Die elastische Pion-Nukleon-Wechselwirkung im Mesonaustauschbild

We report a meson exchange model of pion-nucleon interaction, which has recently been developed by our group. Apart from direct and exchange nucleon and deltapole diagrams the Born term of this model includes potentials for the correlated exchange of two pions in the 0$^{+}$ ('$\sigma$') and 1$^{-}$ ($\rho$) channels. These 2$\pi$-exchange potentials are calculated from partial wave amplitudes for the reaction N$\overline{N} \rightarrow \pi \pi$ using the technique of dispersion integrals. Our 2$\pi$-exchange potentials are compared with potentials derived from the exchange of '$\sigma$'- and $\rho$-mesons in conventional meson exchange models, in which the mass distribution of the exchanged 2$\pi$-system is neglected. By an investigation of the characteristic differences of these potentials we show that the realistic treatment of correlated 2$\pi$-exchange is of crucial importance for the quantitative description of $\pi$N scattering data obtained in our model. The rise of the P$_{11}$ phase shift is reproduced without an explicit pole term involving the N*. The description of this partial wave is based on the cancellation between the strong attraction from correlated 2$\pi$-exchange and a repulsive contribution from the nucleon pole term