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We develop and test an ab initio time-dependent Basis Function (tBF) methodto solve non-perturbative and time-dependent problems in quantum mechanics. Forour test problem, we apply this method to the Coulomb excitation of thedeuteron by an impinging heavy ion. In the tBF method applied to deuterium, weemploy wave functions for its bound and excited states to calculate itstransition probabilities and the r.m.s. radius during the scattering process.For comparison, corresponding results based on first-order perturbation theoryare also provided. For the Coulomb excitation process in a weak andtime-varying Coulomb field, where higher-order effects are negligible, weobtain good agreement of the results based on these two methods. The tBF methodis then applied to the Coulomb excitation process with stronger external field.The higher-order effects, such as those appearing in the reorientation of thepolarization of the deuteron system, are analyzed.

Deuteron Coulomb Excitation in Peripheral Collisions with a Heavy Ion