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612 Letters to the Editut On the Annihilation Cross Section of the Antinucleon and the Nucleon ){oshio ){anruaguchi Department of Physics, Osaka City Uni'l'ersity, Osaka One can expect that the annihilation process takes place at the instant that the proton and the antiproton with the finite size come into contact. Thus the antiproton with high energies (where the classical trajectory of motion can be pictured) should have · the annihilation cross section O"a , February 11, 1957 (3) We have recently obtained further informatian1l about the electro-magnetic structure of nucleons, from the high energy electron scattering experiments of the and (electron-proton group Stanford electron-deuteron scattering experiments) and the electron-neutron interaction. According to these results, the proton has the electro-magnetic radius, r•. v . . rm,v= (0.77 ± 0.10) X 10-13 em, (1) while the neutron seems charge radius re,n . . 0. to have the (2) The latter requires that, although the charge dirtribution inside the neutron should extend intrinsically over a range of the order of (1), it is essentially neutral at every local points. Let us here ask what is expected from such an electromagnetic size of th:e nucleon as to the annihilation cross section2),s) of the anti-nucleon and the nucleon. The most intuitive picture for the antiproton-proton annihilation process may be the neutralization of the charges. An argument based on the charge conjugation proves that the electromagnetic structure of the antiproton is identical with that of the proton except for the sign of charge. and the total cross section 0"1 , including the diffraction scattering O"d ( ==. O"a, optical model) Experimentally it was found thael 0"1 ==-100 mb for high energy (~ 350 Mev) antiproton on hydrogen. It is not clear to the author whether this value of the total cross section is free from an ambiguity of the diffraction scattering. Considering the present stages of both experimental and theoretical aspects of this process, one may conclude that our crude model is quite promising to predict the annihilation cross section. For a low energy antiproton, the classical approximation adopted above will break down, and an increase of the cross section due to the wave mechanic2.l effect is expected. We shall estimate critical energy Ec (in lab. sys.), above which the classical picture should be allowed. Suppose that an antiproton annihilation process involves partial waves up to the order l in the incident channel. Then Ec may be found from the following equati.>n ; l 0",==.1Z'x}2j(2l'+1), ltc"'re, 1,; 1'=0 where 9X 10-13/VEc "'c-"' A ) · M eV. (E cln (5) Letters to the Editor 613 distribution inside the physical proton. we have1l Using eq. (3), we find E 0 .::::.34 Mev for l=O, (ro,p) 2 = ) dr r2 [Pc (r) + p, (r)], E0 =136 Mev for l=l. (ro,n) 2 and If the 2ntiproton is captured by the proton from the p-states beside the s-states, the wave mechanical increase of the cross section will be expected for the antiproton with a kinetic energy smaller than E 0 .::::. 13 6 Mev. Such tendency was clearly seen in the experimental results. Finally, let us add a speculation about the structure of the " physical" nucleon. Recently, Sakata'> has proposed a new theory of elementary p2rticles in which the pion is considered as a composite. system of the nucleon and the antinucleon. 5> According to this model, a physical nucleon is described in terms of (a bare nucleon) (nucleon pairs). Thus, the diff-erence of (1) and (2) can easily be understood6> and it is m.tural to suppose that the annihilation of the 2.ntinucleon and the nucleon should take place just after the contact of the rims of the extended nucleons. + 1) 2) 3) 4) D. R. Y ennie, M. M. Levy, and D. G. Ravenhall, Electromagnetic scructure of nucleons, to be published ; Other references are cited in it. The author is indebted to Prof. Y ennie for sending him this preprint. W. H. Earkas et. al., The antiproton-nucleon annihilation procrss, to be published ; Other referencEs are cited in it. Z. Ko!::a and G. Takeda, to be published ; The experimental rrsults are quoted in it. S. Sakata, Prog. Theor. Phys. 16 (1956), 686 (L). 5) 6} E. Fermi and C. N. Yang, Phys. Rev. 76 (1948)' 1739. According to a conventional meson theoretical picture of the physical nucleon, one can proceed as follows: Let e(Jc (r) and ep.,. (r) be the core pa" and the pion-cloud pare of the charge =) drr [p 2 0 Then (r) -p,(r)]. From the experimental results, eqs (1) and (2), we can learn that the nucleon-core extends over the radius=ro,p (';j:>fi/Mc, the nucleon Compton wave length), which is difficult to understand from the meson theories, see ref. 1) .