Abstract:A simple optical potential of Woods-Saxon form is used within the framework of the Klein-Gordon equation, for the first time, to analyze the elastic differential cross sections for 1.37 GeV (lab) incident α -particles on 12 C and calcium isotopes 40,42,44,48 Ca. The relativistic energy-momentum relation assures the need for relativistic calculations.As such, the previously determined parameters of all optical potential forms, used in the nonrelativistic Schrödinger equation and successfully analyzing the α -12 C and α - 40,42,44,48 Ca data at 1.37 GeV, are to be revised. In the presence of Coulomb potential, as in the cases under consideration, the asymptotic solution of the Klein-Gordon equation differs from the corresponding one for the Schrödinger equation and the codes are modified accordingly.