sign in sign up
<<
Home , Exchange force, Hideki Yukawa

Hideki Yukawa and the theory

Some 50 years ago, in his first research contribution, a young Japanese theoretical explained the strong, short-range force between and as due to an exchange of "heavy quanta."

Laurie M. Brown

A little over 50 years ago, Hideki cist who had never even traveled Yukawa's papers at University. Yukawa, a young Japanese theoretical abroad, but instead by one of the many (These documents have been organized physicist at the University of Osaka, Western , some of them of and cataloged in the Yukawa Hall proposed a fundamental theory of nu- great reputation, who were working on Archival Library, and I am grateful to clear forces involving the exchange of the theory of nuclear forces. Further- Rokuo Kawabe and Michiji Konuma massive charged particles between neu- more, Yukawa's paper was totally ne- for translations and comments.) trons and protons. He called the ex- glected for more than two years, al- changed particles "heavy quanta" to though it was written in lucid English The problem of nuclear forces distinguish them from the light quanta and published1 in a respected journal of The meson theory was the result of a of the electromagnetic field, but now rather wide circulation. The meson powerful creative act. It incorporated they are known as , the lightest theory has turned out to be an impor- a number of ideas that are common- members of a large family of particles tant paradigm for the theory of elemen- called . These days, the meson tary particles, as seminal as Ernest O. theory seems to be a straightforward Lawrence's cyclotron has been for its Hideki Yukawa, at right, with (from left) his father-in-law Genyo Yukawa, his mother-in- application of to experimental practice. In this article I law Michi and his wife Sumi at their home the nuclear forces, but it could not have will trace the intellectual trail Yukawa in Osaka in 1932. (Photos illustrating this appeared so 50 years ago. Otherwise it followed to arrive at his theory, using article courtesy Michiji Konuma; from would not have been invented by an unpublished documents that have re- reference 9, reproduced with permission of obscure, unpublished Japanese physi- cently been discovered among Sumi Yukawa.)

0031-9228 / B6 / 1200 55- 0B / $01.00 1986 American Institute ol PHYSICS TODAY / DECEMBER 1986 55 Manuscript page containing Yukawa's wave equation, based on the , for describing the intranuclear field having the nucleon-exchange current as a source. Equation 1 in the manuscript corresponds to equation 3 in the this article. (The documents illustrating this article come from the Yukawa Hall Archival Library, , courtesy of Ziro Maki.)

would rapidly escape the nucleus. An- other difficulty was that certain nuclei, those with an odd number of intranu- clear , should have had mag- netic fields about a thousand times larger than that inferred from the hyperfine structure of atomic spectra. One such nucleus—nitrogen-14, with 14 protons and 7 electrons—should have had half-integral and obeyed Fermi-Dirac statistics, but was known to have integral spin and to obey Bose- Einstein statistics. As early as 1920, Ernest Rutherford had suggested that there might exist a neutral nuclear constituent that he called the "," consisting of a and an electron much more tightly bound than in the hydrogen atom. , working in the Cavendish Laboratory in Cambridge in 1932, assumed, when he discovered the neutron, that he had found Ruther- ford's composite neutron, which had been sought at the Cavendish for a place today, but which were novel and remember the time when man's decade. Chadwick did consider the surprising 50 years ago. These are chief purpose was to hunt some possibility that