The adiabatic approximation, frequently utilized in treating bound states of quantum-mechanical systems, is shown to be applicable also to scattering processes in cases for which the number of excited states of the target contributing significantly to the wave function is limited, and for which the time of traversal of the scattered particle through the region of interaction is small compared with the period of the target motion excitable in the collision. In this approximation, calculation of partial inelastic cross sections is reduced to two steps: (1) determination of the elastic scattering amplitude for fixed target coordinates and (2) subsequent evaluation of scalar products in the space of the target. The method is illustrated by means of a simple one-dimensional example. Calculation of cross sections for nuclear rotational excitation by neutrons is formulated.