A semiclassical sudden approximation for rotational excitation

Abstract

Within the energy-sudden approximation the motion of the target and the projectiles can be decoupled and the transition amplitude for differential inelastic cross sections can be expressed entirely in terms of transition amplitudes involving only orbital quantum numbers. This property naturally lends itself to a purely quantal treatment of the target dynamics and a classical or semiclassical treatment of the relative motion with no further approximation: the point of this separation being that the former usually involves small and the latter large quantum numbers. For rotational excitation of the linear molecules the axial symmetry reduces the problem further to finding a set of one-dimensional transition amplitudes. The authors show how these elements can be combined to produce a simple yet effective and accurate method of obtaining inelastic differential transition amplitudes using only classical trajectories. The method has none of the problems associated with the usual purely classical descriptions; it treats interference effects and tunnelling accurately and handles target quantisation exactly.