of semi-conductors.

When Adolf Hitler gained power he moved to England where he found work teaching physics at Birmingham University and in 1939 worked on atomic research with James Chadwick and Otto Frisch. In 1940 Peierls and Frisch wrote a paper that explained how a uranium fission bomb could become a weapon that could win the Second World War.

In 1943 Peierls joined the Manhattan Project. In the United States. Over the next two years he worked with Robert Oppenheimer, Edward Teller, Otto Frisch, Felix Bloch, Enrico Fermi, David Bohm, James Chadwick, James Franck, Emilio Segre, Eugene Wigner, Leo Szilard and Klaus Fuchs in developing the atom bombs dropped on Hiroshima and Nagasaki.

After the war Peierls was professor of physics at Birmingham University (1945-63) and Oxford University (1963-74). He wrote several books including The Laws of Nature (1955), Surprises in Theoretical Physics (1979) and an autobiography, Bird of Passage (1985). Rudolph Peierls died in Oxford on 19th September, 1995.


For archival material, see list in Dalitz (2004), to which should be added files related to Peierls in the Public Record Office, the National Archives, Kew, Richmond, Surrey, TW9 4DU, and some sources in the AIP oral history collection, AmericanInstitute of Physics, One Physics Ellipse, College Park, Maryland 20740-3843 (http://www.aip.org/history).


“On the Kinetic Theory of Thermal Conduction in Crystals.” Annalen der Physik 3 (1929): 1055–1101.

“On the Theory of Galvanomagnetic Effects.” Zeitschrift für Physiks 53 (1929): 255–266.

“On the Theory of the Hall Effect.” Physiks Zeitschrift 30 (1929): 273–274.

“On the Theory of Electric and Thermal Conductivity of Metals.” Annalen der Physik 4 (1930): 121–148.

“Elektronentheorie der Metalle.” Ergebnisse der Exakten Naturwissenschaften 11 (1932): 264–322.

“Zur Theorie de Absorptionsspektren fest Körper.” Annalen der Physik 13 (1932): 905–952.

“Statistical Theory of Superlattices with Unequal Concentrations of the Components.” Proceedings of the Royal Society, Series A, 154 (1936): 207–222.

Atomic Energy. London: Penguin, 1950.

The Laws of Nature. London: Allen and Unwin, 1955.

The Quantum Theory of Solids. Oxford: Clarendon, 1955.

“The Development of Quantum Theory. Part 1. Formulation and Interpretation.” Contemporary Physics 6 (1964): 129–139.

The Frisch-Peierls memorandum (in two parts): Part I. “On the Construction of a ‘Super-Bomb,’ Based on a Nuclear Chain Reaction in Uranium.” In Appendix 1, Britain and Atomic Energy, 1939–1945, by M. Gowing. London: Macmillan, 1964. Part II. “The Properties of a Radioactive ‘Super-Bomb.’” In Tizard, by R. W. Clark. London: Methuen, 1965.

“The Development of Quantum Theory. Part 2. Consolidation and Extension.” Contemporary Physics 6 (1965): 192–205. Surprises in Theoretical Physics. Princeton, NJ: Princeton University Press, 1979.

Bird of Passage. Princeton, NJ: Princeton University Press, 1985.

More Surprises in Theoretical Physics. Princeton, NJ: Princeton University Press, 1991.

Atomic Histories. Woodbury, NY: American Institute of Physics Press, 1997.

With R. H. Dalitz. Selected Scientific Papers of Sir Rudolf Peierls: With Commentary. London: Imperial College Press, 1997. Contains a complete bibliography, together with a chronology of Peierls’s life.


Clark, Ronald William. Tizard. London: Methuen, 1965. Dahl, Per F. Superconductivity: Its Historical Roots and Development from Mercury to the Ceramic Oxides. New York: American Institute of Physics Press, 1992.

Dalitz, R. H. “Sir Rudolf Ernst Peierls.” In Oxford Dictionary of National Biography, edited by H. C. G. Matthew and Brian Harrison. Oxford: Oxford University Press, 2004. Contains a list of archival information.

Edwards, S. “Rudolph E. Peierls.” [sic] Physics Today (February 1996): 75–77.

Gowing, Margaret. Britain and Atomic Energy, 1939–1945. London: Macmillan, 1964.

Hendry, John. Cambridge Physics in the Thirties. Bristol, U.K.: Adam Hilger, 1984. Contains essays written by physicists working in Cambridge in the thirties. These, and the introductions, include comments on the relationships between mathematics, theoretical and experimental physics, and the institutional contexts in Cambridge.

Hoddeson, Lillian, Ernest Braun, Jürgen Teichmann, et al., eds. Out of the Crystal Maze: Chapters from the History of Solid-State Physics. New York: Oxford University Press, 1991

———, Paul W. Henriksen, Roger Meade, et al. Critical Assembly: A Technical History of Los Alamos during the Oppenheimer Years, 1943–1945. New York: Cambridge University Press, 1993.

Kapur, P. L. “The Dispersion Formula for Nuclear Reactions.” Proceedings of the Royal Society, Series A, 166 (1938): 277–295.

Rudolph Peierls

Rudolf Ernst Peierls was born on June 5, 1907, in Berlin, Germany. The son of a Jewish businessman, he studied nuclear physics under the tutelage of Werner Heisenberg and Wolfgang Pauli. His early work on quantum physics led to his development of the theory of positive carriers in 1929, which explained the thermal and electrical conductivity behaviors of semiconductors.

Peierls moved to Birmingham, England, when Adolf Hitler came to power in Germany. There, he found work teaching physics at Birmingham University, and in 1939, he started working on atomic research with Otto Frisch and James Chadwick. In 1940, Peierls and Frisch wrote a paper that explained how a uranium fission bomb could become a weapon that could win World War II. The three-page paper estimated that the energy released in a nuclear chain reaction and how one could devise an atomic bomb from a small amount of fissable uranium-235. This paper sparked the interest of British and American authorities, which would eventually lead to the Manhattan Project.

Peierls joined the Manhattan Project in 1943 as part of "The British Mission," being placed in charge of a small group concerned with evaluating the chain reaction and its efficiency. He had been excluded from joining in the early years because of his German origin.

