Phenomenological Hamiltonian for pions, nucleons, and Δ isobars: Applications to the pion-deuteron system

Phys. Rev. C 23, 375 – Published 1 January 1981
M. Betz and T. -S. H. Lee


A phenomenological model of the interactions between pions, nucleons, and Δ isobars is constructed. The mass operator is defined on a Hilbert space made up of NN, NΔ, and NNπ states with the following interaction mechanism: (1) a ΔNπ vertex in the πN-P33 channel, (b) two-body πNπN interactions in other πN channels, and (c) two-body interactions for NNNN, NΔNΔ, and NNNΔ transitions. The model is Lorentz invariant and satisfies cluster separability. The interactions are parametrized by analytic separable forms with parameters determined by fitting the πN scattering phase shifts for l1 up to 300 MeV and NN scattering phase shifts for l4 up to 800 MeV. In fitting parameters and in the applications, nonrelativistic approximations are used for the baryons in the NΔ and NNπ 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 N and Δ as well as NN interactions in NNπ intermediate states are found to be important in channels coupled to NΔ s waves. These effects enhance the cross sections for π++dpp 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 π, N, and Δ. Applications to the pion-deuteron system.


  • Received 9 June 1980
  • Published in the issue dated January 1981

© 1981 The American Physical Society

Authors & Affiliations

M. Betz* and T. -S. H. Lee

  • Argonne National Laboratory, Argonne, Illinois 60439

  • *Present address: TRIUMF, University of British Columbia, Vancouver, Canada.

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