Comparison of exact and approximate cross-sections in relativistic Coulomb excitation

We present a new method of obtaining time-dependent matrix elements of the electromagnetic pulse produced by a highly-relativistic projectile. These matrix elements are used in a coupled-channel calculation to predict the cross-sections for population of 1- and 2-phonon states of the giant dipole resonance. Comparisons are made with the predictions of the long-wavelength and Born approximations.