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A Full Relativistic Treatment In Analyzing $\Alpha $-$^{12}$C And $\Alpha $-$^{40,42,44,48}$Ca Elastic Scattering Data At 1.37 Gev, Zuhair Fayyad Mahmoud Shehadeh

Turkish Journal of Physics

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 $\alpha $-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 $\alpha $-$^{12}$C and $\alpha $-$^{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 …