Nuclear shape dynamics in low-energy heavy-ion reactions

We discuss recent theoretical developments in low-energy heavy-ion reactions. To this end, we put emphasis on a viewpoint of probing nuclear shapes with heavy-ion reactions. We first discuss a single-channel problem with an optical potential model. We particularly discuss a microscopic modeling of the imaginary part of an optical potential as well as a visualization of quantum interference phenomena observed in heavy-ion elastic scattering. We then discuss multi-channel scattering problems, and demonstrate that heavy-ion fusion reactions at energies around the Coulomb barrier are sensitive to the shape of colliding nuclei, providing a powerful tool to probe nuclear shapes. We finally point out that relativistic heavy-ion collisions have large similarities to low-energy heavy-ion reactions in the context of nuclear shape dynamics.