Bakamjian-Thomas Theory and the Serber Model

The Bakamjian-Thomas theory is used to obtain relativistic scattering equations for the relative motion of two particles. These are presented in a squared and in an unsquared form, and both forms are realized in Cartesian coordinates and reduced to partial-wave equations for the case of an isotropic potential dependent only on the Bakamjian-Thomas relative coordinate. These equations are shown to bear a resemblance to the Klein-Gordon equation with Serber's potential $A$. The first Born approximation of the scattering amplitude computed from the Bakamjian-Thomas equations and that computed from the Klein-Gordon equation are shown to agree as $k\to \infty$. Differences between these approaches are expected to show themselves mainly at large-angle scattering, since the (unsquared) Bakamjian-Thomas Green's function differs appreciably from that of the Klein-Gordon equation only for small $r$.