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Richard Feynman to Enrico Fermi

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Richard Feynman to Enrico Fermi CBPF-CS-012/97 Richard Feynman to Enrico Fermi: a letter from Rio de Janeiro, 1951 J. Leite Lop es Centro Brasileiro de Pesquisas Fsicas - CBPF Rua Dr. Xavier Sigaud, 150 22290-180 - Rio de Janeiro-RJ, Brazil and Universidade Federal do Rio de Janeiro Richard Feynman came to Rio de Janeiro for the rst time in 1949. The Centro Brasileiro de Pesquisas Fsicas | CBPF | had just b een founded by a group of Brazilian physicists led by Cesar Lattes | who had contributed in 1947 to the discovery of pions | and mathematicians led by Leop oldo Nachbin and Maurcio Mattos Peixoto, in order to promote researchworkincontemp orary themes of physics and help in the university education of physicists. Feynman liked the atmosphere at the Centro and was attracted by the city and its b eaches. He came backayear later and stayed during his U.S. Sabbatical year, 1951 - 1 1952. He gave lectures at the University and at the Centro on electro dynamics and was working an meson theory after his well-known success in quantum electro dynamics. He prop osed to me that weinvestigate whether the symmetrical pseudoscalar meson eld theory could give a description of the deuteron which could b e exp erimentally checked, in 1 spite of the dicultyofthe -singularity at the origin of the tensor-force in the Yukawa 3 r 4 p otential. Feynman comments this work in his letter to Fermi in the p ort-scriptum P S . The results of this research are in a pap er published in the Pro ceedings of a Symp osium 2 whichwas held in Rio and which I presented after Feynman left for Japan in May 1952. Feynman enjoyed very much his stay in Rio and came back during his summer vaca- tions several times. In 1953, he had his ideas on sup erlfuidity in our city.Ashesays in 1 Details of his activities anf feelings in Rio may b e found in the pap er J. Leite Lop es, RichardFeynman in Brazil: recol lections, QUIPU, Revista Latino-Americano de Historia de las Ciencias y la Tecnologia, vol. 7 numero 3, Mexico (1990) 2 J. Leite Lop es and R.P.Feynman, On the pseudoscalr meson theory of the deuteron New Research Tecniques in Physics, Academia Brasileira de Ciencias, Rio de Janeiro (1954) {2{ CBPF-CS-012/97 this letter to Fermi: \(I) am going to the Copacabana b each to see if I can get one (ideas) of myown. I get lots of ideas at the b each." It was a great joy for me to work and discuss with him. Wewere together in Pasadena, at Caltech, during the year 1956-1957 and in Mexico City in 1972 where we discussed on the emerging gauge eld theories and nally in 1977 when I invited him to come to Stras- b ourg and present a review pap er on the parton mo del to an International Symp osium on multiparticle dynamics whichwas held in the charming Alsacian town of Kaysersb erg, birthday of Alb ert Schweitzer. Here is Feynman's letter to Enrico Fermi: Rio de Janeiro Decemb er 19, 1951 Dear Fermi, Being thousands of miles awayIhave only heard by amateur radio from friends in the U.S. that you are doing exp eriments in meson scattering from protons. I don't know what your theoretical friends are saying, so I should liketomakesomecoments at the risk of only saying what is obvious to everyb o dy in the U.S. To b egin with I am of the opinion that Yukawa's meson theory with pseudoscalar mesons gradient coupling, is wrong, (or least useless) in its present form | b ecause at least p erturbation theory is N.G. and otherwise divergences cloud the issue. But I think 3 mesons are pseudoscalar, and I think the amplitude that a nucleon emits just one may b e prop ortional to .Q (where is the nuclear spin, Q the meson momentum) for Q small. (This is of course in agreement with the Yukawa theory | to all orders in account, H H HHH f i b ecause for low Q one op erator in the series H + + etc. is prop ortional fi E E E i to Q and others, involving all the virtual mesons are not (the virtual moments are of order , the meson mass) so for Q low enough the sum will b e prop ortional to Q, and further will