The cross sections for the elastic scattering reactions
{112,124}Sn(a,a){112,124}Sn at energies above and below the Coulomb barrier are
presented and compared to predictions for global alpha-nucleus potentials. The
high precision of the new data allows a study of the global alpha-nucleus
potentials at both the proton and neutron-rich sides of an isotopic chain. In
addition, local alpha-nucleus potentials have been extracted for both nuclei,
and used to reproduce elastic scattering data at higher energies. Predictions
from the capture cross section of the reaction 112Sn(a,g)116Te at
astrophysically relevant energies are presented and compared to experimental
data.Comment: 20 pages, 10 figures, accepted for publication in Phys. Rev.
