Heavy-ion collisions at energies around the Coulomb barrier provide an ideal opportunity to study quantum tunneling phenomena in systems with many degrees of freedom. It is now well known that a barrier distribution can be extracted experimentally from the fusion excitation function $\sigma_{\rm fus}(E)$. This method has opened up the possibility of using the heavy-ion fusion reaction as a ``quantum tunneling microscope'' in order to investigate both the static and dynamical properties of atomic nuclei.

It has been suggested that the same information as the fusion cross section may be obtained from the cross section for quasi-elastic scattering (a sum of elastic, inelastic, and transfer cross sections) at large angles. In this talk, we will study in detail the properties of the barrier distribution extracted from large-angle quasi-elastic scattering of heavy ions at energies near the Coulomb barrier. We will argue that the quasi-elastic barrier distribution offers an interesting tool for investigating unstable nuclei. We will illustrate this for the $^{32}$Mg + $^{208}$Pb reaction, where the quadrupole collectivity of the neutron-rich $^{32}$Mg remains to be clarified experimentally.