Hyperfine Interactions 72(1992)3-11
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THE EARLY HISTORY OF THE MOSSBAUER EFFECT Harry J. LIPKIN Department of Nuclear Physics Weizmann Institute of Science, Rehovot 76100, Israel and School of Physics and Astronomy Raymond and Beverley Sackler Faculty of Exact Sciences Tel Aviv University, Tel Aviv, Israel
Submitted to Stan Hanna Editors note: In the earliest days of the M~ssbauer effect, much of the interest and excitement centered on confirming the effect and understanding its nature. This period was quickly followed by the emergence of research which demonstrated the power of the effect to uncover new phenomena or to observe and elucidate old ones with greatly enhanced precision. These observations played a significant role in bridging the growing gaps among several disciplines such as atomic, nuclear and solid-state physics and its practitioners, and indeed, in the eventual creation of this journal, Hyperfine Interactions. The following article is a lively, informative, and interesting account of the first phase, which is presented here as an introduction to the main theme of this volume: the beautiful contributions of the M6ssbauer effect to atomic, nuclear, and solid-state physics. DEDICATION During the past year, I have lost two friends whose work and discussions were of great value to me during the early years of the M6ssbauer effect: John Bardeen and Kundan S. Singwi, I should like to dedicate this paper to their memory. I was at the University of Illinois at Urbana in the academic year 1 9 5 8 59 when I first heard about the MOssbauer effect. My contacts with Bardeen and his theory group taught me everything I needed to know about solid-state physics to understand the M6ssbauer effect. I also learned at Urbana from Fred Seitz that my old friend Kundan Singwi had done pioneering work in neutron scattering which was very relevant to the MOssbauer effect. I had met Kundan and his wife Helga in 1953 when we were both postdocs learning about nuclear energy at Saclay, lived in the same pension operated by the French Atomic Energy Commission, and had dinner together every evening. It was a pleasure to renew our contacts after their arrival at Argonne in 1959 when we were both involved in the M6ssbauer effect, and during an extended period while he was at Argonne and we visited it every summer. I shall miss both John and Kundan. O J.C. Baltzer AG, Scientific Publishing Company
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1.
H.J. Lipkin, The early history of the M6ssbauer effect
Prehistory
Rudolf MOssbauer's first paper was followed by an avalanche of papers, many of which simply reproduced M6ssbauer's experiment, obtaining exactly the same results without adding anything new, and were published in refereed journals as original results. This unique phenomenon reflected the general feeling in the nuclear physics community that this experiment must be wrong and that it was necessary to correct this error by doing the experiment right. When I first saw M6ssbauer's paper, I consulted a real solid-state expert Fred Seitz. Fred's immediate response was "Who is this fellow M6ssbauer? Does anybody know him? Is he reliable? Give me a few days to think about it." Several days later, he told me "I've looked at this MOssbauer paper and it is perfectly all right. But I must admit that when I first saw it I thought that it was completely crazy." This sums up the situation in physics at the time of M6ssbauer's first experiment. It was perfectly all right and the theory needed to understand it was well known and published. But the nuclear physicists did not know nor understand the relevant solid-state physics, while the solid-state physicists who could understand it were put off because their initial response based on intuition was wrong. The energy and momentum scales of the experiment were unfamiliar and misled their intuition. The energy of a 129 keV ),-ray is so large compared to lattice energies that an experiment on this energy scale cannot possibly leave the lattice undisturbed. What was not clear was that this energy simply leaves the crystal and that a recoil momentum of 129 keV imparts a kinetic energy of only 0.05 eV to a nucleus with a mass of 190 GeV. All the physics needed to understand the MOssbauer effect had been published long ago by Lamb [1], Ott [2] and others, That photons could be scattered by atoms in a crystal without energy loss due to recoil was basic to all work in X-ray diffraction and crystallography. All the quantitative calculations, including the definition and evaluation of the Debye-Waller factor, were well known. But nobody interpreted this as a probability that a photon could be scattered by an atom in a crystal without energy loss due to recoil. The X-ray physicist worked entirely with the wave picture of radiation and never thought about photons. The Debye-Waller factor written as exp((-k2x2)) clearly described the loss of intensity of coherent radiation because the atoms were not fixed at their equilibrium positions and their motion introduced random phases into the scattered wave. Nobody noted that scattering the X-rays involved a momentum transfer and that coherence would be destroyed if there was any energy loss in the momentum transfer process. They did not see that the Debye-Waller factor also could be interpreted as the probability that the scattering would be elastic and not change the quantum state of the crystal. They did not see that localizing the atoms to the extent needed to get phase coherence in the wave picture meant introducing an uncertainty in the momentum of the atom which was large enough to absorb the momentum
H.J. Lipkin, The early history of the M6ssbauer effect
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transfer without energy transfer. The uncertainty in the momentum of the atom simply means that there is continuous momentum interchange between the atom and the rest of the crystal so that the total momentum is of course conserved. Thus, there can be an appreciable probability that a momentum transfer which is small compared to the momentum oscillations between atom and crystal can be absorbed by the entire crystal without changing the internal energy of the crystal. There was a clear communication barrier between nuclear and solid-state physicists, who spoke different languages and did not understand one another. Maurice Goldhaber summed up the situation by saying that this would teach many old things to new people. 2.
