(Received December 17, 1960)
Pion-pion scattering in the I = l = 1 state is treated by the Tamm-Dancoff method. By making an approximation in which configurations containing up to three particles of meson and nucleon pair are taken into account in the 4th order pion-pion interaction kernel, the existence of resonance is concluded. By adjusting the coupling constant g2/4π between pion and nucleon so as to fit the pion-pion scattering length a = 0.1∼0.3µ-3 in the I = l = 1 state, we have found the resonance level of 600 ∼400 Mev and resonance width of 140 ∼40 Mev, which is quite consistent with what adopted by Takeda et al. in their theory of the 2nd ∼ 3rd maximum in pion-nucleon scattering and also by Frazer-Fulco in the explanation of isotopic vector magnetic form factor of a nucleon. We adopt g2/4π= 6.1 ∼6.8, which is somewhat smaller than the conventional one. This small coupling constant is interpreted as due to the inclusion of the effects of scattering and annihilation of a virtual nucleon pair.
URL :
http://ptp.ipap.jp/link?PTP/25/727/
DOI : 10.1143/PTP.25.727