After the war, Peierls resumed his position as professor of physics at Birmingham University, where he worked until 1963 before joining the University of Oxford. He was knighted in 1968, and he retired from Oxford in 1974. He died in Oxford on September 19, 1995.

Peierls Rudolf A2

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In footnotes or endnotes please cite AIP interviews like this:

Interview of Rudolf Peierls by John L. Heilbron on 1963 June 18,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,

For multiple citations, "AIP" is the preferred abbreviation for the location.


This interview was conducted as part of the Archives for the History of Quantum Physics project, which includes tapes and transcripts of oral history interviews conducted with ca. 100 atomic and quantum physicists. Subjects discuss their family backgrounds, how they became interested in physics, their educations, people who influenced them, their careers including social influences on the conditions of research, and the state of atomic, nuclear, and quantum physics during the period in which they worked. Discussions of scientific matters relate to work that was done between approximately 1900 and 1930, with an emphasis on the discovery and interpretations of quantum mechanics in the 1920s. Also prominently mentioned are: Niels Henrik David Bohr, Bragg, Louis de Broglie, Constantin Caratheodory, Frank Clive Champion, Peter Josef William Debye, Max Delbruck, Enrico Fermi, Otto Halpern, Werner Heisenberg, Friedrich Hund, Lev Davidovich Landau, Ettore Majorana, Walther Nernst, Heinrich Ott, Wolfgang Pauli, Max Planck, Robert Wichard Pohl, Arnold Sommerfeld, Albrecht Unsold, Hermann Weyl, Wilhelm Wien Universitat Berlin, Universitat Leipzig, Universitat Munchen, University of Cambridge, and Zeitschrift fur Physik.


One thing I remember since our talk yesterday arises from the translation of the book by de Broglie I mentioned. This was early in ‘29, and this was a book in which he was reconciling himself with the probability interpretation of quantum mechanics. He tries all sorts of more complicated things giving some reality to the waves and works it all through rather carefully and comes to the conclusion it doesn’t work. The conclusion of the whole book is that the standard interpretation is really right. Of course, he later went back on that. What made it interesting is that at that time, when I really had been a student for three and a half years, something like that, it seemed to me perfectly obvious that this was the right thing — that the conclusion he came to was the right one. One realized that de Broglie was isolated, but one was glad that he himself, by whatever clumsy methods or round-about methods worked himself round to that view. I mean, my own feeling in translating the book was, “Well, what would be my reaction today?” On the whole this exercise is rather unnecessary because it’s clear from the start that that must be the answer. But the book is worth having simply because he is a very distinguished man, and it’s interesting to see how a man like that comes to be what he is. You were asking for people’s attitudes to these developments at the time. Well, certainly at that time this was already perfectly clear to me, and I believe obvious to everybody else. I was not terribly original then.


Among the students, or people who began their college training in ‘25 and afterwards, it’s quite reasonable to expect a ready acceptance.



It seems a little curious that the people who had difficulty accepting it, such as de Broglie and Schrodinger and Einstein, were isolated. Do you recall any others of the older-generation who had difficulty?


Well, there were several people who had difficulty in the sense that they were anxious to convince themselves this thing was really above board and there weren’t any hidden difficulties, such as for example Ehrenfest, whom we mentioned. He certainly was for the new ideas I mean, he didn’t oppose them in any way, but just wanted to make sure that one really understood them. But be had some difficulty. He had some very interesting questions. I remember in this paper he wrote about posing some questions about quantum mechanics — I don’t recall all the questions now without looking it up. One question was “Why do we have to deal with a complex wave function and how does ‘i’ come into these things suddenly?” I think I was, at that time, inclined to be a conformist. I wasn’t inclined to question basic principles I came to it very much from the end of applications and the idea of working things out. Therefore I think I was more interested in seeing how things you knew about — experiments or facts — came out of the accepted principles. There is a great joy in suddenly seeing how to solve an equation, or how to describe a situation when you suddenly see that this is the way it is meant to be, the way it comes out. One came to it with the attitude, as you implied, “Well, this is what we are taught is the physics, and we’re not in a position at this moment to question it that comes later.” That I think was one point I wanted to add. I’ll probably think of other things in the course of it, but will you go on with your points?


At the end of your measurement paper you make a very interesting statement that one place where you can see the difficulties is in the beta decay. Do you remember that part?



Well, it’s quite curious, and the reason it interested me is that this was about the time of the neutrino, was it not?


I think that must be before the neutrino.


Before, but it’s difficult to fix a date for the neutrino, when the concept was rather more officially proposed. I wonder if you can recollect anything about that — discussions about that with Pauli?


Well, this was a time when I think certainly everybody was aware of the fact that the beta decay was a difficulty. The evidence of course came along gradually. First it was clear that energy didn’t appear to be conserved, and then came later experiments which suggested that the top end of the spectrum was the correct energy for balancing things up in other words that in the process energy always appeared to be lost. Therefore, people started thinking “Well, is it possible in principle that there might be a one-sided lack of energy conservation?” And I think nobody was particularly happy and enthusiastic about that idea. However, it was seriously discussed in the way, for example, that the possibility of parity violation was first discussed, before it was actually established. Again, people weren’t too happy about it at first, but said, “Well, we must be prepared for anything.” It was in that sort of spirit. Now I don’t recall exactly what we said about this presumably just mentioned it as one of the places where the theory was in difficulty, and that shows how wrong one can be with such remarks.


It seems that Bohr was willing to abandon the conservation of energy without great qualms.


Well, that was a little earlier in the Bohr-Kramers-Slater paper.


But again, at the end of the twenties and into the thirties he was willing, almost anxious, one would say, to abandon energy conservation. But at Zurich I imagine that wouldn’t be the case.


Well, I think one was always prepared to admit that possibility, but one certainly was not very fond of —. JIH: Where did Landau obtain his great familiarity with all the current problems of physics? He had studied only in Leningrad, hadn’t he?


