The elastic scatterings for the $\alpha$ + $^{40}$Ca and the $\alpha$ + $^{58}$Ni systems at $E_{lab}$ = 240 MeV have been analyzed within the framework of the Coulomb-modified Glauber model using two kinds of Gaussian density parameters for the target nuclei. The first one is to use Gaussian density parameters obtained from the root-mean-square radius. The second one is to use parameters calculated by matching the Gaussian density to the two-parameter Fermi density. The results with surface-matched Gaussian densities provide reasonable agreement with the experimental data, but the results without matching do not. The oscillatory structures observed in the angular distributions of both system can be interpreted as being due to the strong interference between the near-side and the far-side scattering amplitudes. The differences between the phase shifts obtained from the two methods are examined. We also investigate the effect of these differences on the differential and reaction cross sections, the transmission functions and the strong absorption radii.

Keywords: Coulomb-modified Glauber model, Surface-matched Gaussian density, Elastic scattering, $\alpha+^{40}$Ca, $\alpha+^{58}$Ni