  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.