Yes. Well, he’s of course a remarkable man who can pick ideas up extremely quickly, and most of those ideas, I imagine, came straight from books and journals. Frenkel was one of the teachers there, who was a very intelligent man and no doubt helped Landau quite a bit. And there was Fock there were some good people there. And there he no doubt got his basic training. Then he started reading himself, and he is one of the people who will never read a paper in detail. He’ll glance at it to see what the man is trying to do and then will sit down and reproduce the results in his own way.


Fermi would, I understand, work that way too.



But he had a certain amount of iconoclasm that must have been somewhat different from the German school approach.


Oh yes. Particularly in those days when he was young, he was given to very extreme views about everything not only physics. I think one of my favorite recollections is the occasion when, in a discussion, some name came up that Landau hadn’t heard before, some physicist. So he said, “Well, who is this, and where is he, and how old is he?” Somebody said, “Oh, he’s 28, or something.” And Landau said, “What, so young and already so unknown?” You were asking in your notes about Rome and Fermi. Well, I don’t think I actually worked with Fermi very directly, except in a minor way because at that time most of the people in Rome were working on certain features of atom spectra. There were some things that hadn’t been sorted out yet, and that was the time to get those clear. And everybody was working out numerical solutions of Schrodinger’s equation for an outer electron of an atom using the Thomas-Fermi potential or something. It seemed to me that it would be useful once you were in such a place to take part in what was going on, and I asked if I could do a job like that as well. As a result I sat down at a little desk calculating machine solving the equation for some particular case, which I have now forgotten. But it was quite valuable experience because I had no practice in numerical solutions of differential equations and it showed me how easy this was.

Of course it’s true I think everywhere in one’s formal training that numerical methods get neglected people can solve differential equations by series expansions and by contour integrals and by elegant transformations, but they don’t realize how easy it is on the back of an envelope just to run off a numerical solution. Very often in doing that you see something about its structure which then leads you to some analytical or approximate solution. Of course now people are are conscious of numerical methods through computers, but, again, I think the common attitude is that either you can solve an equation in closed form or you put it on an electronic computer. And very often it’s quicker to work it out by hand — if you want one solution for one case — than to get hold of a computer and write a program this also tends to be forgotten. Certainly, nevertheless, one profited enormously from Fermi because of the simplicity of his attitude and the way he could in almost all cases get a simple quantitative answer to a problem without any highbrow methods. In fact he had a series of books that no doubt you’ve heard about, where he had written down all his thoughts and all the arguments. Generally when a problem came up he pulled out a book and turned to some particular page and there it was on one page was the argument written out. Very interesting.


You were just describing some of the peculiarities of the Rome school.


Oh yes. I certainly got a lot of useful ideas of clarification from Fermi and from the other people, including Wick, and Majorana, who died shortly after that. Rasetti —. There was quite a good bunch there.


Majorana was a very clever fellow, was he not?


Yes. He was somewhat strange and retiring he was a Sicilian, and he later was lost from a ferry boat crossing over to Sicily. It was never clear whether this was accident or suicide.


But he didn’t publish a great deal?


No, no. Well, nevertheless, he made his reputation on two important things. One, the exchange nature of the nuclear forces, where essentially he corrected an oversight in Heisenberg’s ideas and then the other was the neutrino theory.


This was about the time at which the Rome group was going over to nuclear physics?


Yes. They were then making plans for getting hold of equipment and so on. It may be that they already had some small experiments going on, but Fermi wasn’t as personally involved in those as he was later.


Would you say that there was a general sort of feeling, elsewhere too, that one had reached the limits of any of the older problems, and it was essential to cultivate some new territory? Was there a general change of fields —?


No. No, there was still plenty to be done, but, of course there was a new field opening up which was exciting. This of course was just the time when the artificial radioactivity had been discovered, and when there were the experiments beginning to come out which led to the discovery of the neutron. Fermi always had a slightly peculiar attitude to that. I think he felt that the Paris group, the Joliots, should really have seen the existence of the neutron from their experiments which were later pointed out by Chadwick. I had the impression that he knew what the experiments meant, but hadn’t got round to publishing it, or felt he must leave it to the experimenters. I don’t know this is only a hunch. But this brings me to another amusing recollection. There was one of the regular conferences in Copenhagen — I think it was just before the discovery of the neutron it may have been the conference of ‘32 or ‘31, I don’t know. The interesting point was that there was a general feeling among some people there, not everybody, that physics was almost finished. This looks ridiculous looking back, but if you look at it from the point of view of the time, practically all the mysteries had now resolved themselves, nearly all. Everything that had bothered one about the atom and molecules and solids, and so on, had suddenly fallen into place just as a result of developing quantum mechanics.

I mean, there were some complicated things like, for example superconductivity, which were completely unintelligible but one understood, I think rightly, that this was in principle contained in the known equations but was just too complicated to see through. The real exceptions were the relativistic problems because one had trouble with the Dirac equation over the negative energy states, which weren’t completely understood. One had trouble with electrodynamics, and then one couldn’t say anything about nuclei in particular the nuclei then still consisted of protons and electrons and one had no idea how the electrons could manage to stay inside the nucleus. In addition there were then only two dimensionless constants in nature: the fine structure constant and the proton and electron mass ratio. They were not so very far from each other one knew about Eddington’s equation that linked them, although nobody believed in his argument. Still whatever you thought of the argument there was a quadratic equation which linked the fine structure constant to the mass ratio, which might be right— or something like it might be right. Then it was natural to think, first of all, that there was one step missing which would resolve the difficulties of electromagnetic theory, or all the relativistic electron theories — these two seemed to be connected. And it was plausible that this would be possible only for one particular value of the fine structure constant and that when you’d understood this.

Then you would also understand the mass of the proton and you would also understand how electrons got to be in nuclei because that evidently was a relativistic problem. Now I’m not saying that this was the common view I don’t think I shared it really I don’t think Niels Bohr for example would ever have had any such illusions. I don’t recall this statement being expressed in his presence, but there were sort of over lunch or sometime quite serious discussions about what we would do when physics was finished. By finished was meant the basic structure of course, there are all the applications. The majority of people said that that would be the time to turn to biology. Only one person really took that seriously and did turn to biology, and that was Max Delbruck, who certainly was present at these discussions.


So the outstanding difficulties were thought to have imminent solutions, or were likely to be set aside soon?


