The Self-energy of Nucleon for the Pion-nucleon Scattering Parameter

The scattering amplitude of the pion-nucleon elastic scattering is calculated by the lowest-order approximation of the perturbative expansion with the non-perturbative term. The self-energy of nucleon is determined so as to give the scattering parameters of the $S$-wave. It is shown that the scattering process mediated by the $\sigma$-meson plays a decisive role together with the pseudovector pion interaction.