BETHE, HANS ALBRECHT

(b. 2 July 1906, Strassburg, Alsace; d. 6 March 2006, Ithaca, New York)

theoretical physics, quantum mechanics.

Bethe was one of the great physicists of the twentieth century. After the advent of quantum mechanics, in two classic articles published in 1933 in the Handbuch der Physik he detailed the applications of the new quantum theory to atomic and solid state physics. After the discovery of the neutron in 1932 in a series of articles in the Reviews of Modern Physics, he did the same for nuclear physics. In 1938 he formulated the nuclear physics responsible for energy production in stars. During World War II he contributed importantly to the development of radar and of atomic weapons. Because of his involvement in making A- and H-bombs possible, he subsequently devoted considerable efforts in limiting further developments of atomic weaponry and bringing about international agreements for the reduction of extant nuclear weapons and the curtailment of their production and design. He made Cornell University, his base of operation from 1935 until his death, an outstanding center of theoretical physics and a model research community in all branches of physics.

Youth and Education. Hans Bethe was born on 2 July 1906 in Strassburg, when Alsace was part of the Wilhelminian empire. His father, Albrecht Julius Bethe, obtained a PhD in zoology at the University of Munich with Richard Hertwig in 1895, and thereafter went to Strassburg to study physiology. He became a Privatdozent there and also acquired a medical degree. In 1912 Hans’s father accepted the chair in physiology at the University of Kiel, and three years later a professorship in the newly established Frankfurt University. Albrecht Bethe became a world renowned physiologist specializing in comparative studies of the nervous system of animals and of animal behavior. Hans’s mother, née Anna Kuhn, was born in Strassburg, where her father was a professor of medicine specializing in diseases of the ear, nose, and throat. Bethe was an only child. He grew up in a Christian household, but one in which religion did not play an important role.

His father was Protestant; his mother had been Jewish but had converted and became a Lutheran before she had met Hans’s father. She was a talented and accomplished musician who became a successful author of children’s plays. A year or two before World War I her hearing was impaired as a result of contracting influenza. The illness left psychological scars. She became prone to what was diagnosed at the time as bouts of “nervous exhaustion,” extended periods of depression. The marriage suffered under the strain and Hans’s parents eventually divorced in 1927. From the mid-1920s on, it was Hans who looked after his mother’s welfare and wellbeing.

Bethe started reading at the age of four and began writing at about the same age. His numerical and mathematical abilities manifested themselves early. At age fourteen he taught himself calculus. At age eighteen he published his first scientific paper: a joint publication with his father on diffusion and fluid flow in living organisms. His mathematics teacher at the Goethe Gymnasium he attended in Frankfurt recognized his exceptional mathematical talents and encouraged him to continue studies in mathematics and the physical sciences. By the time he finished gymnasium in the spring of 1924 he knew he wanted to be a physicist. In the fall of 1924 he enrolled in the University of Frankfurt and took courses in physics with Walther Gerlach, and in mathematics with Carl Ludwig Siegel. After completing two years of studies at the University in Frankfurt, he was advised by one of his teachers there, the spectroscopist Karl Meissner, to go to Munich and study with Arnold Sommerfeld, who at the time was the outstanding university physics teacher in Germany. In the summer of 1926 Bethe joined Sommerfeld’s seminar.

Gregor Wentzel was Sommerfeld’s assistant at the time and helped make the seminar, together with Niels Bohr’s Institute in Copenhagen and Max Born and James Frank’s Physics Institute in Göttingen, the pivotal centers in the development of the new quantum mechanics. Sommerfeld’s seminar attracted many American postdoctoral fellows, and it was in Munich that Bethe first met Edward Condon, Carl Eckart, William Houston, Philip Morse, Linus Pauling, Isador Rabi, and Lloyd P. Smith. In 1927, Rudolf Peierls, a young German physics student a year younger than Bethe, joined Sommerfeld’s seminar. Bethe and Peierls then cemented a very close intellectual bond and personal friendship that lasted until Peierls’s death in 1995. Sommerfeld’s seminar met weekly. In contrast to the usual practice at the other German universities where only invited guests spoke, Sommerfeld had his Doktoranden and Assistent s make presentations in his seminar. Bethe arrived in Munich just as Erwin Schrödinger’s papers on wave mechanics were being published in the Annalen der Physik and his first presentation in the fall of 1926 was on the perturbative methods that Schrödinger had developed.

It was in Munich that Bethe discovered his remarkable talents and proficiency in physics and anchored his self-confidence. Sommerfeld indicated to him that he was among the very best students who had studied with him, and these had included among others, Max von Laue, Paul Ewald, Wolfgang Pauli, and Werner Heisenberg. From Sommerfeld Bethe learned to analyze masses of experimental data, go to the main points of a problem, assimilate the salient features of the data and of the problem into a mathematical model, express the model in appropriate mathematical equations, and then fearlessly use every available mathematical tool to solve the equations quantitatively as exactly as possible.

Early Career. Bethe obtained his doctorate—summa cum laude—in 1928 with a thesis that analyzed and explained the results that Clinton Joseph Davisson and Lester Germer had obtained in their experiments on electron diffraction by nickel crystals. When the de Broglie wave length of electrons is comparable to the lattice spacings of a crystal they diffract in a manner similar to x-rays. Bethe made use of the methods that von Laue and Ewald had formulated for x-ray diffraction by crystals and found that their results could readily and successfully be adapted to the electron case.

During Sommerfeld’s travel around the world in 1928–1929, Bethe spent a semester in Frankfurt as Erwin Madelung’s Assistent, and another semester in Stuttgart as Paul Ewald's. Upon Sommerfeld’s return Bethe went back to Munich and undertook his Habilitation.

