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By Willis Lamb FIVE ENCOUNTERS WITH FELIX BLOCH by Willis Lamb ABSTRACT The impact of Felix Bloch's work on the fields of parity non- conservation, the Mossbauer effect, nuclear induction, chemical shifts, and laser theory is described from a personal point of view. I have benefited enormously from contacts with a number of the great theoretical physicists of the twentieth century. One such relationship far exceeds all the others in respect to duration and meaning to me. I am going to describe five encounters with Felix Bloch that involved purely scientific matters. Personal matters come into the account only to set the times and places of the episodes related. The first two and the last of the five en- counters involved suggestions Felix made to me in connection with my re- search. If I had had the wit, energy, and luck to folIow up properly the earli- est two of these leads, I might have made some very good discoveries. The third encounter involved a request from him for help on his research. It turned out that he did not, after the fact, need this help. Still, the story has a certain interest for me and might provide a footnote for a history of modern physics. The fourth encounter was very slight. I had worked on a certain prob- lem in the early forties. Bloch was working in the same area in the earIy fifties. I had missed following up some interesting aspects of my work. %loch and I talked about his problem and its relationship to my earlier re- search. It later turned out that his work was capable of enormous applica- tion, in chemistry rather than in physics, so that he did not follow it up as far as he might have done. WiIlis Lamb is Professor of Physics at the University of Arizona. 134 RICE UNIVERSITY STUDIES The fifth encounter led me to the development of the theory of lasers and masers, which has been a very productive and useful field of research for over twenty years. I received a B.Sc. at Berkeley in chemistry in 1934, and began the study of theoretical physics with Robert Oppenheimer. In those days, the Physics Departments at Berkeley and Stanford occasionally had joint picnics fol- lowed by a colloquium. One that I remember vividly took place in the spring of 1934 at the Lick Observatory on Mount Hamilton. The speaker was someone from Stanford named Felix Bloch. Solid state physics was not taught at Berkeley then, and I had no notion of the enormous contributions made to that field by the speaker. He had just come from Rome and told us about Fermi's new work on the theory of beta decay. In the fall of 1934, Oppenheimer and Bloch began to conduct joint weekly theoretical physics seminars alternating between Berkeley and Stanford. During the next year I gradually got to know Bloch, who accepted me with an unusual degree of tolerance. In the summer of 1935, I went to the theoretical physics school at Ann Arbor. This was organized by George Uhlenbeck and Samuel Goudsmit and operated during the eleven years before the U.S. entry into WorId War 11. Bloch was one of the lecturers that summer, and I learned from him the elements of his theory of electrical conductivity. I also acquired a little understanding of the theory of beta decay from other lecturers at the summer school, among whom were Enrico Fermi and David Dennison, as well as Uhlenbeck and Goudsmit. PARITY NON-CONSERVATION One day in the autumn of 1935,I was driving with Bloch somewhere in Berkeley, and he told me that the shape of a beta decay electron energy spectrum would depend on the change of angular momentum of the nuclear states. He suggested that 1 calculate this effect in more detail. The angular momentum dependence contemplated by Bloch came from the variation across the nuclear radius of the plane wave electron and neutrino wave functions in the transition matrix element. This brought in additional momentum-dependent factors and thereby changed the shape of the theoretical electron energy spectrum. At that time, the theory of beta decay was very primitive and poorly formulated. Competing with Fermi's originally postulated interaction for the emission of an electron and a neutrino was the proposal of Konopinski and Uhlenbeck that explicitly involved derivatives of lepton wavefunctions, and also changed the momentum dependence of the matrix element for the emission process. Gamov and Teller had also suggested an interaction that differed from Fermi's by the presence of nucIeon and lepton spin operators. FIVE ENCOUNTERS WITH FELIX BLOCH 135 By that time, I had learned from Pauli's 1933 Handbuch der Physik article' on Quantum Mechanics how he had classified the covariant quanti- ties that could be made out of binary combinations