Up to that point things had moved so quickly that it seemed hard to believe that if you have solved all but one of the problems that the last one would take very long. Now it was very naive of course because it was hard to believe that one single step should immediately resolve all the problems about nuclei. But then there weren’t any problems about nuclei basically because so little was known I mean, there wasn’t any quantitative evidence to explain.



Certainly not that, but I mean nuclear levels and anything like that was —. Oh, there was some fine structure of alpha rays where you had to take different nuclear levels, but otherwise nuclear spectroscopy didn’t exist.


When would you say that that attitude was changed? When was it recognized that one was a long way from any solution? Just restricting the conversation to the quantum electrodynamics, when would you say people were convinced that there were fundamental problems that weren’t going to be solved very quickly or easily?


Well, the idea that quantum electrodynamics was very hard I think grew gradually just as time went on and all efforts to get round the difficulties failed that made one realize it was really a tough problem. But more generally, of course the discovery of the neutron which followed shortly after this time immediately made it obvious that physics was richer than we had seen prior to that. Then of course shortly after that came both the work about the interactions of neutrons with nuclei and resonance levels and so on and also the artificial disintegration which immediately started showing up nuclear levels. A new field opened up where it then became obvious that there was a lot to be done and to be understood. For one thing, as soon as you know of the neutron, it was quite clear that you must have new kinds of forces holding nuclei together. I think probably people who had thought seriously about it, always realized this, but not very quantitatively. I think then one just forgot about this idea of physics being finished.


Were there any difficulties in accepting the neutron itself?



You regarded the evidence immediately as convincing and there were no other difficulties?


Well, I mean with any piece of experimental discovery there is a period of discussion about whether the experiments are really conclusive and so on. But there was certainly no theoretical difficulty there was no reason why there shouldn’t be a neutron.


No, except that one hadn’t found them before that’s always a partial reason.


No, but with the neutrons I think it was immediately understood that by the then conventional techniques they were very hard to detect. Therefore it was much less surprising that the neutron had escaped discovery than that the positron had. In fact about the positron there is a nice point. There was one physicist then I think in Cambridge, Champion, who was investigating beta decays with a cloud chamber. He took thousands of photographs of beta ray tracks in a cloud chamber, sometimes with and sometimes without a magnetic field. He used various sources, some of which give positrons and some of which don’t. He had no actual positron emitters, but sometimes you have a mixed decay, or sometimes you have a secondary positron through a pair creation by gamma rays, and so on. And it so happened that he never had a magnetic field on with any sources which contained positrons. I mean, many of his tracks must in fact be positrons. Almost any source gives you, if the energy is high enough, some positrons, but of course if you see one or two tracks of the wrong curvature, then you think there are secondary particles going the other way. He must have felt rather bad after the discovery of the positron because if he’d just happened to have a magnetic field on, on the right occasion, he would have seen lots of them, well before they were discovered.


Was that work done in the early thirties, do you recall?



So that work was going on just when you arrived in Cambridge — those were nearly the final experiments.


Yes, I didn’t see much of the experimental side then, but I knew Blackett whom I had met before, and of course he was just right in this work.


Was the situation at Cambridge much different than it had been in Borne, or in Germany was it more casual perhaps?


Much more casual and, well, also it was summer and there was not very much organized activity going on, though there was some at the beginning. Theoretical work in Cambridge has always been, until quite recently, hampered by the fact that there was no department in the physical sense there was no place where the theoreticians could normally be found. They usually worked in the colleges. Well, you could always go and see someone in a college if you really wanted to see him, but that takes some motivation, particularly as you weren’t sure you’d find him there. It’s very different from having a lot of people in adjacent rooms and running into them five times a day. I remember my first experience coming to the Cavendish. I had arrived there and wanted to call on Fowler, who was my official contact. I knew roughly the wing of the building and the floor he’d be on, and I found myself in a corridor with lots of doors without any labels and nobody around. So I wandered up and down the corridor trying to pluck up courage to knock at one of those doors. I found one door which seemed to be somewhat less conspicuous, or less important than the others, and I thought I might find sour kind of secretary or something in there to give advice. So I knocked at the door and went in, and it happened to be Rutherford’s office Rutherford wasn’t there I would have felt bad otherwise. Then eventually I went to somebody to tell me where Fowler could be found.


Finally I thought if you would, it would be quite interesting if you could perhaps make some remarks in connection with your own work on theory of metals and solid state, at least into the early thirties. I have a partial bibliography which may be of some assistance.


Well, we have already mentioned the Hall effect and the small things. Then, the one paper on the thermal conductance of crystals which was my thesis. I found that extremely amusing because it’s a field which is remarkable in that if you make any of the plausible and obvious approximations, something goes wrong and you get complete nonsense. I mean you really must, to get any approximate idea of what goes on, include a large number of facts which at first sight seem unimportant. Therefore all the previous treatments which had tried to idealize the problem, in some way or other, went wrong. Starting with the theory of Debye for example, who in his usual, nice, way of approaching a subject, had said, “Well, the finite conductivity of a crystal is due to the fact that you don’t have linear equations you have un-harmonic effects, and therefore waves interfere with and influence each other. Now we can picture this as simply due to the density fluctuations. If a wave travels through a medium where the density is not the normal one, that is, has a different refractive index, we can observe the dependence of the compressibility, of the sound velocity, on density. Therefore if you can work out the density fluctuations you get the right answer.” He did that, and he got a finite answer for the thermal conductivity, although one knows from other arguments that in the continuum model he uses the thermal conductivity should still be infinite.