In the fall of 1929 Sommerfeld recommended Bethe for a Rockefeller Foundation fellowship. And so during 1930 Bethe spent a semester in Cambridge under the aegis of Ralph Fowler, and a semester in Rome working with Enrico Fermi. Though only five years older than Bethe, Fermi became the other great formative influence on him. Fermi helped Bethe free himself from the mathematically rigorous and exhaustive approach that was the hallmark of Sommerfeld. For Fermi a mathematical solution served as corroboration and confirmation of his physical understanding of a problem. From Fermi, Bethe learned to reason qualitatively, to obtain insights from back-of-envelopes calculations, and to find the easiest way to solve a problem. Bethe’s craftsmanship became an amalgam of what he learned from these two great physicists and teachers, combining the best of both: the thoroughness and rigor of Sommerfeld’s approach to problems with the clarity and simplicity of Fermi's. Fermi and Sommerfeld both believed that science is also communication and both were also superb lecturers. Bethe followed in their footsteps and honed his skilled in communication. Bethe’s lectures became masterpieces of organization and exposition. Like Fermi and Sommerfeld, Bethe made no concession to expediency when lecturing on a difficult subject, but presented it in a clear, concise, and insightful manner. However, it was difficult at times to reconstruct his lectures, as what was clear and simple to him was not necessarily so for his audiences.

Bethe’s craftsmanship was displayed in full force in the many “reviews” that he wrote. His two book-length “reviews” in volume 24 of the 1933 Handbuch der Physik—the first the result of Sommerfeld asking him to collaborate in the writing of his entry on the Elektronentheorie der Metalle, and the second on the quantum theory of one- and two-electron systems—exhibited his remarkable powers of synthesis and became classics as soon as they were published. Together with the one on nuclear physics in the Reviews of Modern Physics 1936-1937— written in collaboration with his colleagues at Cornell, Robert Bacher and Stanley Livingston and known as the “Bethe Bible”— they are merely the most famous. All of Bethe’s reviews were syntheses of the fields under review, giving them coherence and unity, charting the paths to be taken in addressing new problems. They usually contained much that was new, materials that Bethe had worked out in the preparation of his essay.

In the fall of 1932 Bethe obtained an appointment in Tübingen as an acting assistant professor of theoretical physics. In April 1933, after Hitler’s accession to power, he was dismissed from his position because he had two Jewish grandparents. Sommerfeld was able to help him by awarding him a fellowship in his institute for the summer 1933 and got William Lawrence Bragg to invite him to Manchester. The appointment in Manchester was for a year’s duration and thus the question of what would happen the following year came up early on. There then occurred a confluence of events that determined Bethe’s subsequent life. The physics department at Cornell University was looking for a theorist, and on its faculty was the young theorist Lloyd P. Smith, who had studied with Bethe in Munich and who recommended him strongly. At that very same time Bragg was visiting Cornell for the spring semester and could corroborate Smith’s assessment of Bethe. In the fall of 1934 Bethe accepted a position at Cornell University. But as he had received an offer of a yearlong fellowship in Bristol with Neville Mott, he asked and obtained permission from Cornell to assume his duties there in the spring term rather than at the beginning of the academic year. He went to Bristol during the fall semester of the academic year 1934–1935 and arrived in Ithaca, New York, in February 1935. He stayed there for the rest of his life.

Problems of Stellar Energy. Bethe arrived in the United States at a time when the American physics community was undergoing enormous growth. The influence of the émigré scientists who had come from Nazi Germany was particularly noticeable at the many theoretical conferences that were being organized to assimilate the insights that quantum mechanics was giving to many fields, especially molecular physics and the emerging field of nuclear physics. The annual Washington Conferences on Theoretical Physics, initiated in 1935 and jointly sponsored by the Carnegie Institution and George Washington University, were paradigmatic of such meetings. Their intellectual agenda was set by George Gamow and by Bethe’s friend, Edward Teller. Their purpose was to evolve in the United States something similar to Niels Bohr’s Copenhagen Conferences, in which a small number of theoretical physicists working on related problems would assemble to discuss in an informal way their research. The conferences proved to be extremely influential and seminal, partly because they were restricted to theory and partly because their size was strictly regulated so that they would remain “working” meetings. Bethe attended the 1935 and 1937 Washington Conferences but when invited to the 1938 meeting first declined because he was not interested in the problem of stellar energy generation, the topic for that year that had been chosen by Gamow, who recently had turned his attention to the problem. It was only after Teller’s repeated urgings that Bethe agreed to come.

The opening lecture was given by the Danish astrophysicist Bengt Strömberg, who had just written a seventy-page paper that critically reviewed all that was known about stellar structure and the evolution of stars. In his presentation Strömberg focused on the problem of the temperature and density distribution in the interior of stars. He indicated that spectroscopic data suggested that the most reasonable model for the Sun was for hydrogen to be the prevalent element in its composition. He noted that a model of the Sun with a central temperature of 19 million degrees, a central density of 76 g/cm3, and a hydrogen content of 35 percent by weight would result in its generating 2 erg/g sec. The challenge he posed to the physicists in the audience was to find the thermonuclear reactions that would give rise to the observed luminosities of the Sun and other main sequence stars. In the subsequent discussion Bethe was critical of any theory, such as Gamow’s and Carl Friedrich von Weizsäcker's, that proposed a chain of nuclear reactions that would simultaneously generate energy and account for the building up of heavy elements in stars; this because of the instability of He⁵ and of Be⁶. Thus there was no obvious way to create elements heavier than helium. It seemed more likely to Bethe, given the great abundance of hydrogen in the Sun, that von Weizsäcker’s suggestion that the fusion of two protons to form a deuteron, a positron, and a neutrino,

as the first step in proton reactions that led to the formation of helium was a more likely source of stellar energy. In fact Charles Critchfield, a graduate student of Teller's, had for some months tried to persuade Gamow and Teller to help him investigate this (weak interaction induced) reaction. Upon hearing of Critchfield’s interest in the reaction Bethe proposed that they collaborate. Before the conference’s end they were able to report that the reaction