How I got into the M6ssbauer business
I was fortunate to be in the right place at the right time and with the right background to learn enough of both languages to understand the physics and the significance of the M6ssbauer effect at an early stage. I believe that my article [3] was the first to use the name "MOssbauer effect". At that time, others either did not believe in the effect or felt that it was not important enough to be called by its discoverer's name. I was spending a year at the University of Illinois at Urbana, following up my own experimental research program in beta-ray polarization measurements after the discovery of parity nonconservation. I directed Hans Frauenfelder's group of students and postdocs in their polarization experiments which paralleled those of my group at Weizmann, while Hans was on sabbatical at CERN. We both knew that the parity game was closing down. The exciting controversial days of exploring the weak interaction in beta decay were over. The new data confirmed completely the universal V - A interaction of Marshak and Sudarshan and the two-component neutrinos with left-handed neutrinos and right-handed antineutrinos. We needed a new experimental program, and Hans had met M6ssbauer and was very impressed. He sent us a reprint and suggested that we look into it. This led to my consultation with Fred Seitz and to the beginning of the Urbana M6ssbauer program, which was just getting started when I left and was continued by Hans with great success. At the same time, I was expanding my theoretical work on collective motion in nuclei to the general many-body problem, where ideas from solid-state physics were percolating into nuclear physics, mainly as a result of the then new BCS theory of superconductivity. In addition to directing Hans' experimental group, I attended all of the seminars of John Bardeen's group in the exciting time when BCS was still controversial and there were many VIP physicists insisting that BCS was nonsense because it was not gauge invariant, etc. I learned a great deal from John and from his group of postdocs about physics and how to look through both the forest and the trees to find the physics. BCS was among the first bridges between nuclear and solid-state physicists, and I was there seeing it being built. I became an interpreter between two groups
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H.J. Lipkin, The early history of the MOssbauer effect
speaking different languages. One example was the quasi-spin algebra developed independently by Arthur Kerman in nuclear physics and Phil Anderson in superconductivity to describe pairing correlations in many-fermion systems. Neither knew about the work of the other, and I was for a time the only one who was sufficiently connected to both the nuclear and solid-state grapevines to know about both. I introduced each to the work of the other. As soon as I heard about the MOssbauer effect and understood it, I was able to use my own background in many-body physics and what I had learned at Urbana to write a series of articles explaining the M6ssbauer effect in simple terms [3] and deriving a number of sum rules [4] and other results [5,6] which remain pedagogically useful today for teaching basic principles of quantum mechanics to graduate students [7]. Shortly after I heard about the M6ssbauer effect from Hans, I gave a colloquium talk at Columbia on our parity experiments and had lunch with C.S. Wu and Rudi Peierls, who was then visiting Columbia. When I mentioned that we were considering a M6ssbauer experiment, Rudi said that a group at Los Alamos was doing an experiment. I then asked members of our Urbana group who were attending the Washington APS meeting to contact the Los Alamos people and find out what they were doing. They reported that no one from the Los Alamos M6ssbauer group was at the meeting, but that they heard that a M6ssbauer experiment was being done at Argonne. I found this very amusing, because I had been in contact with David Inglis and Maria Mayer at Argonne, and had been invited to spend the following summer at a Nuclear Physics Workshop that they were organizing at Argonne. They had been working on the theory of the M6ssbauer effect, but somehow the subject had never come up in our previous discussions. Even more amusing was my first meeting with my old friend Kundan Singwi that summer in the Argonne cafeteria. I told him enthusiastically about the M6ssbauer effect, pointing out that his experience with neutron scattering in crystals was just what was needed for exciting investigations into the theory of the effect. The head of the Argonne Solid State Division, who was sitting with us, then said that this was all very interesting and asked whether the experiment had ever been done. He was surprised to hear that it had been done by John Schiffer in the building next door at Argonne. There was truly a communications barrier between nuclear and solid-state physicists. 3.