his neutron was a new some of the original features proposed animals, when he did not have , but said4 that the by Yukawa: chairs to sit in, did not have beds, idea had "little to recommend it." • The nuclear binding force is trans- did not have covers, did not have a Within a few weeks after Chadwick's mitted by the exchange of massive jacket, did not have anything, not announcement, Heisenberg wrote the charged particles (the heavy quanta). to mention that he did not have a first part of a three-part paper present- • The range of the force is inversely radio to speak into. It is hard to ing5 a theory of nuclear structure in proportional to the mass of the quan- remember that. which protons and neutrons were the tum. The physicist's view of matter before principal constituents (Bausteine) of • There are two nuclear forces, one the discovery of the neutron was that the nucleus, instead of the protons and strong and one weak, and hence two everything, including the nucleus, con- electrons (and sometimes alpha parti- coupling constants. sisted of protons and electrons and was cles) of the earlier models. (See the • The is also mediat- held together by electric and magnetic article by Arthur Miller, PHYSICS TO- ed by the exchange of the heavy quanta forces.3 In that picture, the nucleus of DAY, November 1985, page 60.) Heisen- (charged intermediate ). mass number A contained A positive berg did not challenge the idea that the • The heavy quanta are unstable, protons and A — Z negative electrons; neutron was composed of a proton and decaying via the weak interaction. the neutral atom had, of course, Z an electron, but by suppressing the It was a great achievement to pro- extranuclear electrons. Thus, matter electron degrees of freedom in his pose such a bold solution for the nu- was said to be made of pure electricity. nuclear Hamiltonian he was able to clear-force problem, for it was difficult Within this framework, quantum me- construct the first genuinely quantum- at that time even to grasp and to chanics was scoring impressive suc- mechanical nuclear theory. (Dmitri formulate the dimensions of the prob- cesses in explaining phenomena that Iwanenko in Leningrad, at about the lem. At a symposium held in Minne- involved the extranuclear electrons, in same time, suggested6 treating the apolis in 1977 on the subject of nuclear fields such as , chemistry neutron as an elementary particle in physics in the 1930s, and magnetism, but the behavior of the 2 the nucleus, but he does not seem to remarked: intranuclear electrons was quite an- have developed a detailed theory of this The disorientation in physics other matter. The mere presence of type.) So far as nuclear systematics which existed . . . [around 1932] is electrons in the nucleus seemed to violate important principles of physics. was concerned, Heisenberg treated the hard to imagine. We can remem- proton and the neutron as the charged ber it hardly more than we can One problem, apparently insurmount- able within the conventional frame- and neutral states of a single entity, work of quantum mechanics, was that our present-day nucleon, and he intro- Laurie Brown is professor of physics and an electron, having low mass and duced operators that changed the astronomy at Northwestern University, Evan- confined within a space as small as a charge of the nucleon, turning neu- ston, Illinois. This article is based upon a nucleus, would according to Werner trons into protons or vice versa. The paper presented at an international sympo- Heisenberg's force that he introduced between the sium on the golden jubilee of the meson have a kinetic energy so large that it proton and neutron had charge-ex- theory, Kyoto, , 15-17 August 1986. change character, analogous to that in