(1) together with the chain of reactions

—the end result of which is the combination of four protons into one α-particle and thus the release of a large amount of energy—accounted for the energy production of the Sun, but not of other heavier bright stars. From astronomical observations one could show that core temperature of stars increases slowly with increasing mass, but the amount of observed radiation, that is, their luminosity, increases very rapidly. This left unsolved the problem of energy production in larger stars because the proton-proton (pp) reaction could not explain this. Upon his return to Cornell from the conference Bethe started investigating reactions involving heavier nuclei that would explain energy production in massive stars. Lithium, beryllium and boron could be ruled out because of their comparative scarcity in stellar interiors. The next element was carbon. The detailed investigation of the reaction of carbon with protons yielded a positive result:

At the end of the cycle the C¹² nucleus is recovered and four protons have been combined into an α-particle. The C¹² nucleus thus acts as a catalyst for the reaction and hence the relatively low abundance of carbon nuclei could still allow the reaction to proceed frequently. Under the same condition as the rates calculated for the pp cycle, and with a concentration of N¹⁴ of 10 percent, Bethe calculated an energy production of about 25 ergs/g sec. The reaction is extremely sensitive to temperature (a dependence of T¹⁸), and thus accounted for the sharp increase in luminosity with slight increases in core temperature. Bethe could exclude on various grounds almost all other reactions besides the pp and carbon-nitrogen (CN) cycles by detailed investigations of their properties. He was thus able to explain why stars like the Sun and heavier ones burn for billions of years at the rate that they do. His conclusions were rapidly accepted by the astrophysical community. In 1967 he was awarded the Nobel Prize for this work.

Research Style. Bethe’s scientific output during the 1930s was remarkable. More than half of the papers that he characterized as particularly meaningful to him and that he included in his Selected Works were from the 1930s. He was one of the founding fathers of solid state theory. He was one of the first theorists to apply group theoretical methods to quantum mechanical calculations. His theory of energy loss of charged particles in their passage through matter became the basis of the extraction of quantitative information from cloud chamber tracks and later from nuclear emulsions. His calculations of the cross-sections for the production of electron-positron pairs and for bremstrallung (the emission of radiation when charged particles are deflected in their collisions with other charged particles) became classics and important elements in understanding cosmic ray showers. His refinement of the Bragg-Williams method offered important insights into long-range correlations near the phase transition point in alloys—and thus into phase transitions in general. With Rudolf Peierls he laid the foundations for understanding the structure of the deuteron, its photo disintegration, and neutron-proton and proton-proton scattering. The so-called Bethe Bible summarized what was known and understood in nuclear structure and nuclear reactions, and his paper on the energy generation in stars solved that problem and created the field of nuclear astrophysics.

Bethe early on recognized his limitations, and in particular, that his forte was not in the formulation of what Einstein had called principle theories, that is, empirical generalizations such as the first and second laws of thermodynamics, or the principles that specify the special theory of relativity and its domain of validity, or the principles of quantum mechanics. His strength lay in the formulation of constructive theories that offer constructive models for the description of the phenomena under consideration, which, as Einstein had formulated it, “attempt to build up a picture of the more complex phenomena out of the materials of a relatively simple formal scheme from which they start out.” An example of a constructive theory would be the application of non-relativistic quantum mechanics to the Rutherford model of atoms to explain the Mendeleev table of the chemical elements.

From his first acquaintance with quantum mechanics, Bethe immediately recognized its amazing robustness. It was clear to him that the revolutionary achievements of quantum mechanics stemmed from the confluence of a theoretical understanding: the quantum mechanical representation of the kinematics and dynamics of microscopic particles, and the apperception of an approximately stable ontology—electrons and nuclei. Approximately stable meant that these entities, the electrons and nuclei— the building blocks of the atoms, molecules, simple solids that populated the domain that was being carved out— could be treated as ahistoric objects, whose physical characteristics were independent of their mode of production and whose lifetimes could be considered infinite. At the available energies these entities could be assumed to be essentially point-like objects that were specified by their mass, their spin, and their electromagnetic properties such as their charge and magnetic moment. Furthermore they were indistinguishable: all electrons were identical; all protons were identical; all He⁴, Li⁶, and other nuclei in their ground state were identical and by virtue of their indistinguishability obeyed characteristic statistics: Einstein-Bose if their spins were integral multiples of h/2π or zero; Fermi-Dirac, if half integer multiples.

Thus it was only after the discovery of the neutron by James Chadwick in 1932 that Bethe believed that an adequate particle ontology for the description of nuclear structure was at hand—neutrons and protons—and that quantum mechanical models could be introduced. He thereafter began to intensively study developments in the field.

Turn to Quantum Mechanics. With his Handbuch articles Bethe mastered the principles of quantum mechanics, its models and its explanations of various systems and explorations of various domains in atomic, molecular, and solid state physics; for example, the properties and behavior of hydrogen and helium atoms in external electric and magnetic fields, the Thomas-Fermi and Hartree-Fock methods for the calculation of the properties of atoms, the elastical and inelastic scattering cross-section for charged particles interacting with atoms, the Born-Oppenheimer method in the description of molecules, the Heitler-London model to account for covalent bonding in molecules, the various models of and approximations to the motion of electrons in solids, the quantitative explanation of the thermal properties of solids and of their electrical conductivity, and so forth. What is characteristic of these articles—in fact, of all of Bethe’s scientific papers—is the detailed comparison of theoretical predictions with experimental data. Agreement was the criterion used for gauging the validity of the model, discrepancies the criterion for changing the model to include further relevant physical interactions or, if the disagreement was substantial enough, to abandon the model and the theory.

Bethe’s conception of physics was that it is an experimental science. It is concerned with those statements which can be verified by experiments. Knowledge in physics accretes because it is reproducible. The purpose of theory is to provide a classification, systematization, and unification of the reproducible experimental results. Theories are mathematical, quantitative, informative compactifications that can explain and predict new phenomena. And in view of the enormity of the available reproducible data, in order to grasp and comprehend the regularities discerned in experiments it is necessary that theories be in some sense simple: They must describe and represent the maximum amount of experimental information with a minimum of concepts.

