Interaction ofP- andS-Wave Pions with Fixed Nucleons

A method is given of replacing pion scattering parts in a Feynman diagram by experimentally observed quantities. In this paper momenta of nucleons are neglected, although nucleon pair creation is not. It is assumed that only $P$- and $S$-wave pions interact with nucleons. No interaction is assumed between pions. Two examples are given: (1) The anomalous magnetic moment of the proton is rigorously expressed in terms of pion-nucleon scattering amplitudes, or, alternatively, in terms of the renormalized coupling constant and the total cross sections for pions. (2) The internucleon potential is also expressed by means of scattering quantities. In this case the number of virtual pions exchanged between the two nucleons is limited to two, although the number of pions emitted and absorbed by the same nucleon is not limited.