56 PHYSICS TODAY / DECEMBER 1986 + the hydrogen molecular ion H2 ; the senberg regarded the proton and the the Great Depression and a difficult force between neutrons was analogous neutron as sisters, so similar that the time in which to find a job. He to the exchange force in the hydrogen exchange currents in terms of which he therefore continued to live with his molecule, but between protons, which expressed his charge-exchange forces family in Kyoto, where his father, Heisenberg regarded as elementary were formulated in terms of raising Takuji Ogawa, was a professor of geog- particles, there was only ordinary Cou- and lowering operators adapted from raphy at the university. For three lomb repulsion. Thus in assigning the Pauli spin matrices. Those are years, together with Sinitiro Tomon- forces Heisenberg clearly differentiat- precisely the modern isospin operators, aga—his classmate, the son of a Kyoto ed the "elementary" proton from the although Heisenberg employed them philosophy professor, and a future fel- "composite" neutron. Nevertheless, without the accompanying idea of the low Nobel laureate—Yukawa worked despite its unsymmetric treatment of charge independence of nuclear forces. as an unpaid assistant in the theoreti- what we now call the nucleon doublet, Nevertheless, he insisted that electrons cal-physics research room of Professor Heisenberg's theory, especially as of both the bound and loose varieties Kajuro Tamaki. Intensely ambitious, modified during the following year by were present in the nucleus. This view he was afraid that he had arrived upon Wigner and , is cor- so characterized Heisenberg's nuclear the physics scene too late to make a model that in 1933 Wigner, listing8 fundamental contribution to quantum rectly regarded as the foundation of the 9 modern phenomenology of nuclear "three different assumptions possible theory. Much later, Yukawa wrote in structure. concerning the elementary particles" his autobiography, "As I was desperate- While Heisenberg had seized the in the nucleus, began his list: "(a) The ly trying to reach the front line, the opportunity presented by the discovery only elementary particles are the pro- new quantum physics kept moving of the neutron to formulate a pheno- ton and the electron. This point of view forward at a great pace." menological theory of nuclear forces, has been emphasized by Heisenberg After his graduation Yukawa reflect- and treated by him in a series of ed that there were two outstanding he was not the sort of physicist who papers." would sidestep the issues raised by the problems facing physics. One was the presence of composite neutrons (and structure of the nucleus. The other hence, implicitly, electrons) in the nu- Yukawa's first research consisted of the questions of principle cleus. After all, to make a spin-V2 Yukawa graduated from Kyoto Impe- raised by Paul A. M. Dirac's relativistic neutron out of the proton and electron rial University in 1929, the first year of electron theory, especially the puzzle required the suppression of a half- quantum of spin. Furthermore, al- though Heisenberg was as sensitive as anyone could be to the further difficul- ties that arose from a model nucleus containing additional "loose" elec- trons, that is, those not bound in neutrons, his conception of beta-decay radioactivity and of the large radiative effects observed in cosmic-ray and cer- tain laboratory gamma-ray experi- 7 7..,-, ( '••• 1 - ments demanded loose electrons in the J t n y nucleus. In this connection he said,5 in > 'A*? % ft"\ *• -v *' * * ** - part III of his three-part paper, that "the a particles in the nucleus must be t--tf- i ati H, , K , > built of protons and electrons (not protons and neutrons)" and that those electrons must add their contribution to radiative scattering to that of the a " K)\ ih ! I h ^^ i A V i" "fit Liu* • . . "•[$• "free nuclear electrons." Thus, about ^ I \ 'l I L "• iJ '•' ' t^\ 't ''\ \ L /iy i ^ , half of the contents of Heisenberg's (,' 'it*, ^ M>H (^ »"f -) K 1" V three-part paper of 1932 was concerned t" H -* t> I't^t.t^i* i with problems raised by the nuclear electrons and with the theory of the ;k( neutron itself as a proton-electron - / -^-~ ~ J , c*f ^" i-• ~ y.r ^ compound. To summarize: In working out the systematics of nuclear structure, Hei-

