Phenomenological Hamiltonian for pions, nucleons, and. delta. isobars: Applicationsto the pion-deuteron system

Journal Article · Thu Jan 01 04:00:00 EST 1981 · Phys. Rev., C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.23.375· OSTI ID:6729764

Betz, M; Lee, T H

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 NN, N..delta.., and NN..pi.. states with the following interaction mechanism: (1) a ..delta..arrow-right-leftN..pi.. vertex in the ..pi..N-P/sub 33/ channel, (b) two-body ..pi..N..--> pi..N interactions in other ..pi..N channels, and (c) two-body interactions for NN..-->..NN, N..delta -->..N..delta.., and NNarrow-right-leftN..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< or =1 up to 300 MeV and NN scattering phase shifts for l< or =4 up to 800 MeV. In fitting parameters and in the applications, nonrelativistic approximations are used for the baryons in the N..delta.. and 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 NN interactions in 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../sup +/+d..-->..pp by 40% in the resonance region. From the two-baryon Hamiltonian we construct a many-body Hamiltonian for nonrelativistic baryons.

• Research Organization: Argonne National Laboratory, Argonne, Illinois 60439
• OSTI ID: 6729764
• Journal Information: Phys. Rev., C; (United States), Journal Name: Phys. Rev., C; (United States) Vol. 23:1; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653003* -- Nuclear Theory-- Nuclear Reactions &amp; Scattering
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BANACH SPACE
BARYON-BARYON INTERACTIONS
CROSS SECTIONS
ELASTIC SCATTERING
HADRON-HADRON INTERACTIONS
HAMILTONIANS
HILBERT SPACE
INTERACTIONS
INVARIANCE PRINCIPLES
LORENTZ INVARIANCE
MANY-BODY PROBLEM
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATRIX ELEMENTS
MESON-BARYON INTERACTIONS
MESON-NUCLEON INTERACTIONS
MULTIPLE SCATTERING
NUCLEON-NUCLEON INTERACTIONS
PARTICLE INTERACTIONS
PHASE SHIFT
PION-DEUTERON INTERACTIONS
PION-NUCLEON INTERACTIONS
QUANTUM OPERATORS
SCATTERING
SPACE