Problems in understanding the Debye-Waller factor
During the summer of 1959, the few experimentalists working on the MOssbauer effect were wondering how to find other isotopes which would give a larger effect and how to embed them in compounds and crystals where the Debye-Waller factor or MOssbauer fraction would be increased. Meanwhile, the physics community, now convinced by subsequent experiments that the effect was really there, insisted that it was an unimportant curiosity. It was a nice exercise in quantum mechanics, but
H.J. Lipkin, The early history of the M6ssbauer effect
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would not lead to anything new and useful. Nuclear physicists claimed that it would teach us nothing new about nuclear structure. Solid-state physicists claimed that its use as a tool in solid-state physics could not compete with neutron scattering and nuclear magnetic resonance, which would get the same information more easily. A few months later, after the simultaneous discovery in many places that 57Fe was an ideal source, the field exploded. There was a strong effect with a large Debye-Waller factor. It could be inserted into magnetic materials and enable the measurement of nuclear hyperfine splittings for the first time, as well as studying hyperfine interactions in many materials where NMR did not work. It could be inserted into important biological molecules like hemoglobin, thereby opening a new field in biophysics. It provided a source with a linewidth many orders of magnitude smaller than previously available sources, thus enabling precision measurements of quantities like the gravitational red shift. One may well ask why it took several months for the active experimenters to find 57Fe. Here again we see the communications barrier. One of the expressions in the literature for the Debye-Waller factor indicated that it could be increased by using a material with a high Debye temperature. A look through the tables of Debye tempeiatures immediately led to beryllium, and there were proposals to embed M6ssbauer's iridium source in beryllium to enhance the Debye-Waller factor. However, this use of the Debye temperature is based on an erroneous understanding of the basic physics. The standard expression for the Debye-Waller factor as a function of the Debye temperature does not hold for an impurity source with a radically different mass from the lattice host atoms. The general expression exp((-kZx2)) shows that the important physics is the localization of the source atom by strong binding, which makes its position fluctuations small on the scale of the wave length defined by the momentum transfer k. The expression in terms of the free recoil energy R and the Debye temperature are based on the relations k2 = 2 M R ,
(la)
where we set "h= c = 1, while for the ground-state wave function of a harmonic oscillator with frequency 09 (x 2) = 1/(2Moo).
(lb)
Thus, the mass factors cancel in the product
k2(x 2) = Rift).
(lc)
For a source in a homogeneous harmonic crystal, the quantity 09 is replaced by a characteristic frequency of the lattice. For the Debye model of the crystal, this characteristic frequency is proportional to the Debye temperature 0. Evaluation of
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H.J. Lipkin, The early history of the MiSssbauer effect
the LHS of eq. (lc) for the ground state of the lattice which describes the system at zero temperature gives the well-known result k2(x 2) = 3R/2KO,
(ld)
where K is Boltzmann's constant. However, for a source which is an impurity in the lattice there are two relevant masses, that of the impurity and that of the host atoms. Thus, the mass factors in eqs. (la) and (lb) are different and do not cancel in the product. The result is that the high characteristic frequency of beryllium is due to the low mass of the beryllium atom rather than to strong binding. The high Debye temperature is thus irrelevant for the M0ssbauer effect of an impurity embedded in beryllium, and the suggestions to use it were erroneous. The general state of confusion on this issue can be seen in the panel discussion which took place at the Second International M6ssbauer Conference [8]. Similar effects with two masses occur in diatomic lattices, where the two constituent atoms have very different masses, This effect was later calculated in detail and gave relations between the M6ssbauer fraction and the specific heat of such lattices [9].