As experiments yielded information about the higher energy interactions of electrons and photons in the 1930s,

Bethe helped develop the tools to describe the observed phenomena. Thus after Dirac devised his equation to describe quantum mechanically relativistic electrons and formulated its hole theoretic interpretation to accommodate the existence of negative energy solutions and of positrons, Bethe—together with Walter Heitler—used hole theory to calculate the cross-section for the production of electron-positron pairs by γ-rays in the (screened) Coulomb field of an atom. For Bethe, the calculation was also performed in order to gauge the limit of validity of quantum electrodynamics (QED). The interaction between the electromagnetic field and charged particles, when these were assumed point-like, resulted in arbitrarily high energy photons being involved and this gave rise to divergences in higher order perturbative calculations.

The divergences reflected explicit incorrect assumptions about the way the short distance interactions were being described by the theory.

What is most remarkable about Bethe’s approach to this and other problems in physics was the way he consistently handled the experimentally inaccessible aspects of the phenomena being investigated. Thus in 1949 when he analyzed very low energy nucleon-nucleon scattering, he was aware that the short-distance nature of the nucleonnucleon interaction potential was not being probed in the scattering. He devised a method to effectively parametrize this unknown aspect of the interaction by introducing two experimentally determined parameters, the “scattering length” at zero energy and the “effective range.” The energy dependence of low energy scattering is then completely and accurately quantum mechanically described in terms of these two parameters. These insights were further generalized after 1955, in work with Geoffrey Goldstone, to handle the effects of the details of the repulsion between nucleons at very small distances in the theory of nuclear matter.

Bethe’s concern with the limits of validity of theories and how to parametrize unknown aspects of the description was similarly manifested in his non-relativistic, quantum electrodynamic calculation of the Lamb shift in hydrogen. At the Shelter Island conference in June 1947, Willis Lamb had reported on his experimental finding that contrary to the prediction of the Dirac equation describing the motion of an electron in a Coulomb field, the 2s and 2p states of a hydrogen atom were not degenerate: the 2s state lay some 1000 MHz higher than the 2p state. At the conference Hendrik Kramers had indicated that the parameter m₀ that is introduced as the mass of the electron in the equations of quantum electrodynamics is not the experimentally observed mass, m, of the electron.

The parameter m₀ must be “renormalized” to the value of the “experimental” mass as the corrections to the inertia of the electron by virtue of its self interaction are taken into account. Bethe believed the shift was of quantum electrodynamic origin. On a train ride after the conference, he investigated the simple possible model in which the electron in the Coulomb field of the proton is described quantum mechanically but non-relativistically, and the radiation field and the interaction between the electron and the radiation field is treated quantum field theoretically. Bethe then introduced a cutoff which limited the latter interaction to a non-relativistic domain of validity: No photons of energy greater than mc² were to enter in the description. At energies greater than mc² a relativistic field theoretic description of electrons and photons was to be used. Bethe followed Kramers’s prescription and somewhat to his surprise the model accounted for most of the observed shift. Subsequent fully relativistic quantum field theoretic calculations, making use of the recently formulated notions of mass and charge renormalization, verified that indeed Bethe’s calculation accounted for most of the Lamb shift and that the quantum electro-dynamic explanation of the Lamb shift was correct.

Wartime Work. In 1941 Bethe was naturalized as a U.S. citizen. During World War II he first worked on problems in armor penetration, then worked on radar and spent a year at the Radiation Laboratory at MIT, and in 1943 he joined the Los Alamos Laboratory and became the head of its theoretical division. He and his division made crucial contributions to the feasibility and design of both the uranium and the plutonium bomb. It was at Los Alamos that there occurred the first rift between Bethe and Teller, who had been Bethe’s closest friend during the 1930s. Teller had aspired to be the head of the theoretical division, but Oppenheimer appointed Bethe instead. It was also at Los Alamos that Bethe first met Richard Feynman. After the war Feynam joined the Cornell physics department and Bethe was instrumental in helping Feynman develop his approach to quantum field theory and thereafter to disseminate it.

The years at Los Alamos changed Bethe’s life. On 14 September 1939 Bethe had married Rose Ewald and their two children were born at Los Alamos. At the professional level his wartime work introduced him to applied and engineering physics, and in particular to the challenges of combining knowledge in very different fields. The design of the plutonium bomb was based on the idea that the best way to bring a critical mass together was to compress a spherical shell of plutonium by the simultaneous detonation of a surrounding spherical shell of high explosives. The detonation of the explosives would ignite a converging ingoing shock wave that would almost instantaneously implode the plutonium into a compact sphere well beyond the critical mass, with a density well beyond that of the normal plutonium metal. In order to calculate the evolution of the explosions—chemical and nuclear—it was necessary to determine the equation of state of plutonium at the very high pressures, density and temperature that were created by the initial shock wave of a few million atmosphere, and thereafter to calculate how the plutonium would move and react. All this involved hydrodynamics, statistical mechanics, shock wave theory, nuclear physics, metallurgy, and immense, extremely complicated calculations on primitive IBM computers. Bethe continued working on such applied problems, combining many disciplines, after the war by becoming a consultant at Los Alamos, Oak Ridge, General Electric, Detroit Edison, and AVCO. The problems he addressed ranged from the design of nuclear reactors and their shielding, and the choice of materials for the heat shields of rockets and space vehicles, to the design of lasers, for which he obtained several patents.

Bethe’s researches in interdisciplinary areas of science gave him much satisfaction. It gave proof of the effectiveness and usefulness of science. And at a deeper level, particularly in his work in astrophysics, the result of the theorizing and its confrontation with the observational data gave proof of the consistency of the web of interconnections. Physics thus says something which, to an impressive accuracy and thus with a high probability, is true of the world.

