Investigation of the accuracy of the tomonaga intermediate-coupling approximation

The Tomonaga intermediate-coupling approximation and a two-wave-function generalization of it are applied to the system consisting of charged scalar mesons interacting with a static-source nucleon. The generalization allows mesons in the nucleon ground state to occupy either of two states in momentum space. Expressions are obtained for the ground-state wave functions and energy, and for the differential cross section for the elastic scattering of positive mesons by protons. The cross section associated with the one-wave-function approximation differs significantly from the two-wave-function cross section. There is good agreement between the one- and two-wave-function results for static properties of the nucleon.