Yukawa's Green's function solution of the wave equation (equation 3 in the text) for the hypothetical Bose electron of mass m within the nucleus. (From document F01 010 U01.)

PHYSICS TODAY / DECEMBER 1986 57 that the theory required negative-ener- quantum of action became recognized should search for an easier prob- gy states, for which there appeared to as setting the scale of quantum effects lem. be no meaning in the theory of relativi- in matter as well as radiation. The The demons, in fact, continued to haunt ty. With these problems in mind, mystery was only deepened by Louis de him throughout the rest of his career. Yukawa began to look into hyperfine Broglie's conjecture that electrons Even after the provisional solution of structure, a small but observable split- have a wavelike in addition to in the 1940s, he con- ting of atomic spectral lines. The effect their particulate properties, which was tinued to regard the forging of a finite was believed to be due to the action of soon experimentally confirmed. By quantum field theory as the prime the nuclear magnetic field on the 1929, after the new quantum mechan- objective of , and he extranuclear atomic electrons, the ics of Heisenberg and Erwin Schro- continued to investigate fundamental main influence being on those electrons dinger had resulted in a broad under- theories (for example, nonlocal field that penetrate nearest to the nucleus standing of atomic phenomena, theory) that were alternatives to the and thus feel the strongest magnetic Yukawa felt that the time had come to accepted renormalized theories. field. At the same time, because of the make a fresh attack on resolving the strong attractive electric field near the wave-particle paradox. The meson theory nucleus, those electrons would attain Dirac had already in 1927 introduced For the time being, however, velocities near that of light. Thus the methods that took into account the Yukawa resolved to think of other problems associated with electrons in quantum nature of the electromagnetic matters. He saw Chadwick's an- or near the nucleus and the problems of field when calculating, for example, the nouncement of the neutron and soon Dirac's electron theory would be pres- spontaneous decay rates of atomic ent at the same time, and Yukawa afterward read part I of Heisenberg's states (determining the intensity of the paper on the stucture of atomic nuclei. hoped they would shed light upon each lines in atomic spectra), but Heisenberg other. This rekindled his interest in the nu- and Pauli's 1929 paper was the first clear-force problem, although he was As it happened, in fully relativistic quantum theory of the not prepared to accept a purely pheno- Rome was thinking along the same electromagnetic field. Dirac had quan- menological theory such as Heisen- lines. He was an experienced and tized only the transverse degrees of berg's. An unpublished document of established theorist and, moreover, did freedom of the field, those correspond- early 1933 by Yukawa is entitled12 "On not have to deal with Tamaki. When ing to free radiation, and he had left the the problem of nuclear electrons. I." It Yukawa handed his manuscript to static Coulomb potential in its classical is in English, and begins, "The prob- Tamaki, the professor stored it in a safe form. Heisenberg and Pauli found a lems of the , especially place and said that he would study it way to quantize both transverse and the problems of nuclear electrons, are when he had the time. Meanwhile, longitudinal components of the electro- 0 magnetic vector potential, as required so intimately related with the problems Fermi published' his treatment of the of the relativistic formulation of quan- problem, discouraging Yukawa from in a fundamental relativistic theory. But they were discouraged to find that tum mechanics that when they are pursuing it further or from considering solved, if they ever be solved at all, they what it might mean for nuclear struc- the theory predicted an infinite elec- ture, as he had originally planned. tron mass, as well as other infinities will be solved together." Nevertheless, Instead, his attention was drawn to the that contradicted observation. Finding recognizing the importance of Heisen- appearance" of the first part of a and curing the source of those infinities berg's contribution, he prepared a sum- monumental paper by Heisenberg and became a major task of theoretical mary in Japanese of the two parts of , which set forth a physics in the 1930s, a task that was at Heisenberg's paper that had appeared; relativistic quantum theory of the elec- least provisionally accomplished only it became his first publication, al- tromagnetic field in interaction with in the 1940s by the so-called renormal- though his first published research was Dirac electrons. That paper Yukawa ization program, in which Tomonaga his later meson paper. later repeatedly called a partial "set- played a leading role. In introducing his summary, tling of accounts" and "in certain Yukawa discussed the strengths and respects the final balance sheet of the Partly out of disappointment over weaknesses of Heisenberg's model, quantum theory originated by Planck." losing his unwitting race with Fermi on placing particular stress on issues of the hyperfine-structure problem, principle. He wrote:13 The account that needed settling was Yukawa applied his energy to quantum In this paper Heisenberg ignored wave-particle duality. The quantum of field theory, hoping that he could the difficult problems of electrons action (Planck's constant) was intro- complete the "settling of accounts" within the nucleus, and under the duced into physics by in that Heisenberg and Pauli had begun. 9 assumption that all nuclei consist 1900 in his treatment of the spectrum In Tabibito he vividly describes the of protons and neutrons only, con- of blackbody radiation. In 1905 Ein- frustration of his attack on the infini- sidered what conclusions can be stein showed that Planck's theory im- ties of : plied that electromagnetic radiation, drawn from the present quantum Each day I would destroy the ideas mechanics. This essentially whose behavior had been seen as funda- that I had created that day. By the mentally wavelike, must at times be- time I crossed the Kamo River on means that he transferred the have in ways that are particlelike. But my way home in the evening, I problem of the electrons in the waves and particles are conceptually was in a state of desperation. nucleus to the problem of the incompatible, so Einstein's quantum Even the mountains of Kyoto, makeup of the neutron itself, but it theory gave rise to what was called the which usually consoled me, were is also true that the limit to which wave-particle paradox. After Niels melancholy in the evening sun. . .. the present quantum mechanics Bohr's successful treatment of the hy- Finally, I gave up that demon can be applied to the atomic nu- drogen spectrum in 1913, Planck's hunting and began to think that I cleus is widened by this approach. Though Heisenberg does not pres-