In the aftermath of the wartime development of fission weapons, Bethe became deeply involved with investigating the feasibility of developing fusion bombs, hoping to prove that no terrestrial mechanism could accomplish the task. He believed their development to be immoral. When in 1951 the Ulam-Teller mechanism for igniting a fusion reaction was advanced and hence the possibility of an H-bomb became a reality, Bethe helped design such a weapon. He believed that the Soviets would likewise be able to build one and that only a balance of terror would prevent the use of these genocidal weapons. The political and military issues surrounding the development of the hydrogen bomb were important factors in the revocation of Oppenheimer’s clearance in 1954. Bethe was one of Oppenheimer’s staunchest supporter at his trial. In 1955, as a consultant for AVCO Corporation, he devised a general theory of ablation that was applied to the construction of warheads that could withstand the searing heat of reentry through the Earth’s atmosphere. His idea helped design an effective intercontinental ballistic missile.

Political Physics. After World War II Bethe became deeply involved in what he called “political physics,” the attempt to educate the public and politicians about the consequences of the existence of nuclear weapons. He became a relentless champion of nuclear arms control. He also became deeply committed to making the peaceful applications of nuclear power economical and safe. Throughout his life he was a staunch advocate of nuclear power, defending it as an answer to the inevitable fossilfuel shortages. Bethe served on numerous advisory committees to the government, including PSAC, the President’s Science Advisory Committee. As a member of PSAC, he helped persuade President Eisenhower to commit the United States to a ban on atmospheric nuclear tests, and such a partial nuclear test ban treaty was ratified in 1963. In 1972 Bethe’s arguments against the use of antiballistic missile systems helped to prevent their deployment. He was an influential opponent of President Ronald Reagan’s Strategic Defense Initiative, the missile defense system popularly known as Star Wars, arguing that it would involve impossible tasks to make lasers of unheard-of power and thereafter to deploy them on satellites in space. By virtue of all these activities Bethe became the science community’s liberal conscience.

Throughout the political activism that marked his life after World War II, Bethe never abandoned his scientific researches. As noted earlier, in 1947 he made a crucial calculation which explained the discrepancy between the predictions of Dirac’s relativistic quantum mechanical equation for the level structure of the hydrogen atom and the observed spectrum determined by Willis Lamb and Robert Retherford. From the mid-1950s until the early 1970s he was an important contributor to the understanding of the properties of nuclear matter. Well into his nineties, from the 1970s until a few years before his death, Bethe remained an extremely productive scientist, making important contributions at the frontiers of physics and astrophysics. He helped elucidate the nature of neutrinos and explain the observed rate of neutrinos emission by the sun. And with Gerald Brown he worked to understand why massive old stars can suddenly become supernovae, exploding with the brilliance of an entire galaxy. To this problem he brought to bear all he had learned at Los Alamos about shock waves and explosions.

It was indicative of Bethe’s constant grappling with moral issues that at age eighty-eight, on the occasion of the fiftieth anniversary of Hiroshima, he went to Los Alamos and called on “all scientists in all countries to cease and desist from work creating, developing, improving and manufacturing further nuclear weapons—and, for that matter, other weapons of potential mass destruction such as chemical and biological weapons.”

Hans Bethe died of congestive heart failure on 6 March 2005 in his retirement community home in Cayuga Heights, New York. He was one of the greatest of the theoretical physicists of the twentieth century. He was an outstanding teacher: Among his PhD students and post-doctoral fellows were many of the best theoretical physicists of the second half of the twentieth century. At Cornell University he endowed the physics department and the Newman Laboratory, the center for high energy

physics he helped create there after World War II, with the qualities and norms to which he was committed: honesty, integrity, and a deep commitment to science and to the institution. Physics at Cornell became a model of a communicative community: one that exists under the constraint of cooperation, trust, and truthfulness, one that is uncoerced in setting its goals and agenda. For Bethe such a community was the guarantor that one of the most exalted of human aspirations—the desire to be a member of a society which is free but not anarchical—could indeed be achieved.

BIBLIOGRAPHY

WORKS BY BETHE

“Quantummechanik der ein und zwei-Electronenprobleme.”

Hanbuch der Physik, Part I. Berlin: Springer Verlag, 1933.

With Arnold Sommerfeld. “Elektrotheorie der Metalle.”

Hanbuch der Physik, Part II. Berlin: Springer Verlag, 1933.

With Edwin E. Salpeter. Quantum Mechanics of One- and Two-Electron Atoms. New York: Plenum, 1977.

With Robert F. Bacher and M. Stanley Livingston. Basic Bethe:

Seminal Articles on Nuclear Physics, 1936–1937. New York: American Institute of Physics, 1986. (A republication of the Bethe Bible.)

The Road from Los Alamos. New York: American Institute of

Physics, 1991.

With Roman Jackiw. Intermediate Quantum Mechanics. 3rd ed.

Reading, MA: Addison Wesley, 1997.

A Life in Science. Told to Sam Schweber. London: Science Archive

Limited, 1997. A transcript of a videotape.

Selected Works of Hans A. Bethe: With Commentary. Singapore:

World Scientific, 1997. Contains a bibliography of 290 of Bethe’s publications (1928–1996) and reproduces 28 of his papers with brief introductory comments by Bethe.

With Gerald E. Brown and Chang-Hwan Lee. Formation and

Evolution of Black Holes in the Galaxy: Selected Papers with Commentaries. Singapore and River Edge, NJ: World Scientific, 2003. Includes many of the papers that Bethe wrote with Gerald E. Brown and others dealing with astrophysical subjects, giving commentaries on how the ideas came up and the papers came to be written.

OTHER SOURCES

Bahcall, John N. and Edwin E. Salpeter. “Stellar Energy”

Generation and Solar Neutrinos.” Physics Today 58 (October 2005): 44–47. (Special issue on Hans Bethe.)

Bernstein, Jeremy. Hans Bethe: Prophet of Energy. New

York: Basic Books, 1980.

Brown, Gerald E. “Hans Bethe and Astrophysical Theory.”

