The process rr+N-+N*(3/2, 3/2) +1r caused by the exchange of 21r system T=J=1 is investigated.· Within a pretty good approximation, the desired reaction amplitude can be obtained by making use of the dispersion theory of single pion production by a virtual photon. The theory involves only one adjustable parameter, the 1r-1r coupling constant,\.As an example, the theory is compared with the Stonehill-Kraybill data for the small .J2 events of 7r+p-+p7r+1l"o at 1.26 Bev (.J2 being the nucleon four-momentum transfer squared). The shape of experimental Q-value spectrum of final (p, rr+) pair can be reproduced fairly well by taking into account both of the one-pion exchange (OPE) and our N*-production processes with a reasonable choice of the value of the parameter ,\.From this result it is concluded that, even in the relatively small .d2 region, the N* effect .can be comparable to the OPE contribution, against the conventional simplified supposition of predominance of the latter in this region. Finally a possibility is suggested that the value of the parameter ,\ be determined more definitely from the more precise measurements of the reaction in question. § I. IntroductionSince the discovery 1 l of several " resonances " of pion systems, the pion-pion interaction has become one of main topics in the elementary particle physics, and many attempts have been done to obtain the information on this interaction from the reaction, for example, nN~N2n in the Bev-region. For this purpose it is very often supposed 2 l that, at least in the small J 2 region (J 2 being the nucleon four-momentum transfer squared), the reactions are dominated by the one-pion-exchange (OPE) process, i.e. the process where only one pion is exchanged between the incident pion and target nucleon. 3 l Recently, however, there have been gradually accumul~ted the data that cannot be interpreted by the OPE· model alone. 4 l' 5 l For example, in the reaction (1·1) at T/"b=910-, 1090-, and 1260-Mev reported by Stonehill and Kraybill/l the Dalitz plot shows an obvious concentration of the events in the (3/2, 3/2) reso-*' On leave of absence from Department of Physics, Tohoku University, Sendai. by guest on March 21, 2015 http://ptp.oxfordjournals.org/ Downloaded from *l In fact, the existing data of low energy nN-+N2n (and rN-+N2n) can be interpreted fairly well as caused mainly by the process nN-+N*n (and rN-+N*n).6> **l On this point, we shall present later ( § 5) somewhat more detailed discussions. by guest on March 21, 2015 http://ptp.oxfordjournals.org/ Downloaded from *l In the ordinary isobar model theories,Bl there is simply assumed the S-state production of N*, and moreover the magnitude of the N*-production amplitude itself is purely phenomeno· logical free parameter. **l Goebel and Schnitzer14l have estimated as .l= -0.182 from the static-theoretical analysis of pion production in sub-Bev region. by guest on March 21, 2015 http://ptp.oxfordjournals.org/ Downloaded from F: Nunokawa for her help in preparing the manuscript.Appendix. Calculation of (...

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915Effects of the (r, 3rr) vertex in the reaction r+p-7 p+2rr 0 is studied. It is shown that the (r, 3rr) -part of the amplitude for this reaction is given by the " meson current part" of the amplitude for the single rrO production by a virtual photon, multiplied by a certain numerical factor including the effective coupling constant of the (r, 3rr) vertex. Thus referring to the theory of Fubini, Nambu and Wataghin for the single pion electroproduction, the (r, 3rr) -part of the double rrO photoproduction amplitude can be obtained almost exactly.It is also shown that, under appropriate experimental conditions, the major contribution to the reaction r+p--?p+2rrO comes from the absorption of the incident photons via the (r, 3rr) vertex, unless its effective coupling constant ,\ be much smaller than the value expected from the simple perturbation calculation. Thus, the experimental study of this reaction would possibly provide an alternative and rather unambiguous method for the determination of J.. An example for such a measurement is proposed, and the cross section under the proposed conditions is calculated. § I. IntroductionRecently, the (r, 3n) interaction or the reaction (1·1) has become one of the most interesting problems in the elementary particle physics. The problem has been raised mainly in connection with the theory of the isoscalar electromagnetic form factor of the nucleon 1 ) and the dis-covery2) of the various resonance states of pion systems. Also, in the second and third resonances of the pion photoproduction, the (r, 3n) vertex may play a decisive role 3 > analogous to the supposed role of the pion-pion interaction in the corresponding resonances of the pion-nucleon scattering. 4 > The effects of the (r, 3n) interaction in the various types of the elementary particle reaction have been theoretically examined and several methods for experimental determination of its interaction strength are proposed. 5 >-B> However, the problem is considerably delicate, and perhaps the conclusions expected from the methods thus far proposed can not be so conclusive.This is mainly owing to the expected smallness of the (r, 3n) coupling *l On leave of absence from Department of Physics, Tohoku University, Sendai. at UCSF Library and Center for Knowledge Management on March 21, 2015 http://ptp.oxfordjournals.org/ Downloaded from 916 K. Itabashi and T. Ebata constant A. *l In all the reactions that have thus far been considered for de-termination of A, the process via the (r, 3n) vertex is only a minor one, namely the most part of the total yields is the background to be subtracted. Thus, naturally one tends to consider the interference effects between the major processes and the process via the (r, 3n) vertex, since the interference effects are generally sensitive to the small admixture of the minor processes. However, by just the same reason, one cannot necessarily ignore the other minor processes, about which we have not so much information. Therefore, in general, the theoretical results cannot be so conclusive.As ...