58 PHYSICS TODAY / DECEMBER 1986 The Ogawa family. In front are Takuji, a professor of geography at Kyoto University, and his wife Koyuki; standing are (from left) Tamaki, Shigeki, Hideki and Masuki. Hideki adopted his wife's family name when he married Sumi Yukawa in 1932.

ent a definite view on whether current density jM is regarded as the matrices that change a neutron into a neutrons should be seen as sepa- "source" of Afl. In a region free of proton or vice versa. Whilejfl (like A,,) rate entities or as a combination of charges and currents j/t vanishes, and transforms as a relativistic four-vector, a proton and an electron, this equation 1 describes the free electro- J (like ip) must transform as a relativis- problem, like the beta-decay prob- magnetic field. The equation holds also tic spinor. That was an essentially new lem ... cannot be resolved with in quantum electrodynamics, with AM and problematic aspect, as Yukawa today's theory. And unless these as the quantized electromagnetic field realized. In QED the same j^ that is problems are resolved, one cannot and jfl the appropriate quantized responsible for the exchange of say whether the view that elec- charge-current density, for example, between charges, accounting for forces, trons have no independent exis- that of the Dirac electron-positron is also the source of free photons. But if tence in the nucleus is correct. field. J were to account for as During 1933, Yukawa argued in sev- What Yukawa did was to start from well as nuclear forces, then beta decay eral unpublished documents that Hei- the Dirac relativistic electron equation, would necessarily be nonconserving of senberg's program could be carried one regarded as the free-field equation of energy and angular momentum, as in step further toward a fundamental the classical electron field, any theory where the electron emerges unaccompanied from the nucleus. Of theory of nuclear forces and beta decay. Dip = 0 (2) However, that step made it necessary course, that was the case in Heisen- to treat the neutron as a truly elemen- where D is the 4x4 matrix Dirac berg's theory as well; Yukawa was tary particle because, he said,14 any differential operator (including the trying to construct a theory that would treatment of its structure would lie electromagnetic potentials) and ip is the justify Heisenberg's phenomenology, "outside the applicability of present four-component Dirac relativistic and not necessarily one with different quantum mechanics." He attempted to spinor wavefunction of the electron. practical consequences. formulate the Heisenberg charge-ex- He then modified this equation by Yukawa used the known properties change force by analogy to quantum introducing on its right-hand side a of the Green's function for the Dirac electrodynamics, taking the exchange source term J depending on the neu- equation (with the electromagnetic of an electron between a neutron and a tron and proton (regarded as the neu- four-potential set to zero) and wrote a proton in the theory of the nuclear tral and charged states, respectively, of solution to equation 3 in the following force as analogous to exchange the nucleon): form: A Dirac operator acts upon an integral that for vanishing electron between charged particles in QED. Dip = J (3) In classical electrodynamics, the mass is entirely analogous to the re- electric and magnetic fields are derived While the source term J has a form tarded potential due to the source J. from a relativistic vector potential A somewhat similar to the electromag- Explicitly, for zero electron mass, the M integral is that obeys the wave equation netic current_/;/, it is significantly more complicated: It is constructed out of an , J(r,t- |r' -r|/c) eight-component nucleon spinor and its Here, D is the d'Alembertian operator adjoint, and it contains Dirac matrices jr' — r V2 — d2/c2dt2. The four-vector charge- that act upon the spinor as well as Here r' is the source point, r is the field

PHYSICS TODAY / DECEMBER 1986 59 point, t is the time and c is the velocity Yukawa was trying to derive Heisen- to me one night in October.. . . My of light. However, for an electron of berg's nuclear theory from deeper prin- new insight was that [the range of mass m there is an additional exponen- ciples. However, that theory contained the force] and the mass of the new tial factor, with oscillating character, the questionable feature that the emis- particle that I was seeking are in the integral. In his manuscript, sion of an electron by a neutron violat- inversely related to each other. Yukawa says:14 ed the conservation of angular momen- Why had I not noticed that before? Substituting this solution into [the tum, whether the neutron was treated The next morning I tackled the Hamiltonian] H. we find the inter- variously as fundamental or composite. problem of the mass of the new action energy that corresponds to Pauli had proposed as early as 1930 particle and found it to be about Heisenberg's "PlatzwechseV inter- that the electron emitted in beta decay two hundred times that of the action. Its exact form and the might be accompanied by a light, neu- electron. retardation effect can be seen, and tral particle of spin V2 (the neutrino), Within weeks, Yukawa completed a factor thus permitting