Physics Today 58 (October 2005): 62–65. (Special issue on Hans Bethe.)

———, and Chang-Hwan Lee, eds. Hans Bethe and his Physics.

Singapore: World Scientific, 2003. Gives a survey of Bethe’s accomplishments by outstanding members of the physics community.

Dyson, Freeman. “Hans Bethe and Quantum Electrodynamics.” Physics Today 58 (October 2005): 48–50. (Special issue on Hans Bethe.)

Garwin, Richard L., and Kurt Gottfried. “Hans in War and

Peace.” Physics Today 58 (October 2005): 52–57. (Special issue on Hans Bethe.)

Marshak, Robert E., ed. Perspectives in Modern Physics: Essays in

Honor of Hans A. Bethe on the Occasion of his 60th Birthday. New York: Interscience Publishers, 1966. Describes Bethe’s life and work.

Negele, John W. “Hans Bethe and the Theory of Nuclear

Matter.” Physics Today 58 (October 2005): 5861. (Special issue on Hans Bethe.)

Schweber, Silvan S. “The Happy Thirties.” Physics Today 58

(October 2005): 38–43. (Special issue on Hans Bethe.)

———.In the Shadow of the Bomb: Bethe and Oppenheimer and the Moral Responsibility of the Scientist. Princeton, NJ: Princeton University Press, 2000.

Silvan Schweber

Bethe, Hans Albrecht

(b. 2 July 1906 in Strassburg, Alsace-Lorraine, Germany; d. 6 March 2005 in Ithaca, New York), scientist and Nobel laureate who helped develop the atomic bomb and later championed nuclear weapons reduction.

Bethe was born in Strassburg (which became Strasbourg, France) when Alsace was part of the Wilhelminian empire. Bethe was an only child who grew up in a Christian household but one in which religion did not play an important role. Bethe’s father was Protestant; his mother had been Jewish but became Lutheran before she met Bethe’s father. Bethe’s father, Albrecht T. Julius Bethe, was a world-renowned physiologist specializing in the nervous systems of animals. His mother, Anna (Kuhn) Bethe, was a musician and writer who soon before World War I contracted influenza, which led to a hearing impairment and extended periods of depression. The marriage suffered under the strain, and Bethe’s parents divorced in 1927, Bethe becoming responsible for his mother’s welfare.

Bethe taught himself calculus at age fourteen. His mathematics teacher at Goethe Gymnasium, a secondary school in Frankfurt, Germany, recognized Bethe’s talent and encouraged him to continue studies in mathematics and the physical sciences. After finishing secondary school in the spring of 1924 and two years of study at the University of Frankfurt, Bethe was advised by one of his teachers to go to Munich to study with Arnold Sommerfeld, who at the time was the outstanding physics teacher in Germany. In the summer of 1926 Bethe joined Sommerfeld’s seminar.

Bethe obtained his PhD summa cum laude from the University of Munich in 1928 with a thesis on electron diffraction in crystals. He then spent a semester in Frankfurt as Erwin Madelung’s assistant and another semester in Stuttgart, Germany, as assistant to Peter Paul Ewald. Bethe then returned to Munich and undertook his postgraduate education.

Having been awarded a Rockefeller Foundation fellowship, Bethe spent a semester in Cambridge, England, under the aegis of Ralph Fowler, and a semester in Rome working with Enrico Fermi. From Fermi, Bethe learned to reason qualitatively, to obtain insights from back-of-envelopes calculations, and to think of physics as challenging problems to be solved. Bethe’s craftsmanship was an amalgam of the thoroughness and rigor of Sommerfeld and the clarity and simplicity of Fermi.

Bethe’s craftsmanship was displayed in his writing. His two book-length reviews in the 1933 Handbuch der Physik—the first on solid state physics and the second on the quantum theory of one- and two-electron systems—exhibited Bethe’s remarkable powers of synthesis and became classics as soon as they were published. They were the first of many reviews Bethe wrote. Three reviews on nuclear physics that appeared in Reviews of Modern Physics in 1936–1937 became known as the Bethe bible, which was republished as Basic Bethe: Seminal Articles on Nuclear Physics, 1936–1937 (1986). All of Bethe’s reviews were syntheses of the fields under review, giving them coherence and unity and charting the paths to be taken in addressing new problems. The reviews usually contained much that was new, materials that Bethe had worked out in the preparation of his essays.

In the fall of 1932 Bethe obtained an appointment at Tübingen University, Germany, as an acting assistant professor of theoretical physics. In April 1933, after Adolf Hitler’s accession to power in Germany, Bethe was dismissed from his position because he had two Jewish grandparents. Bethe returned to work with Sommerfeld, who awarded him a fellowship for the summer of 1933. Bethe then went to Manchester, England, to work with William Lawrence Bragg. Bethe spent the academic year 1934–1935 in a fellowship in Bristol, England, with Neville Mott.

Bethe arrived at Cornell University, Ithaca, New York, in February 1935 and stayed there for the rest of his life, except for the war years and his stays at other universities during his sabbaticals. At Cornell, Bethe endowed the physics department and the Newman Laboratory, the center for high-energy physics he helped create after World War II, with the qualities and norms to which he was deeply committed: honesty, integrity, and a commitment to science and the institution. Physics at Cornell became a model of a communicative community: one that exists under the constraint of cooperation, trust, and truthfulness; that is uncoerced in setting its goals and agenda; and one that recognizes that human emancipatory interests are involved. For Bethe such a community was the guarantor that one of the most exalted of human aspirations—to be a member of a society that is free but not anarchical—could be satisfied.

