Meson-Nucleon Scattering. I

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Abstract
An approximate quantum-mechanical solution of the meson-nucleon scattering problem for intermediate values of the coupling constant is presented. The particular case treated here is that of charged scalar mesons interacting with a static nucleon. In finding the cross section, attention is focused upon the matrix elements of the field and isotopic spin operators and on the equations of motion, no attempt being made to calculate explicitly the scattering state vector. It is shown that in both the weak and strong coupling limits the procedure described here gives the scattering correctly. For intermediate coupling the cross section must be found numerically. Computations have been carried out for several intermediate values of the coupling constant and the results are presented in the form of curves showing cross section vs meson energy. Since certain information about the one-nucleon problem (i.e., one real nucleon and no real mesons) is needed for these calculations, a detailed numerical solution of that problem has been carried out using the Tomonaga approximation. The relevant results of this work are presented in several graphs. Although it is not a part of the scattering problem, the calculation of the isobar separation in the strong coupling limit can be carried out so easily by the methods of this paper that a brief account of it is also given. In the appendix, a variational method of calculating the scattering-state vector for intermediate coupling is described. It is shown that this, however, fails to give the correct strong coupling limit.