the conservation of the formulation of his theory and both linear and angular momentum, as reported on it at a branch meeting of c r r well as energy. At the Solvay Confer- exp(i/v" : ' — |/^) 16 PMSJ in Osaka. On 17 November ence of 1933, held in Brussels, he gave 1934, he spoke on it at the annual [ ps is a Dirac matrix] appears as a kind of phase factor, so that the his first public notice of the neutrino PMSJ meeting in . Meanwhile, that he allowed to be published. Fermi he prepared1 a paper in English on his term corresponding to Heisen- also attended the conference, and upon berg's [Platzwechselintegral] J(r) 1 theory—his first original research pa- has a form like the Coulomb field returning to Rome made ' a new, per—and submitted it to the Proceed- and does not decrease sufficiently strikingly successful quantum field ings of the Physico-Mathematical So- theory of beta decay that incorporated ciety of Japan. with distance. the neutrino. He is referring here to the most strik- ing difference between the nuclear At first Yukawa thought that Fermi Mesons and 'mesotrons' force and or gravita- had once again beaten him to the Yukawa's article, which appeared in tion: its short range of influence. In the punch (as he had in the case of the February 1935, aimed at nothing less expression Yukawa derived from the hyperfine structure of spectral lines), than a quantum field theory that would Green's function, the small length fil for Yukawa had assumed with Heisen- unify the nuclear binding force and the me does appear in the exponent and berg that the beta-decay interaction nuclear beta-decay interaction. That sets the scale of oscillation of the was the same as that responsible for is, he set out, in the light of the insight "phase factor," but it does not limit the nuclear forces. The success of Fermi's gained by the analyses of Tamm and range of the force. beta-decay theory suggested that the Iwanenko, to modify the theories of However, for a time in preparing the charge-exchange force might be imple- Heisenberg and Fermi in such a way quantized-field version of the theory mentable by the exchange of a pair of that they could be combined. The based on equation 4, Yukawa thought particles, namely an electron and a model for such a theory was QED; he had the kind of solution he was neutrino, rather than just a single following that model closely had impor- seeking. On 3 April 1933, he gave his electron. That would preserve all con- tant heuristic and pedagogical advan- first talk to a meeting of the Physico- servation laws. Yukawa began calcula- tages. His paper appears transparent Mathematical Society of Japan; in the tions along this line, as did Heisenberg and appealing to us now, and it remains and others. The first results using this published abstract of that talk, he 18 something of a puzzle why it was claims'1 to have obtained the nuclear approach were published in indepen- entirely ignored for two years in both charge-exchange force of range ii/mc, dent letters to Nature by two Soviet Japan and the West. Yukawa's work where the mass m is that of the physicists, Iwanenko and . began to be noticed only in 1937, when electron. This gives a range that would They both concluded that the Fermi a particle whose mass closely fit the still have been about 200 times too field, as electron-neutrino exchange requirements of meson theory was large. Nevertheless, had the result was called, could explain either the detected in cosmic rays. been mathematically correct, it would short range or the great strength of the In his meson paper, Yukawa exploit- have been highly suggestive, for a nuclear binding force, but that the ed the electromagnetic analogy from heavier "electron" would have given a theory as formulated could not explain the outset, beginning with the "classi- shorter range. Yukawa later recalled both simultaneously. cal" theory. Generalizing d'Alembert's that when he gave the talk at Sendai, When Yukawa read the results of equation for the scalar potential of (of Klein-Nishina Tamm and Iwanenko in the fall of 1934, electromagnetism, which has the well- fame) actually proposed to him that he his explicit reasoning and subconscious known static solution 1/r for a point introduce a "Bose electron." But in the intuition began to come together. As source, Yukawa pointed out that a manuscript that he read at Sendai, he he recalled9 in his autobiography: potential having a finite range, namely withdrew the promising result, saying, I was heartened by the negative The practical calculation does not result [of the Soviet scientists], and Uir)= ± 2^Z_ yield the looked-for result that the it opened my eyes, so that I g interaction term decreases rapidly thought: Let me not look for the as the distance becomes larger particle that belongs to the field of is a spherically symmetric static solu- than -h/mc, unlike what I wrote in among the known tion of the generalized wave equation the abstract of this talk. particles, including the new neu- 2 On the blank reverse side of the pre- trino. . . . When I began to think in {n-A )U=0 vious page is written, "mistaken conjec- this manner, I had almost reached He then introduced a source term J' on ture." my goal. .. . The crucial point came the right-hand side of this equation,

