Trajectory Effects in Coulomb Excitation

Coulomb excitation has proven itself as an important tool for studying the structure of both stable and exotic nuclei.[1– 4] The phenomenon has been well-studied in a nonrelativistic context[5] and studied perturbatively in a relativistic one[6] by Alder and Winther. More recent experimental studies have considered multiple Coulomb excitation at relativistic energies.[2–4] Many calculations of high-energy Coulomb excitation include the effects of Coulomb deflection, but only through the effective impact parameter used in a straight-line trajectory.[7–11] The curvature of the trajectory is usually not taken into account. The curvature of the Coulomb trajectory increases the distance between the projectile and target, relative to a straight-line trajectory, and is thus expected to decrease Coulomb excitation, which is strongly dependent on the separation. In the following, we derive the semiclassical coupled-channel equations for Coulomb excitation and then use them to compare excitation cross sections obtained using straight-line and Coulomb trajectories.