Theory of vibrational, rotational, and phonon inelastic collisions of a triatomic molecule by a crystal surface. II. Approximate methods and applications to resonance and adsorption.

Abstract

Realistic theoretical approximation schemes for the calculation of phonon and vibrational-rotational (triatomic) molecule--crystal-surface inelastic scattering were derived from the formulation in the preceding paper. These schemes can be adopted to a flexible input potential and are at the same time capable of yielding effective ab initio computation. An iterative coupled-integral-equation method thus obtained is much more tractable than its counterpart of the coupled differential equation when phonons in the solid and vibrations and rotations of the molecular projectile are taken into account. This approach is further useful for the triatomic projectile case where multiphonon transitions become more probable compared to the light atom and/or diatom projectile, since it yields calculational procedures of DWBA of any higher orders as a byproduct. A rotationally impulsive integral-equation scheme appropriate for the triatomic molecular projectile (and basically applicable to the polyatomic case) with simplification of the rotational states of the molecule in the calculational procedures is also derived from this method.For the purpose of studying direct (nonresonant) inelastic scattering of the simultaneous diffraction, phonon, and vibrational-rotational transitions, angular, velocity, and vibrational-rotational state distribution of the scattered molecule, a coupled-diffractive-channel transition-matrix (CDCTM) method and a coupled-molecular-state transition-matrix (CMSTM) method with an exponential unitarization scheme are obtained. The former may be used when the corrugation of the molecule--crystal-surface interaction potential is significant as in nonmetallic crystals and the latter could be used when the dependence on the internal coordinates of the molecule or the anisotropy is considerably large in the interaction potential. As an application of the present scattering formulation, a bound-state resonance scattering method for a (triatomic) molecule-surface system is presented within the framework of a Feshbach-type internal excitation approach. Our emphasis here is on a systematic and unified treatment of the mediations of the diffraction, phonon, and vibration-rotation in selective adsorption and desorption, which are analogous to compound nucleus theory in nuclear reaction studies.The present method describes such trapping-desorption processes for inelastic (indirect) resonance scattering. Our method is adoptable again to arbitrary input potentials, and even with inclusion of phonons and vibrations and rotations, it yields efficient ab initio calculational procedures from which the resonance energies, the energy shift, width function, line shapes, and the intensities of the simultaneous diffraction, phonon, and vibrational-rotational transitions can be obtained. Among other effective calculational schemes, we discuss a method where the bound-state resonance scattering amplitude is computed from our explicit expressions with simplified wave functions. They are obtained as products of the spatial wave function generated from the elastic diffraction potential and vibrational-rotational and phonon states. The nonresonant potential scattering amplitude is obtained within open channels from, e.g., a coupled-diffractive-channel transition-matrix approach. Finally, a method of obtaining the quantal trapping or physisorption probabilities of the molecule, which deals with a half-collision process, is presented as another application of our scattering formulation.