  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.
