Interplay of classical and quantal descriptions of heavy-ion interactions

Quasielastic collisions between complex nuclei, elastic, inelastic, and few-nucleon transfer are discussed both as a classical and quantal process. The classical trajectories can be used to illuminate the dependence of the quantal calculations on the physical parameters, and indeed can be used in a predictive way to suggest under what circumstances ambiguities can be resolved. The $S$-matrices for various quasielastic processes are exhibited and the quantal analog of the classical deflection function is compared with the classical one. The smooth behavior of the $S$-matrix for large angular momentum $l$ suggests the possibility of a two-part approach where the lower $l$ region is computed quantum mechanically, and the high-$l$ region is either parametrized, treated semiclassically, or interpolated between widely spaced $l$'s. The much greater sensitivity of several-nucleon transfer reactions to the interior region compared to elastic and inelastic scattering is stressed. Various aspects of two-nucleon transfer are discussed, including multiple-step processes, their dependence upon collectivity of the intermediate states, and the opposite sense of the interference involved in pickup and stripping reactions to vibrational states.