The reason for that is that he put in formulae for static refractive index, whereas, of course, the density fluctuations caused by the lattice vibrations are in the form of waves which run with the same velocity, or approximately the same velocity, as the wave they’re trying to scatter. Therefore a static description is of course complete nonsense. And so it goes. This you see had nothing to do with the fundamental problems of the time, except in so far as it was important to check that the theory was now ready to account for the things that could not previously be handled. I learned in particular from this work the importance of what one might call momentum conservation in the collisions of the phonons with each other, so that you may get a kind of drift set up in a phonon system which would tend to persist in spite of collisions. I realized that this could or would be of importance also in electric conductivity of metals, and proceeded to look into that. This had not been taken account of in the work of Bloch. I thought at the time that this was a dominant effect probably under all circumstances later one learned that it was important only at rather low temperatures. It has recently become of interest in connection with the so-called phonon drift in very peculiar experiments on thermoelectric effects at low temperatures, where one sees that this phenomenon really exists and is important, but not as generally important as I at first assumed. Also, similarly, the main point of the thermal conductivity in crystals, my Ph.D. thesis, was to predict that in a pure crystal at low temperatures the thermal conductivity should rise exponentially as the temperature goes down. This is true, but it was discovered only in the 50’s.


Were there any attempts to discover it before?


No, I don’t think so. Well, first of all this was experimentally a difficult problem. That’s one reason another reason was I think my paper wasn’t very easy to read and nobody believed it. Also, I probably overestimated the temperature at which this should start. I mean, I had the impression that if you just went down to liquid air or something you should see the beginning of this — actually you have to go to liquid helium temperatures. There was one other thing I’ve mentioned that everybody previously got the treatment of this problem wrong. Well, I still made some quite serious omissions, a most important one being that I was talking about a pure crystal, not realizing that pure for this purpose meant also consisting of a pure isotope. If you have an isotopic mixture, then of course the random difference in the masses of the atoms, which is important for the lattice vibrations, of course, causes an irregularity which is quite enough to give you thermal resistance. This was of course something one shouldn’t have overlooked. It was pointed out by Pomeranchuk that this was an effect, but again it wasn’t noticed, and it was only when the Oxford people did experiments and noticed that some substances gave the exponential rise and others didn’t that it dawned on them that the substances which did were those which consisted of practically only one isotope. Then it was clear what was going on.


Those were the experiments in the 50’s?




Then this paper about metals [Paper No. 6] where I try to follow similar ideas. There I made the mistake of writing too many things into the same paper, because it really contains a lot of quite disconnected things, or independent things. I had always been bothered by the fact that for the whole picture one had, at the time, of the band structure — I think the word band structure wasn’t used yet — it was important that you should have energy levels which were separated by gaps, and in which, at the top, again, the velocity went to zero as it does at the bottom. Now this came out very easily from the Bloch picture of tightly bound electrons, where you just make the approximation that the state of the system is almost that of separated atoms which just interact slightly. But it was not clear now that would come out on the opposite limits starting from free electrons. Then I suddenly saw, and that was a great pleasure, that if you took free electrons and you put in a periodic potential, allowing, in the ordinary way, for the scattering of the electrons by that potential, these gaps would arise no matter how weak the potential. Only if the potential was weak the gap would be small, but the fact that it was there and that the velocity then at the highest level in the band was a standing wave, comes out.

Now that’s today a very elementary argument, but I think I was the first to point that out, and it was then picked up by Brillouin, and that satisfied me that I could see what was going on. And Brillouin then discussed the three dimensional case and came out with the Brillouin zones. But this was hidden away and Brillouin had noticed it. I believe today I would write that as a separate paper and not hide it away in. a paper on transport problems. Paper No. 7 we have discussed No. 8 was essentially I think some corrections to paper No. 6 where I had noticed —. No. 9 was a lecture at a conference and a discussion really about what one could say about magneto-resistance, which then also was a problem, because what Sommerfeld had got out of his simple theory was wrong in order of magnitude. This was rather embarrassing because I thought I had an explanation and therefore gave a lecture at the conference. By the time the conference started I had realized that in the model I was then trying everything again canceled out and was in effect as small as Sommerfeld had it. But still I had announced the lecture, and well, I gave just a general review of the situation, and then in the paper No. 11 I had really seen what was going on. Paper No. 10 we have discussed. 12 was just a little point.

Eugene Guth was then in Zurich and was interested in solving the Fermi-Thomas model for a positive and negative ion. You can’t do it for a negative ion — that’s of course wrong — but certainly for a positive ion. There is then a question of what boundary conditions you have to assume and what happens there. This is one of the typical things I got annoyed with there were some errors I saw him make, and so we started on this. And we thought we got it right. No. 13 is probably that famous paper where I had an argument with A. H. Wilson. He had come out with a paper saying the whole Bloch theory was nonsense and my papers too. Then I got interested in. optical properties of solids, and No. 15 was essentially my Habilitations schrift. Here the concept of excitons I think comes up for the first time. I didn’t use the word excitons that was used by Frenkel.


I noticed that you contributed to the first volume of the ‘Phys. Zeits.’ of the Soviet Union, and I was curious as to how that journal got started. Did they ask for contributions to their early volumes? Do you remember how that came about?


I don’t remember. I think that — now let’s see — that was in ‘32. I think that must have been during a visit there. Let’s see, ray recollection is that’s it’s probably quite a short paper and might have been just the basis of a talk given at a conference. Maybe it’s part of a talk. I was then visiting the Soviet Union several times. The first time in 1930 when I went to a conference there in Odessa — I think I went largely on the invitation of Frenkel who had been interested in my work on the Hall effect. Then I was invited the next year — that was presumably in ‘31 — to spend two months in Leningrad giving lectures on the theory of solids as it then was, and that’s when I got married also. Now this was published in ‘32, so it probably was written during one of those visits. I think it’s essentially a summary of the results of the paper No. 15. Well, I don’t know how far we should go on with that. Then come two papers on diamagnetism which are really extensions of Landau’s idea of electron diamagnetism in which I was very interested. Particularly the second one shows how one gets the de Haas-van Alphen effect out, which has now become a very interesting tool for studying metals. It seemed a complete mystery at that time.


Was there much interest in this work of yours at Rome?


No. There was a polite interest, but I essentially worked on this by myself. I don’t know whether you would like for me to go over the rest. It’s really getting away from the fundamental period.

