On the Dirac Scattering Problems.

We consider a method of solving the Dirac scattering problem based on an approach previously used by the authors to solve the Schrodinger scattering problem to develop a conditional exact scattering solution and an unconditional series solution. We transform the Dirac scattering problem into a form that facilitates a soltuion based on the relativistic Lippmann-Schwinger equation using the relativistic Green's function that is transcendental in terms of the scattered field. Using the Dirac operator, this solution is transformed further to yield a modified relativistic Lippman-Schwinger equation that is also transcendental in terms of the scattered field. This modified solution faclitates a condition under which the solution for the scattered field is exact. Further, by exploiting the simultaneity of the two solutions available , we show that it is possible to define an exact (non-conditional) series solution to the problem.