Pion-Nucleon Scattering and Pion-Pion Interaction

概要

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S-wave pion-nucleon scattering is investigated from the viewpoint that pion-pion interaction is important. Starting from the interaction Lagrangian L_1[numerical formula] (where the third term corresponds to the effective potential obtained from the original pion-pion interaction H_<1^<π-π>>=λ(φ・φ)^2, we solve directly the Klein-Gordon equation on the matrixelements of the meson field operator between the nucleon state and the nucleon plus onemeson state. Choosing Yukawa type for the form factors pi(γ)=(4πγ)^<-1>Λ_<i^2> exp [-Λ_<i^γ>. we can obtain the best fit to the experimental behavior of the S-wave phase shifts for the following value of the parameters: Λ_c≈5μ, Λ_π≈3.5μ,(2/(4π))(G^2/(2M+V(0))=(2/(4π))(G^2/(2M))(2/10)~0=(0.4~0)μ^<-1>. This choice of V(0) corresponds to the original pion-pion coupling constant λ/(4π)=0.3~0.5 and is consistent with the value (|λ|)/4π≈1 determined from the (π-2π) process at 1.4 Bev. On the basis as obtained above, the qualitative nature of the small P-wave phase shifts is discussed. And we obtain the results which coincide with the ones of analysis by Lomon and Chiu.
一般社団法人日本物理学会の論文
1960-12-25