Abstract
A phenomenological optical-model analysis is performed for the elastic scattering of alpha particles on $^{40.42}$,44,48Ca at 1.37 GeV. Two geometries are considered for optical potentials, i.e., the traditional Woods-Saxon form and the double-Woods-Saxon form which can represent a change of the potential shape from the Woods-Saxon one. Among them, the best-fit potential has a ``Mexican-hat'' shape which is characterized by a long-ranged and weak attractive part in the surface region and a repulsion in the central region. From discussions on shape dependence of chi-square values, reaction cross sections, volume integrals, notch tests, and global potentials, a reasonable shape of the real part of the optical potential is suggested to be the ``Mexican-hat'' shape at this energy.
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