Two Body Dirac Equations and Nucleon Nucleon Scattering Phase Shift Analysis

In this dissertation, the nucleon-nucleon interaction is investigated 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 this approach is also valid in the two body nucleon-nucleon scattering problem. This test involves a number of related problems.

First we must reduce our two body Dirac equations exactly to a Schr¨odinger-like equation. This can be done without making any assumptions or approximations and unlike other relativistic approaches these equations have effective potentials that are local. We then develop a matrix scale transformation that successfully removes first derivative terms that appear naturally in those Schr¨odinger-like equations because they are inherent in the our two body Dirac equations. This removal is important since it then allows us to use techniques to solve our two body Dirac equations that have been already developed for Schr¨odinger-like systems in nonrelativistic quantum mechanics.

We use nine mesons in our two body Dirac equations to fit the experimental scattering phase shifts for n-p scattering. The data involves seven angular momentum states including the singlet states1S0, 1P1, 1D2 and the triplet states 3P0, 3P1, 3S1, 3D1. Two models that we have tested give us a fairly good fit. The nucleon-nucleon potentials that we use are also called the semi-phenomenological potentials due to the incorporating of the meson exchange model into the invariant potentials appearing in our Dirac equation. Our approach gives the nucleon-nucleon interaction a physical meaning beyond just the curve fitting which a purely phenomenological potentials provides.

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 shift (for states of singlet 1S0, 1D2 and triplet 3P0, 3P1). This means that the two body Dirac equations of constraint dynamics show promise in describing the nucleon-nucleon interaction. We outline generalizations of the meson exchange model for the invariant potentials that may possibly improve the fit.