A full relativistic treatment in analyzing $\alpha $-$^{12}$C and $\alpha $-$^{40,42,44,48}$Ca 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 $\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 the Klein-Gordon equation differs from the corresponding one for the Schrödinger equation and the codes are modified accordingly.

Keywords: Alpha-nucleus potential, elastic scattering, high energy physics

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