b e Qtimes the sum with the op erator in place of one of the H's | which 1 means Q.times a spin ob ject which can only therefore b e prop ortional to ). Let us say 2 1 then the coupling is G(Q)( Q)u for emission of one meson amplitude u, momentum Q, mass where G(Q) is a function of Q (and p ossibly the nucleon moments at higher Q??) and I exp ect G to have the prop erties of not varying muchfor Q small, just is a 3 Imake all analyses thinking of the theory non-relativistic in the nucleons. {3{ CBPF-CS-012/97 reasonable function of Q=.For Q =0,callG(O )=G (If p ert theory were OK G is just 0 0 the usual g ). Further this is most reasonale on nearly any theory | for the meson b eing pseudoscalar the co ef to emit one (even if proton is a p ositron + 18 neutrinos + 4 neutral mesons) must b e ps.scalar | which , if it do esn't involvethenucleon momenta (and I can't see how it easily can b e galilean invariant | but Nature's imagination always has my resp ect) can hardly b e other than Q. (According to Yukawa theory, standard form, 2 the total series would givea G(Q)which, if g were very small and integrals converged, 2 would b e nearly constant for all Q andequaltog | but if g is larger, correction terms set in for Q of order ). I wish to app eal to exp eriment to try to establish, if p ossible, wheter the ab oveis correct and the coupling is like Q for one meson absorption. You see tho I mean only to refer to low energy mesons |for Q or higher I have no arguments ab out what to exp ect. Yet it is imp ossible to measure the absorption of one meson bynucleon directly for the conservation of energy demands that another coupling enter to take out the energy. If we do it with a -ray, or a collision b etween nucleons new uncertainties arise, but if we do it by means of another meson (scattering) the situation would app ear to b e as simple as p ossible. The \intermediate states" (if they mean anything) have, mayb e, energy of order so that as long as Q remains small enough (non-rel. mesons) the intermediate states do not dep end muchon Q. Then, if we assume the coupling for two mesons is essentially like the double action of the lst order coupling, we see that the matrix element for scattering 4 ought to b e prop ortional bilinearly to Q and Q .Itmust therefore have the form 1 2 M = X Q Q + X i (Q Q ) 1 1 2 2 1 2 of if Q ;Q lie in x; y plane at angle one to other using c.g. system Q = Q = Q 1 2 1 2 2 M = Q (x cos + i sin X ) 1 2 where X ;X are some functions of Q, insentitiveto Q for small Q. But in principle 1 2 knowledge of the coupling of one meson do es not determine that for two. There could still b e a term with arbitrary co ecient in the Hamiltonian of form u u which is scalar. 1 2 Hence we mightexpect 2 M = Q (X cos + i sin X )+X 1 z 2 3 (For example, gradient and direct coupling theories agree on Q for one meson, but for two X is very di erent b eing very small for grad. and very large for direct- in p ert. 3 theory). 4 Because, if you like, now in the p ert series one of the H is prop. Q , other to Q and otherwise 1 2 nothing is sensitivetothevalues of Q ;Q . 1 2 {4{ CBPF-CS-012/97 Naturally such a form is completely general | but what I wanttoverify is that 3 X is very small (mayb e order =M smaller than X ;X); (1) 3 1 2 (could in principle dep end on spin | I will assume it do esn't) 2 2 2 X ;Xare insensitiveot Q for Q well b elow : (2) 1 2 I am not in p osition to calculate X ;X in terms of G, nor to get a relation b etween 1 2 them | for wehave no go o d theory. (One p ossibility of course is that relations of the lst order p ert theory may b e true, but let us rst nd out if (1), (2) are true and that b eing established go on from there.) Coments: (1) is a pure guess | various evidence (suchas emission comp eting 0 favorably with emission in H capturing ) indicates it is so | all the evidence which is usually aduced to prefer the grad. to direct coupling is just a question of how big X 3 is. I assume for no excellent reason that X do es not dep end on spins. 3 (2) could b e wrong. It would b e very interesting.
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