Classical S-Matrix for Vibrational Excitation of H2 by Collision with He in Three Dimensions

Abstract

Complex‐valued classical trajectories have been computed by direct numerical integration of the equations of motion for three‐dimensional collisions of He and H2, and from such trajectories classical S‐matrix elements for transitions between specific rotational‐vibrational states of H2 have been constructed. At the collision energies employed (∼1–2 eV) all vibrationally inelastic transitions are classically forbidden, thus the need for analytically continued, complex‐valued trajectories. Comparison with the quantum mechanical calculations of Eastes and Secrest shows excellent agreement between the quantum and uniform semiclassical transition probabilities. Since, however, for three‐dimensional collision systems one is seldom concerned with individual S‐matrix elements, but rather sums over many of them, an important practical feature is developed which shows how one can combine the usual Monte Carlo classical treatment of some of the internal degrees of freedom with a semiclassical state‐by‐state description of others; i.e., one can ``quantize'' only those degrees of freedom that are highly quantumlike (e.g., vibration). This ``partial averaging'' approach also greatly simplifies the practical aspects of applying classical S‐matrix theory to systems with several internal degrees of freedom.