The pion-nucleon coupling constant is calculated from first principles by use of the $\frac{N}{D}$ matrix method. Three models are introduced which contain pions, nucleons, and weakly interacting intermediate bosons of the scalar, pseudoscalar, and vector variety. The basic interactions are taken to be parity and isotopic spin conserving. Certain physical assumptions in the nature of boundary conditions and the known fact that the weak coupling is very weak, together with use of the Born approximation for N, enable us to obtain an eigenvalue equation which expresses the pion-nucleon coupling constant in terms of the three masses in the problem. The correct value for ${g_{\pi }}^2$ can be obtained for an intermediate vector meson of mass comparable to the nucleon mass with essentially no cutoff employed; on the other hand, the experimental value is also obtained with a spin-zero boson and a relatively small cutoff energy.

• Received 13 June 1961

DOI:https://doi.org/10.1103/PhysRev.124.624