Obituary: Sir Rudolf Peierls

Rudolf Ernst Peierls, physicist: born Berlin 5 June 1907 Assistant, Federal Institute of Technology, Zurich 1929-32 Rockefeller Fellow 1932- 33 Honorary Research Fellow, Manchester University 1933-35 Assistant in Research, Royal Society Mond Laboratory 1935-37 Professor of Mathematical Physics, Birmingham University 1937-63 FRS 1945 CBE 1946 Wykeham Professor of Physics, Oxford University 1963-74 Fellow, New College, Oxford 1963- 74 (Emeritus) Kt 1968 Professor of Physics (part-time) University of Washington, Seattle 1974-77 married 1931 Eugenia Kannegiesser (died 1986 one son, three daughters) died Oxford 19 September 1995.

A question gave Rudolf Peierls his place in history. He was so brilliant and so thoughtful he would certainly have found his way there by another route, but that question was enough. It was asked in Birmingham in early 1940 by Otto Frisch, one of the discoverers of nuclear fission, and it concerned certain properties of the element uranium. The answer, ultimately, was the atomic bomb.

Peierls, like Frisch, was a refugee from Hitler, a physicist, and concerned about the implications of the latest discoveries about uranium. By the spring of 1940, the prevailing scientific view was that a uranium bomb was impossible, because it would be too enormous, too unwieldy to be useful.

What if, Frisch asked, you did not use ordinary uranium? What if you used a refined lump of the rare type known as U-235? Would that be more practical?

Peierls had already developed a mathematical formula model for a calculation of this kind and the two set to work. They found that the "critical size" of the uranium weapon could be measured in pounds, not tons. This was something that could be dropped from an aeroplane.

Could enough U-235 be made? Between them they determined that it could. Their discovery set in motion the British atomic effort, code-named first Maud and then Tube Alloys, which in turn provided the vital stimulus for the American Manhattan Project. The bomb dropped on Hiroshima used U-235, as Frisch and Peierls had suggested. The bomb dropped on Nagasaki, which used plutonium and followed a quite different design, also owed a great deal to Rudolf Peierls.

The nuclear age had many fathers, and Peierls's place among them is beyond dispute. To those inclined to think this a dubious distinction, Peierls's later life offered an answer. From 1945 to within a few weeks of his death on Tuesday, he was among the most intelligent, informed and dynamic critics of nuclear weapons and the nuclear arms race.

Peierls was born in Berlin in 1907, the son of an engineering factory manager. Although his father's forebears were Jewish and his mother a Roman Catholic, he was baptised a Protestant. "My father," Rudolf wrote much later, "thought this would allow us to make our own choices when we grew up." This pragmatism, and the innocent spirit of subversion that went with it, were to rub off on the boy.

His pre-war career in science made him the embodiment of the old international physics of discovery, open exchange and free debate. He toured Europe, studying in almost every significant centre of research - Berlin, Munich, Leipzig, Zurich, Odessa, Leningrad, Rome, Cambridge, Manchester - and befriending all the "greats" of the period. On his travels he married a Russian physicist, Genia Kannegiesser.

He abandoned Germany just before Hitler took power and settled in Britain, becoming a professor at Birmingham in 1937. When he and Frisch had their conversation that day in 1940, Peierls was still not a British citizen but an "enemy alien", although this was very soon put right.

The "Frisch-Peierls Memorandum", setting out their findings, was the first practical blueprint for the atomic bomb. Central to its argument was the warning, which the writers were well qualified to issue, that German physicists were sufficiently able to think of this too, and that Hitler might already be working on the bomb.

Soon the bomb work transferred to the United States, and here Peierls made two distinct contributions. First, he advised on the complex technology required for separating U-235 from natural uranium. Then he moved to Los Alamos, the famous laboratory established in the New Mexico mountains under Robert Oppenheimer to design and manufacture the finished bombs.

At Los Alamos, this little man with bottle-end spectacles and a pipe clamped between his teeth became a popular fixture. His wife joined him, and their little house - one of the few with a bathroom - became something of a social salon. Peierls led the small but distinguished British team and was also in charge of an important theoretical research group known as the hydrodynamics group. This was remarkable in itself - not only was he neither American nor British, he was a German.

But Oppenheimer worked by merit alone and Peierls combined scientific ability of the first order with unusual gifts of managerial and political judgement. He was patient and kind, yet practical and quick-thinking. Progress reports he wrote to the British scientific mission in Washington were so thorough and yet so succinct that the US military authorities began to ask for their own copies.

Peierls's scientific contribution, particularly to the plutonium bomb which became the model for early post-war nuclear weapons, was considerable. A number of patents (subsequently to prove meaningless) were taken out in his name and they betray his extraordinary versatility, relating as they do to several quite distinct aspects of the design. He saw the first weapon tested at Alamogordo, New Mexico, in July 1945.

If Peierls later campaigned against nuclear weapons, this was not the result of guilt, or of some Damascene conversion. His views before and after 1945 were remarkably consistent. At first, he believed, it was necessary to build a bomb in case Hitler was doing so too. When the Germans surrendered, he continued because there was a bloody war going on in Asia which the bomb might shorten. The decision to drop it on a city may have been wrong, he believed, as its power could have been demonstrated in other ways. To drop it on two was "unnecessary". But he was certain that neither decision should or could have been made by scientists such as himself.

That he thought deeply about these issues from the start can be seen from the 1940 Memorandum, which included the observation that "the bomb could probably not be used without killing large numbers of civilians, and this may make it unsuitable as a weapon for use by this country".

After the war, Peierls was president of the Atomic Scientists' Association, pressing in vain for a better understanding of nuclear issues both among politicians and the general public, and campaigning for some form of international control of nuclear weapons as a means of forestalling the Cold War.

More recently he was involved in Pugwash, the East-West scientific forum for disarmament, and he was among the many distinguished scientists publicly to express opposition to Star Wars. As recently as this spring, he was one of the authors of a Pugwash pamphlet, Does Britain Need Nuclear Weapons? The answer was no.

In 1963 he moved to Oxford, as Wykeham Professor, where he worked until his retirement in 1974. He loved Britain, praising the "reasonableness" of its people and their gift for rubbing along with one another despite differences. This gift, he admitted to me in a conversation in March, was less evident now than it was in the 1930s.

