Scattering of Charge Symmetric Pseudoscalar Mesons by Nucleons

The Pauli theory of extended source interacting with the neutral pseudoscalar field with pseudovector coupling has been extended to the case of the charge symmetric pseudoscalar field, and has been applied to the problem of the scattering of mesons by the nucleons. The results of our calculation show that the scattering cross sections are strongly dependent upon the energy of the incoming mesons, that the cross section for the scattering of ${\pi }^{+}$ by protons is larger than that for ${\pi }^{-}$ by factor 2.25 at all kinetic energies up to about 150 Mev, and that within the scattering of ${\pi }^{-}$ by protons the cross section for the scattering involving charge exchange interaction is larger than that with ordinary interaction by a factor which varies from 2.1 to 1.5 as one goes from zero kinetic energy to 150 Mev. When the coupling constant ${\left(f_{\mu }\right)}^2$ is taken to be about 0.3, the maximum of the theoretical cross section curve coincides with the experimental maximum if one assigns 1.25μ ($\mu$=the reciprocal Compton wavelength of the meson) for the spin and isotopic spin inertia of the nucleon. The scattering cross-section curves for ${\pi }^{+}$ and ${\pi }^{-}$ approximately agree with the experimental curves if one assigns a value 1.58 for $\mathrm{}\left|G\right(K\left)\right|$, which appears in the original theory of Pauli.