We study in detail the barrier distributions extracted from large-angle quasielastic scattering of heavy ions at energies near the Coulomb barrier. Using a closed-form expression for scattering from a single barrier, we compare the quasielastic barrier distribution with the corresponding test function for fusion. We examine the isocentrifugal approximation in coupled-channels calculations of quasielastic scattering and find that for backward angles it works well, justifying the concept of a barrier distribution for scattering processes. This method offers an interesting tool for investigating unstable nuclei. We illustrate this for the Mg-32+Pb-208 reaction, where the quadrupole collectivity of the neutron-rich Mg-32 remains to be clarified experimentally.
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