4.
Why M6ssbauer could not use S7Fe
Rudolf MOssbauer himself claims that he had thought of using 57Fe while still in Germany, but he was unable to get it. 57Fe could be produced only in cyclotrons, and the authorities running the relevant cyclotron in Germany told Rudolf that they had more important things to do than make sources for graduate students. By the time that Rudolf was settled at CALTECH, others had discovered 5VFe and the work was in full swing. I remember hearing a number of stories like this from Rudolf when I visited him in Pasadena in November 1962, and he was debating whether to remain at CALTECH or return to Germany. At CALTECH he was free to carry out his research and received encouragement and support from experts in all related fields. Feynman and GelI-Mann were always ready to discuss theoretical questions. Solid-state physicists, low-temperature physicists, metallurgists and chemists were all very friendly and cooperative in helping him to solve the "interdisciplinary" problems arising in proper preparation of sources and absorbers and in interpreting results. In Germany he received no such support; each expert closely guarded his "secrets" and Rudolf would have to discover all the relevant techniques by himself. Furthermore, at CALTECH he could rise to the highest positions, especially after his Nobel Prize, and still do fulltime research without large teaching loads or administrative responsibilities. In Germany, this was impossible. One would have to become The Herr Professor of the department or the director of an institute to advance in status and salary.
H.J. Lipkin, The early history of the M6ssbauer effect
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But Heisenberg, who was attempting to convince Rudolf to return, responded with arguments very familiar to me as what we in Israel call "Zionism". "You are needed. You should give up your comfortable life in America, retum to your homeland and contribute to its rebirth and rebuilding. Of course your criticisms are correct. These things must change. But only people like you can change them. Come." Rudolf responded to this challenge and attempted to induce needed reforms in Germany, like creating a department where there could be many professors with full privileges and no administrative responsibilities. Many years later, Rudolf told me that he was amused by my calling him a "Zionist", but admitted that this description was essentially correct, and that unfortunately his achievements had fallen short of his expectations. He is not alone. Many of us Zionists in Israel feel the same way about our own achievements. 5.
The generalized M6ssbauer effect
Once the basic physics underlying the MOssbauer effect was understood, it became evident that this physics of momentum transfer to bound systems occurs everywhere in physics and can be described by the same formalism. This is discussed in detail, with many examples from different areas of physics, in my Quantum Mechanics book [7], where it can give the student an introduction into exciting frontier physics at a very early stage before he has mastered a great deal of formalism. The analog of the Debye-Waller factors appears everywhere and is called various names, such as form factor or structure factor. It is just the probability that momentum can be transferred to a constituent in a bound system, with no change in the internal wave function of the bound system and the recoil momentum taken up by the whole system.