60 PHYSICS TODAY / DECEMBER 1986 EO 1 0'' ' P I) | >M

DBTMlIMEm- OP PHYSICS * ~ W • W > " >~ '*"* <+>lH *\ t \ H •> fk. .,. | \. OS/VKA IHPE1UAL UN.VEKSITY. it *«• «- + t ' ll f • ' .UAt « k 1 W ^

neutrino replacing the proton and neu- I. Ui tron. Thus he made the meson an .'•A->->. "intermediate ," carrying the weak as well as the . The very notions of strong and weak nuclear interaction were not part of the general thinking before Yukawa made his meson theory. On the con-

1 N IVJ trary, as we have seen, Heisenberg r tried to make the beta decay and the a <> nuclear charge-exchange forces the G same; that is, he characterized them by Q a single coupling strength. After Fer- o • mi's beta-decay paper appeared, the I' N I C? o same single-coupling idea was carried over into the so-called Fermi-field ap- proach to nuclear forces. However, Yukawa introduced one large con- stant, g, and another small one, g', so that the decay amplitude of a neutron, say, into a proton, electron and neu- trino was proportional to gg'. If one substituted for Fermi's coupling con- stant gF the quantity (ATTI'A~)gg', then, Yukawa pointed out, his theory of nuclear beta decay was effectively equivalent to Fermi's. There was, however, an important additional consequence of Yukawa's Notes for Yukawa's talk on meson theory at a meeting of the assumption that the meson had a beta- Physico-Mathematical Society of Japan on 17 November 1934. This decay interaction. It implied that the talk introduced the meson theory of nuclear forces. (Document E01 092 P01.) meson itself would decay radioactively if it were produced in a free state (that something like the source term J of to proton by emission of a positive U is, not bound in the nucleus). Curious- equation 3. However, in this case the particle (a meson): ly, Yukawa and his associates ignored particle to be created has the transfor- this fact until 1938, when the Indian physicist Homi J. Bhabha pointed mation character of U—that is, it 20 transforms like the electromagnetic out that important prediction of the scalar potential rather than a spinor. theory. The short mean lifetime of the (I shall refer to Yukawa's U particle, Thus, providing the energy difference meson is the main reason why such which has no spin, as a "scalar" parti- is less than Acfi, the exponential is a particles are not found in abundance cle even though it does not transform decreasing function of |r' — r|, and not on the Earth. as a Lorentz scalar.) the oscillating one found earlier in The question of why mesons were The new source term J' is construct- connection with the electron-emission not commonly observed was raised at ed of nucleon spinors (as J had been) in theory. Upon quantizing the U field, Yukawa's first presentation of the the- such a way that the emission of a Yukawa showed immediately that the ory, at one of the informal luncheon negatively charged particle corre- quantity A is mclfi, so that the range of meetings of the nuclear-physics group sponds to the transition neutron to the force is inversely proportional to at Osaka Imperial University, which proton, while the emission of a positive- the mass of the C/quantum. (That was Yukawa regularly attended. Yukawa ly charged particle corresponds to the the insight that crystallized the meson responded that an energy sufficient to transition proton to neutron. Yukawa theory in Yukawa's mind that sleepless create a meson was required, that is, at sought a solution analogous to that October night in 1934. While the least its rest energy of about 100 Mev, given in equation 4, and he obtained range-mass relation is today so com- and such energies were in those days nearly the same result, but with an monplace as to seem self-evident to not available in the nuclear-physics important difference: The exponential most physicists, that was not the case laboratory. The only terrestrial anvil factor that appears when the mass m of in the 1930s. As late as 1938, the well- on which such a particle could be known Italian physicist Gian Carlo forged was the atmosphere, the ham- the U particle is not zero here has the 19 form Wick took the trouble to present an mer being the cosmic rays; Yukawa anschaulich explanation of Yukawa's suggested to his experimenter col- result.) leagues at Osaka that they should look Yukawa also assumed that the U for U quanta in cosmic-ray cloud- chamber photographs. The factor /n is determined from the field (or equivalently, the U quantum) change in energy WN - WP in the was coupled to an additional charge- In the Physical Review of 15 August transition of the heavy particle (what changing current constructed analo- 1936, Carl Anderson and Seth Nedder- we now call a "nucleon") from neutron gously to J' but with the electron and meyer published photographs of parti-

PHYSICS TODAY / DECEMBER 1986 61 First page of Yukawa's rejected letter to Nature suggesting that particles observed in cosmic rays might be the mesons of his theory. I) The letter was sent on 18 January 1937. (From document E06 030 U02, Yukawa Hall Archival Library.)