His affection for this country was tested more than once down the years. During the war, Peierls recruited to the bomb project the German-born physicist Klaus Fuchs, who later turned out to have been a Soviet spy. No one was more stunned when Fuchs was unmasked in 1950. The connection, his own family link with Russia and his activities in the Atomic Scientists' Association led to suggestions in the press that his loyalty was in doubt. On each occasion, he took care courteously to rebut the claim, and in 1979 he successfully sued the author of a book containing a similar implication.

Genia Peierls used to classify scientists as either "golfers", pursuing a lone quest for a known goal, or "tennis players", whose strengths are brought out in exchanges with others. It was no accident that "Rudi" was drawn into the making of the atomic bomb by a question, for he was the tennis player par excellence. He avoided specialising in any field of physics, and his gift was to spot flaws or openings in the work of others and then to turn them into new ideas.

Aside from his research, which he continued to pursue well after retirement, his principal pleasure was to foster the careers of others, a task which both he and his wife pursued with devotion and pleasure.

It is said that he once overheard another scientist saying: "Did you know that two of Rudi's former students are now lords?" The professor observed: "I have had more than 200 research students. I cannot be blamed if one or two go to the bad."

Rudolf Peierls's life has ended in the 50th year of the nuclear weapons age. He re- mained to the last a patient, lucid and generous spokesman for the bomb-makers and also for that remarkable generation of scientists who taught him or worked beside him in the golden years before the bomb.

Rudolf Peierls

Peierls entstammt einer großbürgerlichen assimilierten jüdischen Berliner Familie. Er studierte Physik an der Friedrich-Wilhelms-Universität in Berlin, ab 1926 an der Universität München bei Arnold Sommerfeld und 1928 bei Werner Heisenberg in Leipzig, wo er promovierte. 1929 war er Assistent bei Wolfgang Pauli in Zürich. Hier und in Leipzig entstanden heute klassische Arbeiten von Peierls zur Festkörperphysik, teilweise in Zusammenarbeit mit Felix Bloch, der ebenfalls bei Heisenberg in Leipzig mitarbeitete.

Nach Abschluss des Studiums arbeitete Peierls zunächst auf verschiedenen Gebieten der Festkörperphysik und Halbleiterphysik, wobei er die neuen Ideen der sich entwickelnden Quantenmechanik auf diese Fragestellungen anwandte. Er beschrieb erstmals den Umklappprozess und veröffentlichte fundamentale Arbeiten über das Verhalten von Elektronen in Metallen, wobei er auch die Loch-Leitung positiver Ladungsträger in Halbleitern entdeckte. Viele seiner damaligen Ideen flossen in den „Festkörper-Kanon“ ein oder wurden sogar später wiederentdeckt (wie die Brillouin-Zone). Zusammen mit Niels Bohr und Georg Placzek formulierte er 1939 das optische Theorem (Bohr-Peierls-Placzek-Theorem). Neben Kernreaktionen beschäftigten ihn auch andere Bereiche der Kernphysik wie kollektive Anregungen in Kernen und Quantenfeldtheorie.

Zum Zeitpunkt der Machtergreifung 1933 befand er sich gerade als Rockefeller-Stipendiat in Cambridge und beschloss, angesichts der politischen Ereignisse nicht mehr nach Deutschland zurückzukehren. Zunächst arbeitete er zusammen mit anderen Emigranten (u. a. Hans Bethe) unter Lawrence Bragg in Manchester [1] bei James Chadwick an Problemen aus der statistischen Thermodynamik von Legierungen. Er wurde dabei durch einen Hilfsfonds für deutsche Flüchtlinge unterstützt. Später nahm er eine Stelle in Cambridge an und arbeitete über Supraleitung, Supraflüssigkeiten und an Problemen der Kernphysik. 1937 erhielt er eine Professur an der Universität Birmingham, wo er im Laufe der folgenden Jahrzehnte eine eigene Schule der theoretischen Physik aufbaute.

Besorgt über die scheinbaren Fortschritte der Atomforschung in Deutschland und über die Möglichkeit des Baus einer Atombombe in Hitlers Deutschland verfasste er 1940 zusammen mit dem österreichischen Emigranten Otto Frisch, einem Pionier der Kernspaltung, der ebenfalls in Birmingham arbeitete, das später so genannte Frisch-Peierls-Memorandum, in dem eindringlich vor einem Atombombenbau im nationalsozialistischen Deutschland gewarnt und zur verstärkten Forschung in Hinsicht auf die Konstruktion einer britischen Atombombe aufgefordert wurde. Als kritische Masse für eine Bombe aus Uran-235 gaben sie 1 kg an, weit unterhalb der sonst damals kursierenden Schätzungen. Sie zeigten damit insbesondere, dass der Bau einer Atombombe prinzipiell im Bereich des damals Möglichen lag. Über den MAUD-Bericht gelangte ihr Memorandum auch 1941 in die USA, wo es Einfluss auf den Beginn des Manhattan-Projekts hatte, an dem Peierls ab 1943 mitarbeitete, nachdem er die britische Staatsbürgerschaft erhalten hatte (von Arbeiten z. B. am kriegswichtigen britischen Radar war er wie Frisch zuvor ausgeschlossen gewesen, weil er kein britischer Staatsbürger war). Dass er auch den später als sowjetischen Spion enttarnten Klaus Fuchs mit zum Manhattan-Projekt brachte, machte ihn später bei offiziellen Stellen in den USA verdächtig. [2]

Nach dem Krieg war er wieder an der Universität Birmingham und ab 1963 an der Universität Oxford, und war gleichzeitig Berater des britischen Atomprogramms in Harwell, setzte sich aber auch früh für Abrüstung ein und war aktiv in der Pugwash-Bewegung. 1974 ging er in den Ruhestand, hielt aber noch drei Jahre Vorlesungen an der University of Washington.

Peierls war seit 1931 mit der russischen Physikerin Jewgenija Nikolajewna Kannegiesser (1908–1986), einer Cousine Leonid Kannegiessers, verheiratet und hatte mit ihr drei Töchter und einen Sohn. Er lernte seine Frau auf einer Konferenz 1930 in Odessa kennen und heiratete sie bei einem Aufenthalt in Leningrad ein Jahr später.

