Pion-nucleon Scattering and Nucleon Isobar

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The cross sections for pion-nucleon scatterings are calculated in the symmetrical ps-ps and ps-pv theory, assuming phenomenologically the effective interaction Hamiltonian which permits the virtual transitions of a nucleon to or from its excited state of spin and τ-spin 3 / 2, which is described by the Rarita-Schwinger theory for spin 3 / 2 particles, accompanied by one pion emission or absorption. For ps-ps theory, the linear ps-ps coupling term is transformed into the sum of the equivalent pv coupling term and the meson pair term, the coupling constant for the latter being chosen effectively small relative to that for the former, taking account of the strong damping effect of nucleon pair formation. The basic equations are solved quite analogously to the well-known treatment of resonance fluorescence, in the approximation of neglecting nucleon recoils. In order to obtain the agreement of the theoretical curves with the experimental ones, the various coupling constants and the characteristic two adjustable parameters G and ΔE are determined quite sharply, G being the effective coupling constant determining the strength of virtual transitions to or from excited states and ΔE being the excitation energy of nucleon isobars. The determined values of the above coupling constants are quite reasonable and the satisfactory agreement of the theoretical curves with the experimental ones is obtained for both types of couplings. It can be said, however, that the ps-ps coupling is rather preferable to ps-pv coupling, thus concluding that the symmetrical ps-ps theory can be considered to be satisfactory if the appropriate accounts are taken of nucleon isobars and the present model for isobars is also satisfactory at least as far as the pionnucleon scatterings are concerned.
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Pion-nucleon Scattering and Nucleon Isobar

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