Bethe arrived in the United States at a time when the American physics community was undergoing enormous growth. The influence of the émigré scientists who had come from Nazi Germany was particularly noticeable at the many conferences organized to assimilate the insights from quantum mechanics in many fields, especially molecular physics and the emerging field of nuclear physics. The annual Washington Conference on Theoretical Physics initiated in 1935 was a paradigm of such meetings. The purpose of these conferences was to assemble a small number of theoretical physicists working on related problems to discuss their research in an informal way. The conferences proved extremely influential, partly because they were restricted to theory and partly because their size was strictly regulated so they could remain working conferences. Bethe attended the 1935 and 1937 Washington conferences but when invited to the 1938 conference first declined because he was not interested in the problem of stellar energy generation, the topic for that year. It was only after repeated urging by Edward Teller that Bethe agreed to attend. After attending the conference and being made aware of the problem, Bethe gave the definitive answer to the problem of energy generation in stars. By stipulating the nuclear reactions responsible and calculating the rate at which energy is produced, Bethe explained why stars such as the sun and heavier ones burn for billions of years at the rate they do. In 1967 Bethe was awarded the Nobel Prize for Physics for this work. Among Bethe’s other awards were the A. Cressy Morrison Prize of the New York Academy of Sciences, 1938–1940; the Presidential Medal of Merit, 1946; the Henry Draper Medal of the U.S. National Academy of Sciences, 1947; the Max Planck Medal, 1955; the Enrico Fermi Award of the U.S. Atomic Energy Commission, 1961; and the Los Alamos National Laboratory Medal, 2001.

Bethe’s scientific output in the 1930s was remarkable. More than half of the papers that he characterized as particularly meaningful to him and that he included in his Selected Works (1996) were from the 1930s. The volume contains a bibliography of 290 of Bethe’s publications (1928–1996) and reproduces twenty-eight of his papers with brief introductory comments by Bethe. Bethe was one of the founding fathers of solid state theory. He was one of the first theorists to apply group theoretical methods to quantum mechanical calculations. His theory of energy loss of charged particles in their passage through matter became the basis of the extraction of quantitative data from cloud chamber tracks and later nuclear emulsions. His calculations of cross sections for the production of electron-positron pairs and for bremsstrahlung (the emission of radiation when charged particles are deflected in their collisions with other charged particles) became classics and elements in the understanding of cosmic ray showers. Bethe’s refinement of the Bragg-Williams method offered important insights into long-range correlations near the phase transition point in alloys and thus into phase transitions in general. Bethe helped lay the foundation for understanding the structure of deuteron, neutron-proton, and proton-proton scattering and photo-disintegration of the deuteron. The Bethe bible summarized what was known and understood about nuclear structure and nuclear reactions. His paper on energy generation in stars solved that problem and created the field of nuclear astrophysics.

On 14 September 1939 Bethe married Rose Ewald; their two children were born in Los Alamos, New Mexico. Bethe was naturalized as a U.S. citizen in 1941. During World War II Bethe first worked on problems in radar, spent a year at the radiation laboratory at the Massachusetts Institute of Technology, and in 1943 joined the Los Alamos Laboratory as the head of its theoretical division. He and his division made crucial contributions to the feasibility and design of both the uranium and the plutonium bombs.

In the aftermath of the development of fission weapons, Bethe became involved with investigating the feasibility of developing fusion bombs, hoping to prove that no terrestrial mechanism could accomplish the task. He believed the development of such a bomb immoral. When in 1951 the Ulam-Teller mechanism for igniting a fusion reaction was advanced and the possibility of an H-bomb became a reality, Bethe helped design such a weapon. He believed that the Soviets would likewise be able to build one and that only a balance of terror would prevent the use of these genocidal weapons. In 1955, as a consultant for AVCO Corporation, Bethe devised a general theory of ablation that was applied to the construction of warheads that could withstand the searing heat of reentry through the Earth’s atmosphere. His idea facilitated the design of an effective intercontinental ballistic missile.

After World War II Bethe became involved in what he called political physics, the attempt to educate the public and politicians about the consequences of the existence of nuclear weapons. He became a relentless champion of nuclear arms control. He also became committed to making the peaceful applications of nuclear power economical and safe. Throughout his life Bethe was an advocate of nuclear power, defending it as an answer to inevitable fossil-fuel shortages. Bethe served on numerous advisory committees to the government, including the President’s Science Advisory Committee. As a member of the committee, Bethe helped persuade President Dwight D. Eisenhower to commit the United States to a ban on atmospheric nuclear tests, and such a partial nuclear test ban treaty was ratified in 1963. In 1972 Bethe’s arguments against the use of antiballistic missile systems helped prevent their deployment. Bethe was an influential opponent of President Ronald Reagan’s Strategic Defense Initiative, the missile defense system known as Star Wars, arguing that it involved impossible tasks to make lasers of incredible power and thereafter to deploy them on satellites in space. By virtue of these activities Bethe became the liberal conscience of the science community.

Throughout the political activism that marked his life after World War II, Bethe never abandoned his scientific research. In 1947 he made a crucial calculation that explained the discrepancy between the predictions of Paul Dirac’s relativistic quantum mechanical equation for the level structure of the hydrogen atom and the observed spectrum determined by Willis Lamb and Robert Rether-ford. The discrepancy for the 2s and 2p states of hydrogen became known as the Lamb shift. From the mid-1950s until the mid-1960s Bethe was an important contributor to the understanding of the properties of nuclear matter. From the 1970s until a few years before his death—that is, until well into his nineties—Bethe was a productive scientist making important contributions at the frontiers of physics and astrophysics. He helped elucidate the nature of neutrinos and explain the observed rate of neutrino emission by the sun. With Gerald Brown he worked to understand why massive old stars can suddenly become supernovae, that is, explode with the brilliance of an entire galaxy. To this problem Bethe brought to bear what he had learned at Los Alamos about shock waves and explosions. It was indicative of Bethe’s constant grappling with moral issues that when he was eighty-eight he urged fellow scientists to collectively take an oath not to work on designing new nuclear weapons. Bethe died of congestive heart failure on 6 March 2005 in Ithaca.