1945 wurde er als Mitglied („Fellow“) in die Royal Society gewählt, die ihm 1959 die Royal Medal und 1986 die Copley-Medaille verlieh. 1946 wurde er mit als Commander of the Order of the British Empire ausgezeichnet, 1968 wurde er zum Knight Bachelor geschlagen. [3] 1962 erhielt er die Lorentz-Medaille, 1963 die Max-Planck-Medaille und 1980 den Enrico-Fermi-Preis. 1962 wurde er in die American Academy of Arts and Sciences gewählt, 1970 in die National Academy of Sciences, 1981 zum Mitglied der Leopoldina [4] und 1984 zum auswärtigen Mitglied der Académie des sciences.

Mathematics Genealogy Project

Click here to see the students listed in chronological order.

Bell, JohnUniversity of Birmingham1956
Boya Balet, LuisUniversitat de Barcelona196472
Brenner, SheilaUniversity of Birmingham19544
Flowers, BrianUniversity of Birmingham1953
Hoyle, FredUniversity of Cambridge 259
MacDowell, SamuelUniversity of Birmingham19581
Preston, MelvinUniversity of Birmingham19491
Ravenhall, DavidUniversity of Birmingham19501
Reading, JohnUniversity of Birmingham19641
Salpeter, EdwinUniversity of Birmingham194823
Scheffler, BernhardUniversity of Oxford19701
Swiatecki, WladyslawUniversity of Birmingham19502

According to our current on-line database, Rudolf Peierls has 12 students and 377 descendants.
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Selected Scientific Papers of Sir Rudolf Peierls

This book is a collection of the major scientific papers of Sir Rudolf Peierls (1907–95), including the Peierls–Frisch Memoranda of 1940 on the feasibility, and the predicted human effects, of an atomic bomb made of uranium-235. His papers range widely in topic. They include much on the fundamentals of solid state physics, the thermal and electric conductivity of materials as a function of temperature T (especially T→0), the interpretation of the de Haas–van Alphen effect observed for a metal in a magnetic field, and the basics of transport theory. Many are on problems in statistical mechanics, including his constructive paper demonstrating the existence of a phase transition for Ising's model for a two-dimensional ferromagnet. In nuclear physics, they include the first calculations (with Bethe) on the photo-disintegration of the deuteron (made in response to a challenge by Chadwick), the Kapur–Peierls theory of resonance phenomena in nuclear reactions, the Bohr–Peierls–Placzek continuum model for complex nuclei (which first explained the narrow resonances observed for low energy neutrons incident on very heavy nuclei), and the Peierls–Thouless variational approach to collective phenomena in nuclei. Several of Peierls's wartime papers, now declassified, are here published for the first time.

Brief commentaries on most of the papers in this book were added by Peierls, to indicate subsequent developments and their relationship with other work, or to correct errors found later on. A complete bibliography of his writings is given as an appendix.

  • Theory of the Hall Effect
  • Kinetic Theory of Thermal Conduction in Crystals: Theory of Electric and Thermal Conductivity of Metals
  • Theory of the Diamagnetism of Conduction Electrons
  • Quantum Theory of the Diplon (Deuteron)
  • Ising's Model of Ferromagnetism
  • Dispersion Formula for Nuclear Reactions
  • Critical Conditions for Neutron Multiplication
  • The Peierls–Frisch Memorandum of 1940
  • Commutation Laws of Relativistic Field Theory
  • Field Equations in Functional Form
  • Collective Model of Nuclear Motion
  • Two-Stage Model of Fermi Interactions
  • Complex Eigenvalues in Scattering Theory
  • Resonance States and Their Uses
  • Momentum and Pseudomomentum of Light and Sound
  • Broken Symmetries
  • and other papers
  • Acknowledgements
On the Theory of Galvano-magnetic Effects

It will be shown that one can derive from Bloch's calculations qualitatively correct conclusions about the galvano-magnetic effects: in particular, both signs are obtained for the Hall effect, which the Sommerfeld Theory had not been able to produce, and the order of magnitude of the changes in resistance is obtained…

On the Theory of The Hall Effect

The phenonmenon of the Hall effect is largely analogous to the deflection of cathode rays in a magnetic field, except that in some metals it produces a sign that is different from what is expected. An explanation of this paradox was impossible as long as the electrons were visualised as freely-moving in the metal, for then the analogy to cathode rays would be literally true…

On the Existence of Stationary States

The conditions for the existence of stationary states are established for a special type of potential functions, such as they exist in connexion with problems arising from the formation of molecules. Among other results, it is found that there always exist stationary solutions for a simple potential “well”, although this is not necessarily so in the presence of short-range repulsive forces.

Oral history interview with Rudolf Ernst Peierls, 1969 August 11 to 13.

Individual letters are regularly acquired, usually by purchase, to complement holdings of personal papers and institutional archives within the Special Collections Department.The letters are added to either a general sequence of autograph letters (described here) or one of a small number of separate sequences of autograph letters devoted to a particular individual. Reference: University of Birmingham, Guide to Special Collections Archives and Manuscripts (http://www.is.b.

Chadwick, James, 1891-1974

Chadwick (1891-1974) was Lyon Jones Professor of Physics, University of Liverpool, 1935-1948. From the description of Papers, ca. 1921-1974. (Unknown). WorldCat record id: 78411798 From the description of Conversation with A. W. Merrison, 1968. (Unknown). WorldCat record id: 79016747 Physicist (1891-1974). From the description of Papers, 1940-1974. (Unknown). WorldCat record id: 78630825 Died 1974. From the description of Oral histor.

University of Cambridge.

Harvard University celebrated its 250th anniversary in 1886. Many institutions of higher education, governments, and individuals sent greetings and congratulations to commemorate the occasion. This seal accompanied greetings from the University of Cambridge, England, to the university in Cambridge, Massachusetts. From the description of Sigillum coe cancellarii mror et scholariu Universitat Cantebrigie, 1886. (Harvard University). WorldCat record id: 228509847 The University.

Frisch, Otto Robert, 1904-

Died 1979. From the description of Oral history interview with Otto Robert Frisch, 1967 May 3. (Unknown). WorldCat record id: 83622710 From the description of Oral history interview with Otto Robert Frisch, 1963 May 8. (Unknown). WorldCat record id: 79789841 .

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