Folding model study of the elastic $\alpha + \alpha$ scattering at low energies

The folding model analysis of the elastic $\alpha + \alpha$ scattering at the incident energies below the reaction threshold of 34.7 MeV (in the lab system) has been done using the well-tested density dependent versions of the M3Y interaction and realistic choices for the $^4$He density. Because the absorption is negligible at the energies below the reaction threshold, we were able to probe the $\alpha + \alpha$ optical potential at low energies quite unambiguously and found that the $\alpha + \alpha$ overlap density used to construct the density dependence of the M3Y interaction is strongly distorted by the Pauli blocking. This result gives possible explanation of a long-standing inconsistency of the double-folding model in its study of the elastic $\alpha + \alpha$ and $\alpha$-nucleus scattering at low energies using the same realistic density dependent M3Y interaction.