Theory of vibrational, rotational, and phonon inelastic collisions of a triatomic molecule by a crystal surface. I. A quantum-mechanical treatment of the scattering dynamics.

Abstract

Based on time-independent scattering theory, we present a systematic formulation of triatomic-molecule--crystalline-surface scattering dynamics including the vibrational states of the solid (phonons) and the vibrational and rotational states of the molecular projectile. The vibrational and rotational motions of the triatomic molecule are treated by separating out the motion of the center of mass of the molecule in a manner that is suitable for treating the surface collisions with a molecular projectile. This method can be essentially applied to a general polyatomic projectile case. From the translational invariance of the full Hamiltonian, we employ the total (projectile+phonon) momentum representation parallel to the surface to derive the properties of the total scattering wave function of the triatomic-molecule--crystalline-surface system, a representation of the simultaneous phonon and vibrational-rotational transition potential matrix, and the characteristics of the independent physical solutions for a given energy and momentum of the system.