of Dirac wave func- tions: scalar, polar vector, tensor, axial vector, and pseudovector. A par- ticular combination of these interactions was used by Fermi, and, stimu- lated by Bloch, I began to investigate the effect on the beta spectrum of taking wild mixtures of the various Pauli building blocks. I remember that Robert Serber (then at Berkeley) showed me that some of the mixtures I was considering did not conserve parity! This might have been responsible for a missed opportunity, but 1936 was simply too early for the discovery2 of non-parit~conserving interactions. In fact, it took over twenty years before physics was ready for the theoretical analysis of Lee and Yang. The experimental state of measurement of beta spectra in 1936 was very confused because of thick source effects. I never really accomplished anything very useful with beta decay theory, and the work was publi~hed'.~ only in two abstracts of talks given before meetings of the Pacific Coast Section of the American Physical Society. SUMMERS AT STANFORD There wasn't much theoretical physics going on in Berkeley during the summers. Oppenheimer invariably spent about six weeks in the late spring at Cal Tech. I usually folIowed him there, but never to his summer retreat in New Mexico. Bloch stayed working at Stanford during the summers, and kindly provided me with a desk and library facilities. I was there during the summers of 1436-1939 and 1941. Each year there was a visiting lecturer, and in these years I came to know George Gamov, Edward Teller, Victor Weisskopf, J. H. Van Vleck, George Placzek, Samuel Allison, I. I. Rabi, George Kistiakowski, and many others who passed through Pa10 Alto on their summer travels., I also met most of the Stanford physicists: David Webster, Paul Kirkpatrick, Norris Bradbury, William Hansen, Russell Varian, Arnold Siegert, and Arnold Nordsieck (I had already known Nord- sieck at Berkeley, and we later were colleagues at Columbia for many years). My meeting with Rabi led to an appointment as Instructor in Physics at Columbia in the fall of 1938 after I received a Ph.D. THE M~SSBAUEREFFECT At Ann Arbor, I had heard Fermi lecture on the effect of chemical binding of a hydrogen atom on its scattering of slow neutrons. This interest- ed me, and I began to work on related problems. It seemed that there might also be an effect of the binding of a hydrogen atom on the capture cross 136 RICE UNIVERSITY STUDIES section for slow neutrons. At first I thought the effect would be large, but finally had to settle for a very rough estimate of the cross section for a very unlikely process: the radiationless capture of neutrons by bound protons to form deuterons, with the excess energy and momentum going into vibra- tional motion of the deuteron instead of a gamma ray. The normal capture process was very little affected by the chemical binding. Even today, this radiationless capture has never been seen, but I am still hoping that some- day it may be. This work5 formed part of my doctoral thesis. The other part6dealt with electromagnetic properties of nuclear matter. That summer, I came across a paper by Hans Bethe and Placzek7 on the resonant capture of slow neutrons by nuclei in a gas. The resulting com- pound nucleus could decay in a number of ways that contributed to rhe natural width of the resonance curve. The Lorentzian resonance curve of the Breit-Wigner theory of capture of slow neutrons to form a compound nucleus was modified because of the Doppler effect. In the limit of small gas atom velocities, the resonance curve was Lorentzian, while for rapid motions it became a Doppler-broadened Gaussian. In the general case, Bethe and Placzek obtained the Voigt8profile, which was well known in the theory of Doppler broadening of naturally broadened spectral lines emitted or absorbed by atoms in a gas. Since most of the experimental studies on resonant neutron capture in- volved atoms in a solid, I began to generalize the Bethe-Placzek theory to deal with nuclei bound in a crystal lattice. For the case of a simple harmonic oscillator (Einstein) model of the solid, it was clear that the neutron reso- nance curve would be a sum of Lorentzians with centers displaced by the separation of the vibrational energy levels of the oscillator. Then using what was learned from Bloch in a previous summer, I worked out the theory for a Debye model solid. Instead of a single oscillator frequency, there was a fre- quency continuum extending from zero up to a maximum value simply related to the Debye temperature of the solid. I derived a general, but complicated, expression for the neutron capture cross section as a function of neutron energy.
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