The double-folding formalism for the $\alpha$-nucleus optical potential is revised to study the exchange effects and density dependence of the effective nucleon-nucleon $\mathrm{}\left(\mathrm{NN}\right)\mathrm{}$ interaction in detail. A realistic density dependent M3Y interaction, based on the G-matrix elements of the Paris NN potential, has been used in the folding calculation. The local approximation for the nonlocal one-body density matrix in the calculation of the exchange potential was tested by using the harmonic oscillator representation of the nonlocal density matrices of the $\alpha$-particle and target nucleus. The inclusion of a realistic density dependence into the effective NN interaction was shown to be vital for a correct description of the refractive $\alpha$-nucleus scattering data. A high sensitivity of the density distributions of the $\alpha$-particle and target nucleus to the shape of the $\alpha$-nucleus potential was found, which can be used in the folding analysis to test various density models for the $\alpha$-particle and target as well as to choose the most realistic approximation for the overlap density in the dinuclear system. Our results also stress the importance of $\alpha$-nucleus scattering experiment in the nuclear structure study.

• Received 19 September 2000

DOI:https://doi.org/10.1103/PhysRevC.63.034007