On a Model of Nucleon Structure and Meson-Nucleon Interaction. III

Abstract

It is shown that Im Fi (t) (Fi: the iso-vector part of the form factors of r-nucleon vertex) have one or two additional zero points in general in our representation which did not appear in Frazer and 'Fulco's dynamical theory.sl Using this representation, the ratios of the p-nucleon coupling constants to the p-rr coupling constant are estimated from the experimental values of the form factors. The results suggest strongly the presence of Sakurai's vector current J <rl. These results are also quite consistent with our· model. § l. Introduction The presence of two different types of resonance is well-known in nuclear physics. One of them arises from the attractive force between the incident particle and nucleus which can be described by optical potential and is observed as the resonances of broad width in general. The other arises through some unstable mediate state i.e. compound nucleus, and is observed as · sharp resonance. (Hereafter, we call the former the dynamical resonance and the latter kinematical resonance according to Chew and Mandelstam. 4l) These two types of resonance appear also in the problems of field theory. For example, the so-called (3, 3) resonance which was studied by Chew and Low6l is clearly a dynamical resonance, while the K-particle which decays into two or three pions is considered as a kinematical resonance (elementary particle) by the reason of its long life. But, with respect to the new resonances p, lll, K*, N**, N***, Y*, Y** which were discovered successively by Maglic et al., 6J the Bro­ okhaven groups 7 l~BJ and other groups,9l it may be difficult to determine whether they are dynamical resonating states or new elementary particles (or composite particles), because the widths of these resonances are always narrower than the one calculated by dynamical description but not so narrow as to be accepted as elementary particles (composite particles) undoubtedly. By many authors, various attempts to deduce these resonances from dy­ namical theory have been proposed within recent two years. Especially, the case of S- and P-wave 7r-7r resonance was studied skillfully by Chew and Man­ delstam4l using dispersion relation theory and was applied to the problems of