#### Abstract

A phenomenological model of the interactions between pions, nucleons, and $\Delta $ isobars is constructed. The mass operator is defined on a Hilbert space made up of $\mathrm{NN}$, $N\Delta $, and $\mathrm{NN}\pi $ states with the following interaction mechanism: (1) a $\Delta \rightleftarrows N\pi $ vertex in the $\pi N-{P}_{33}$ channel, (b) two-body $\pi N\to \pi N$ interactions in other $\pi N$ channels, and (c) two-body interactions for $\mathrm{NN}\to \mathrm{NN}$, $N\Delta \to N\Delta $, and $\mathrm{NN}\rightleftarrows N\Delta $ transitions. The model is Lorentz invariant and satisfies cluster separability. The interactions are parametrized by analytic separable forms with parameters determined by fitting the $\pi N$ scattering phase shifts for $l\le 1$ up to 300 MeV and $\mathrm{NN}$ scattering phase shifts for $l\le 4$ up to 800 MeV. In fitting parameters and in the applications, nonrelativistic approximations are used for the baryons in the $N\Delta $ and $\mathrm{NN}\pi $ 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 $\Delta $ as well as $\mathrm{NN}$ interactions in $\mathrm{NN}\pi $ intermediate states are found to be important in channels coupled to $N\Delta s$ waves. These effects enhance the cross sections for ${\pi}^{+}+d\to \mathrm{pp}$ 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 $\pi $, $N$, and $\Delta $. Applications to the pion-deuteron system.

DOI: http://dx.doi.org/10.1103/PhysRevC.23.375

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

© 1981 The American Physical Society