  In evaluating differential cross section of elastic scattering, different
theories were applied to low-momentum and relativistic particles. For
low-momentum motion, Lippmann-Schwinger scattering equation was applied, called
fundamental formula; while for relativistic particles, a general scattering
theory was used which calculates S matrix. In this paper, Lippmann-Schwinger
equation is applied uniformly to both low-momentum and relativistic particles.
The cross sections are valuated to the first order of Born approximation.
One-body time-independent Green's functions for relativistic free particles are
given. Compared to the general scattering theory, the fundamental theory has a
clearer physical picture and the approximations made are more explicit.
