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Non-local effects on the heavy-ion fusion at sub-barrier energies

We investigate the effect of Pauli non-locality in the heavy-ion optical potential on sub-barrier fusion reactions. The São Paulo potential, which takes into account the Pauli non-locality and has been widely used in analyzing elastic scattering, has also recently been applied to heavy-ion fusion. However, the approximation employed in deriving the São Paulo potential, based on the Perey-Buck semi-classical treatment of neutron induced reactions, must be assessed for charged particles tunneling through a barrier. It is the purpose of this note to look into this question. We consider the widely studied system $^{16}$O + $^{208}$Pb at energies that span the barrier region from 10 MeV below to 10 MeV above. It seems that the non-locality plays a minor role. We find the São Paulo potential to be quite adequate throughout the region.