Coulomb dissociation is an especially simple and important reaction mechanism. Since the perturbation due to the electric field of the (target) nucleus is exactly known, firm conclusions can be drawn from such measurements. Electromagnetic matrixelements and astrophysical S-factors for radiative capture processes can be extracted from experiments. We describe the basic elements of the theory of nonrelativistic and relativistic electromagnetic excitation with heavy ions. This is contrasted to electromagnetic excitation with leptons (electrons), with their small electric charge and the absence of strong interactions. We discuss various approaches to the study of higher order electromagnetic effects and how these effects depend on the basic parameters of the experiment. The dissociation of neutron halo nuclei is studied in a zero range model using analytical methods. We also review ways how to treat nuclear interactions, show their characteristics and how to avoid them (as far as possible). We review the experimental results from a theoretical point of view. Of special interest for nuclear structure physics is the appearence of low lying electric dipole strength in neutron rich nuclei. Applications of Coulomb dissociation to some selected radiative capture reactions relevant for nuclear astrophysics are discussed. The Coulomb dissociation of 8B is relevant for the solar neutrino problem. The potential of the method especially for future investigations of (medium) heavy exotic nuclei for nuclear structure and astrophysics is explored. We conclude that the Coulomb dissociation mechanism is theoretically well understood, the potential difficulties are identified and can be taken care of. Many interesting experiments have been done in this field and many more are expected in the future.
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