Abstract
From the usual relativistic pseudoscalar Hamiltonian we derive a model Hamiltonian for low-energy pion-nucleon scattering which is a generalization of the static model to take into account the recoil of the nucleon. An approximate expression is derived for the elastic low-energy pion-nucleon scattering amplitude by making a partial summation to infinite order of the perturbation expansion of the resolvent operator. The amplitude obtained converges after coupling constant renormalization in the infinite momentum cut-off limit. Determining the value of the coupling constant by requiring the theory to reproduce the experimental scattering length one obtains g 2 4π = 23.25 giving 1368 MeV for the mass and 260 MeV for the width of the N ∗ resonance.
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