A phenomenological model of the interactions between pions, nucleons, and isobars is constructed. The mass operator is defined on a Hilbert space made up of , , and states with the following interaction mechanism: (1) a vertex in the channel, (b) two-body interactions in other channels, and (c) two-body interactions for , , and transitions. The model is Lorentz invariant and satisfies cluster separability. The interactions are parametrized by analytic separable forms with parameters determined by fitting the scattering phase shifts for up to 300 MeV and scattering phase shifts for up to 800 MeV. In fitting parameters and in the applications, nonrelativistic approximations are used for the baryons in the and channels. The model so determined gives a satisfactory description of pion absorption by deuterons and of elastic pion-deuteron scattering. Multiple rescattering of pions between and as well as interactions in intermediate states are found to be important in channels coupled to waves. These effects enhance the cross sections for by 40% in the resonance region. From the two-baryon Hamiltonian we construct a many-body Hamiltonian for nonrelativistic baryons.
NUCLEAR REACTIONS A model of interactions between , , and . Applications to the pion-deuteron system.
- Received 9 June 1980
- Published in the issue dated January 1981
© 1981 The American Physical Society