F= ~ Pi I(ileikxli)12,
(2a)
i
where k denotes the momentum transfer, x is the coordinate of the active constituent, and Pi denotes the probability that the system is initially in the l i). This can be rewritten
F = ~ Pi IfPi (x) eik'xd3x 12 = e-k2(x2},
(2b)
i
where pi(x) denotes the probability density for the variable x in the state l i ), (x 2) is averaged over the entire distribution of initial states, and the approximate equality holds if the density pi(x) is a Gaussian. Measuring this factor as a function of the momentum transfer or a scattering angle measures the Fourier transform of the probability density for the active constituent. In X-ray crystallography, it gives the Fourier transform of the electron density. In elastic electron scattering on nuclei, it is the probability of elastic as opposed to
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H.J. Lipkin, The early history of the M~ssbauer effect
inelastic scattering and gives the Fourier transform of the electric charge distribution in the nucleus. The probability of momentum transfer without energy loss due to recoil is large when the Debye-Waller factor is large, i.e. when the fluctuations in the position of the active ~ constituent is small in comparison with the wave length 1/k defined by the momentum transfer. Such effects occur even in macroscopic experiments. An amusing example occurs in an experiment measuring the tiny mass difference, 3 • 10-~2 MeV, between the two neutral kaon states, Klong and Kshort. A Klong beam is passed through two slabs of material and the conversion Klong ~ Kshort is observed as a function of the macroscopic distance d between the two slabs by detecting the decay Kshor t --~ 2~r in the emergent beam. The measurement depends upon the coherence and interference between the components which underwent conversion in the two slabs. However, the conversion, because of the mass difference, involves a momentum transfer, and the kinetic energy loss in the momentum transfer to the particular slab where the conversion took place would destroy the coherence. But both slabs are bound by gravitational and frictional forces to some apparatus like a table, which is in turn bound to the earth. There is a M6ssbauer effect in which the whole earth takes up the recoil and not the individual slab. The probability that this occurs is again given by the Debye-Waller factor exp((-k2x2)), which is immediately seen to be close to unity. All practical experiments are automatically designed to make -~(x2) small in comparison with the wave length 1/k. The oscillations can be observed only if each slab is "bound strongly enough" to the rest of the experimental apparatus so that the fluctuations in its position are small compared to the wave length that one wishes to measure, which is just 1/k. This can be called Lipkin's MOssbauer principle for macroscopic interference experiments: "If you can measure it, then you can measure it. Don't worry about recoil."
6.
A curious recollection from the past
I conclude with an amusing incident that occurred when Willis Lamb visited Israel while traveling around the world. When I met him at the airport upon his arrival from India, one of his first questions was whether Bruria Kaufman was at the Weizmann Institute. When he met Bruria, he immediately told her that she had made an important contribution to the theory of the MOssbauer effect and pulled out of his briefcase a letter that she had written to him in 1939. Bruria's response was "What is the M~Jssbauer effect?" Lamb then explained that Bruria was a graduate student at Columbia at the time when he had written his now famous paper on neutron absorption in crystals. In the paper, he had made an approximation of using only the leading term in (l/N), where N is the number of atoms in the crystal, in order to obtain the approximate expression (2b) for the Debye-Waller factor. Bruria wrote a letter to Lamb pointing out that this approximation was not necessary; the problem could be solved exactly for a harmonic crystal by using mathematical
H.J. Lipkin, The early history of the MOssbauer effect
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techniques developed by Ott for X-ray scattering [2]. This was the letter that Lamb pulled out of his briefcase over twenty years later. Lamb then explained that he had thanked Bruria at the time but did not think it was worth publishing this correction. The paper had already been submitted for publication, and terms of higher order in (I/N) were certainly negligible. Besides, this paper wasn't all that important at the time. Now, however, with all this attention paid to the MOssbauer effect, it would be useful for pedagogical purposes to publish the exact treatment. Bruria and I then collaborated in writing up the exact treatment for publication [10], with my contribution being to explain the Mtissbauer effect to Bruria and introduce the new notations of creation and destruction operators for oscillator quanta, which made the treatment much simpler than Ott's use of properties of Hermite polynomials. References [1] [2] [3] [4] [5] [6] [7] [8]
W.E. Lamb, Jr., Phys. Rev. 55(1939)190. H. Ott, Ann. Physik 23(1935)169. H.J. Lipkin, Ann. Phys. 9(1960)332. H.J. Lipkin, Ann. Phys. 18(1962)182. H.J. Lipkin, Ann. Phys. 23(1963)287. H.J. Lipkin, Ann. Phys. 26(1964)115. H.J. Lipkin, Quantum Mechanics (North-Holland, Amsterdam, 1973), pp. 33-110. M. Hamermesh et al., in: The M6ssbauer Effect, Proceedings of the Second International Conference on the M6ssbauer Effect held at Saclay, France, 1961, ed. D.M.J. Compton and A.H. Schoen (Wiley, New York, 1962), p. 19. [9] H.J. Lipkin, Y. Disatnik and D. Fainstain, Phys. Rev. A139(1965)292. [10] B. Kaufman and H.J. Lipkin, Ann. Phys. 18(1962)294.
