The cut-off theory for the interaction of pions with nonrelativistic nucleons is tested against experiments involving a single nucleon, with and without the presence of an electromagnetic field. It is concluded that most of the existing information about the $P$-wave pion-nucleon interaction can be understood with a renormalized coupling constant, $f^2=0.058\mathrm{}$ and a cut-off energy, ${\omega }_{max}=5.6\mathrm{}$ μ. No light is shed on the $S$-wave pion-nucleon interaction.

• Received 10 June 1954

DOI:https://doi.org/10.1103/PhysRev.95.1669