An Application of the Theory of the Effective Range to Meson-Nucleon Scattering

A theory of the effective range for $P$-state scattering is developed and the extent of its validity is investigated. It is found that a parameter of the theory can meaningfully be identified as an effective range and that the energy dependence of the effective range is very weak. The resulting formula for the energy dependence of the phase shift is shown to be exactly equivalent, if the relativistic energy is used, to a simple form of the Wigner-Eisenbud one-level formula for $P$-states in which the level shift is neglected. An application to meson-nucleon scattering is made which illustrates the use of the method and which suggests a high lying resonance in the scattering.