Two-Body Dirac Equations for Nucleon-Nucleon Scattering

Abstract

We investigate the nucleon-nucleon interaction by using the meson exchange model and the two body Dirac equations of constraint dynamics. This approach to the two body problem has been successfully tested for QED and QCD relativistic bound states. An important question we wish to address is whether or not the two body nucleon-nucleon scattering problem can be reasonably described in this approach as well. This test involves a number of related problems. First we must reduce our two body Dirac equations exactly to a Schroedinger-like equation in such a way that allows us to use techniques to solve our two body Dirac equations already developed for Schroedinger-like systems in nonrelativistic quantum mechanics. Related to this we present a new derivation of Calogero's variable phase shift differential equation for coupled Schroedinger-like equations. Then we determine if the use of nine meson exchanges in our two body Dirac equations give a reasonable fit to the experimental scattering phase shifts for n-p scattering. The data involves seven angular momentum states including both singlet and the triplet spin states with orbital angular momentum 0,1,2. Two models that we have tested give us a fairly good fit. The parameters obtained by fitting the n-p experimental scattering phase shift give a fairly good prediction for most of the p-p experimental scattering phase shifts examined (for the spin singlet S and D states and spin triplet P states). Thus the two body Dirac equations of constraint dynamics presents us with a fit that encourages the exploration of a more realistic model. We outline generalizations of the meson exchange model for invariant potentials that may possibly improve the fit.

87 pages, 22 figures

Cited by in corpus (17)

• Vacuum Choices and the Predictions of Inflation
• Lectures on string theory and cosmology
• Relativistic Calculation of the Meson Spectrum: a Fully Covariant Treatment Versus Standard Treatments
• Singularity Structures in Coulomb-Type Potentials in Two Body Dirac Equations of Constraint Dynamics
• Hamiltonian Relativistic Two-Body Problem: Center of Mass and Orbit Reconstruction
• Tests of Two-Body Dirac Equation Wave Functions in the Decays of Quarkonium and Positronium into Two Photons
• Applications of Two-Body Dirac Equations to the Meson Spectrum with Three versus Two Covariant Interactions, SU(3) Mixing, and Comparison to a Quasipotential Approach
• Magnetic States at Short Distances
• Two fermion relativistic bound states
• Representations of relativistic particles of arbitrary spin in Poincaré, Lorentz, and Euclidean covariant formulations of relativistic quantum mechanics
• Two fermion relativistic bound states: hyperfine shifts
• Baryon Spectrum Analysis using Dirac's Covariant Constraint Dynamics
• Microscopic analysis of K^+-nucleus elastic scattering based on K^+N phase shifts
• Relativistic Nucleon-Nucleon potentials using Dirac's constraint instant form dynamics
• Two gamma quarkonium and positronium decays with Two-Body Dirac equations of constraint dynamics
• Meson-Meson Scattering in Relativistic Constraint Dynamics
• Relativistic correction to the dissociation temperature of B_c mesons in the hot medium