Utter to the Editor

A Consistent Ihflorj of the Kuolear Force and the b -X>lslntegrstlon

In spite of -aany atteajits to develop the BO-Oailed " 6- hypothesia of the nuclear fare*?1'' there still renains In the current theory the well Jiown Inconsistency totween the snail probability of the ^,-deo/ay and the large Interaction of the neutron and the proton. Hence, It will not be iseless to ^ivw on thia occasion a brief account of one posaible way of solving this difficulty wMch was .xopoaed by the present writer aaout References i) two years ago. PLrst, we introduce the field rniloh la responsible for the 1. H. Yukawa, Proc. Phys.-Math. Soc. Jpn. short rwice force between the neutxon and the proton anJ assura* 17, 48 (1935). It to be sonethlnc different frorarf the so-called "olectron- 2. E. P. Wigner, in in Re- neutrlno field" In contradistinction to the current t:»or7. Tho trospect, R. Stuewer, ed., U. of Minneso- ta P., Minneapolis (1979), p. 160. slaplest conceivable one is perhaps such that can be derived from two scalar potentials 'J and U, which are oonju.>te conplex to eac 3. G. Gamow, Constitution of Atomic Nu- each ot:«r mn& satisfy, in the presence of a ^avj partlcl*, the clei and Radioactivity, Oxford U. P., Ox- ford (1931). th equations e i A _ -L :*_ - ?C" t U •= ^ H-^ M ^^ ^- ^ 4. J. Chadwick, Proc. R. Soc. London, Ser. A 136, 692 (1932). 5. W. Heisenberg, Z. Phys. 77, 1 (1932); Z. Phys. 78, 156 (1932); Z. Phys. 80, 587 (1933). 6. D. Iwanenko, Nature 129, 1312 (1932). 7. L. M. Brown, D. Moyer, Am. J. Phys. 52, 130 (1984). 8. E. Wigner, Phys. Rev. 43, 252 (1933). cle tracks obtained in a cloud chamber (Pauli liked to call his theory "anti- 9. H. Yukawa, Tabibito (The Traveler), L. operated in the field of a strong magnet Dirac" because it flouted some of the M. Brown, R. Yoshida, trans., World Sci- atop Pike's Peak in Colorado. In some basic assumptions Dirac made in deriv- entific, Singapore (1982). cases they could not positively identify ing his relativistic electron theory. 10. E. Fermi, Nature 125,16 (1930); Z. Phys. the tracks as belonging to either elec- Dirac's work had been interpreted to 60, 320 (1930). trons or protons. Yukawa wrote a imply that fundamental particles had 11. W. Heisenberg, W. Pauli, Z. Phys. 47, 1 letter to Nature pointing out that it was to have spin V2.) (1929). "not altogether impossible" that the After the mesotron discovery, 12. Document E05 030 U01, Yukawa Hall ambiguous particles were his heavy Yukawa and his students redoubled Archival Library, Kyoto University. quanta. That letter was rejected by the their efforts and soon became engaged 13. H. Yukawa, J. Phys.-Math. Soc. Jpn. 7, editor, but Yukawa succeeded in pub- in the development of the theory and 21 195 (1933). lishing a "Short note" having the its consequences, a process that so 14. Document E05 060 U01, Yukawa Hall same contents in the Proceedings of the closely paralleled similar efforts in the Archival Library, Kyoto University. Physico-Mathematical Society of Japan West that one of the chief Western 15. H. Yukawa, Bull. Phys.-Math. Soc. Jpn. in July 1937. By then, several experi- meson theorists, , 7, 131A (1933). mental groups had reported22 the ob- later referred25 to the Japanese and the servation of particles of both signs of Western efforts as a "joint enterprise." 16. See, for example, L. M. Brown, PHYSICS electric charge and of mass between The mesotron turned out to be the TODAY, September 1978, p. 23. 17. E. Fermi, Ric. Sci. 4(2), 491 (1933); that of the electron and the proton, at second-generation heavy electron that Nuovo Cimento 2, 1 (1934); Z. Phys. 88, roughly one-tenth of the proton mass. we now call the , and the true 161 (1933). The observations of the new cosmic- meson of Yukawa, the , was found ray particles, which came to be called in cosmic rays only in 1947. That is 18. I. Tamm, Nature 133, 981 (1934). D. mesotrons, aroused23 interest in another story, of course, one well worth Iwanenko, Nature 133, 981. Yukawa's theory. Yukawa and his the telling. 19. G. C. Wick, Nature 142, 994 (1938). 20. H. J. Bhabha, Nature 141, 117 (1938). students at Osaka had not been idle Fifty years later, the meson theory is during the more than two years during 21. H. Yukawa, Proc. Phys.-Math. Soc. Jpn. still alive and well. In spite of its 19, 712 (1937). which no one had paid attention to the grandeur, today's has heavy quantum. With , not been able to calculate "low-energy" 22. S. H. Neddermeyer, C. D. Anderson, Yukawa used the meson theory in a processes, such as meson-nucleon scat- Phys. Rev. 51, 884 (1937). J. C. Street, calculation of the K-capture process. E. C. Stevenson, Phys. Rev. 51, 1005 tering, or the nuclear forces. But even (1937). Y. Nishina, M. Takeuchi, T. Ichi- That weak-interaction process had not when that becomes possible, Yukawa's been observed, but its existence had miya, Phys. Rev. 52, 1198 (1937). meson will still be a shining star. 23. J. R. Oppenheimer, R. Serber, Phys. been suggested by the Austrian physi- * * * cist Guido Beck, who visited Japan in Rev. 51, 1113 (1937). E. C. G. Stueckel- 1935. By mid-1936, Yukawa had al- / wish to thank the US-Japan Cooperative berg, Phys. Rev. 52, 41 (1937). ready begun to reformulate24 the me- Science Program and the Program in History 24. Document E02 130 P12, Yukawa Hall son theory using the Pauli-Weisskopf and Philosophy of Science, both of the Archival Library, Kyoto University. relativistic theory of scalar particles. National Science Foundation, for research 25. See N. Kemmer, Biog. Mem. Fellows R. support. Soc. 29, 661 (1938). •

62 PHYSICS TODAY / DECEMBER 1986