A full relativistic treatment in analyzing α-12C and α-40,42,44,48Ca elastic scattering data at 1.37 GeV

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 12C and calcium isotopes 40,42,44,48Ca. 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 Schr¨odinger equation and successfully analyzing the α- 12C and α-40,42,44,48Ca 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 Schr¨odinger equation and the codes are modified accordingly.