Bethe’s life and work are described in R. F. Bacher and V. F. Weisskopf, “The Career of Hans Bethe,” Perspectives in Modern Physics: Essays in Honor of Hans A. Bethe on the Occasion of his 60th Birthday (1966), edited by R. E. Marshak; and Jeremy Bernstein, Prophet of Energy: Hans Bethe (1980). Bethe was the focus of a special issue of Physics Today (Oct. 2005). Obituaries are in the New York Times (7 Mar. 2005) and Washington Post (8 Mar. 2005).

Silvan S. Schweber

Hans Albrecht Bethe

The Alsatian-born American theoretical physicist Hans Albrecht Bethe (born 1906), prolific and creative contributor to several vital fields of nuclear physics, discovered the mechanism of energy production by stars (including the sun).

Hans Bethe was born in Strasbourg, Alsace-Lorraine— (now part of France)—on July 2, 1906, to Albrecht Theodore Bethe, a physiologist, and Anna Kuhn Bethe. At the age of 22 he earned his doctorate at the University of Munich and was given an assistantship at the Institute of Theoretical Physics of the University of Frankfurt. After a year he transferred to the Technische Hochschule in Stuttgart and then for three years was privatdozent —unsalaried lecturer—in physics at the University of Tübingen. He worked at Cambridge University and in Rome in 1930-1931 and then returned to Tübingen as an assistant professor.

After Hitler came to power, Bethe fled first to England and then to the United States, where Cornell University welcomed him. At age 31 he was elevated to the post of Wendell Anderson professor of physics. In 1939 he married Rose Ewald, the daughter of Paul Peter Ewald, a professor of physics in Munich. They had a son and a daughter.

In 1939 Bethe published a paper, "Energy Production in Stars," in which he advanced a theory of stellar fuel. He discovered that, by a series of transformations, carbon, acting as a catalyst, changes four atoms of hydrogen into an atom of helium of atomic weight four. During these transformations the carbon is rejuvenated and there is a very small loss of mass which is converted into the enormous amount of energy which stokes the stars. For this achievement as well as for his many important contributions to the theory of nuclear reactions, Bethe was awarded the Nobel Prize in physics in 1967.

Bethe published the first theory of electron-positron pair creation and an improved theory of how charged particles interact. The latter is a key to the determination of the amount of radiation shielding required by nuclear reactors and by astronauts in space. It is also critical to the understanding of cosmic-ray phenomena, the design of experiments in high-energy nuclear physics, the theory of the structure of metals, the shock-wave theory, the scattering of mesons, and the energy levels of the hydrogen atom.

In 1941 Bethe became a naturalized American citizen, and between 1943 and 1946 he worked as head of the Division of Theoretical Physics at the Los Alamos Scientific Laboratories, where the first nuclear bomb was being manufactured. His assignment was to determine the amount of uranium or plutonium that would be necessary to produce a nuclear explosion and to calculate the total energy that might be released in such an explosion. Bethe was also responsible for a group which had to determine the mechanism of assembling an atom bomb implosion; that is by bringing together, in a split second, a spherical ball of either uranium or plutonium by means of a high explosive. After his work at Los Alamos, Bethe returned to his teaching position at Cornell University. He retired from Cornell in 1975 but maintains an office there and continues to serve as a lecturer and consultant.

In addition to his academic work, Bethe was also active in the disarmament movement and sought to educate the public about the destructive power of nuclear weapons. He remains committed to this cause. He sent a letter to President Clinton in 1997, calling for a complete ban on nuclear testing.

On July 2, 1996—Bethe's ninetieth birthday—it was announced that the American Physical Society would begin awarding the Bethe Prize for contributions to the field of physics.

Further Reading

R.E. Marshak, ed., Perspectives in Modern Physics: Essays in Honor of Hans A. Bethe on the Occasion of His 60th Birthday, July 1966 (1966), contains an account of Bethe's career and a bibliography of his writings. He is discussed at length in Henry A. Boorse and Lloyd Motz, eds., The World of the Atom (1966). See also Stéphane Groueff, Manhattan Project: The Untold Story of the Making of the Atomic Bomb (1967) and Richard Feynman, Surely You're Joking, Mr. Feynman! (1985). □

BETHE, HANS ALBRECHT

BETHE, HANS ALBRECHT (1906–2005), nuclear physicist and Nobel Prize laureate in physics (1967). Bethe was born in Strasbourg, Alsace-Lorraine. He studied physics at Frankfurt-am-Main University and received his Ph.D. in theoretical physics at Munich University in 1928. He held successive appointments at the universities of Munich, Stuttgart, and Tubingen. He emigrated to England in 1933 because his mother was Jewish, but he never acknowledged any personal Jewish affiliation. After a temporary appointment at Manchester University and a fellowship at Bristol University, he became assistant professor at Cornell, Ithaca, in the U.S., in 1935. He was full professor in 1937–75 and then professor emeritus. In 1943–46 he worked in Los Alamos on the Manhattan Project as director of the theoretical physics division. His work in theoretical physics led to the Nobel Prize for his studies on atomic structure in general and more specifically for elucidating the sequence of energy-creating nuclear reactions in stars which culminate in helium production. His many awards include the Presidential Medal in 1948 and the Max Planck Medal in 1955. He was a member of the President's Science Advisory Committee in 1956–64 and in 1958 was scientific adviser to the U.S. at the Geneva test ban talks. In the 1980s and 1990s he campaigned for international control and peaceful use of nuclear energy. The books he wrote between 1955 and 1964 remain important sources of information on nuclear particle interactions and quantum theory.

[Michael Denman (2^nd ed.)]

Hans Albrecht Bethe

1906-

German-born American physicist who was awarded the 1967 Nobel Prize for Physics for contributions to nuclear reactions, especially for his 1939 theory describing stellar energy production. One of his many contributions to quantum electrodynamics was the theoretical explanation of the "Lamb shift" (1947). Bethe also co-authored (with Ralph Alpher and George Gamow) the alpha-beta-gamma "big bang" theory of the universe's origin. During World War II, Bethe's research was crucial for developing the atomic bomb, though he later actively opposed its use.