Theory of phonon inelastic atom–surface scattering. II. Approximate methods and applications to resonance and adsorption

Abstract

Approximate theoretical schemes for the calculation of the phonon inelastic scattering were derived from the formulation in the preceding paper. They can be adopted to flexible input potentials and are more realistic compared to the schemes that have been employed so far and at the same time are capable of yielding effective ab initio computation. An iterative coupled integral equation method thus obtained is much more tractable than that of the coupled differential equation when the phonons are taken into account. In this approach, the multiphonon transitions are readily obtained as higher order processes with the potential matrix elements being limited to the dominant one-phonon transitions. The S matrix elements of both elastic reflection and simultaneous diffraction and phonon transitions can also be obtained from the coupled channel transition matrix (CCTM) approach derived from the diffractive wave Green function where the coupling between the reciprocal lattice points due to the atom–surface interaction are taken into consideration. A unitarization method of CCTM S matrix was also discussed. Employing the diffractive standing wave Green function, we derived the coupled channel reactance matrix (CCRM) method. Some advantages of this scheme over CCTM are that the scattering wave functions needed for the calculation are all real, and the unitarized S matrix can be directly obtained within a truncated basis set. As an application of the present scattering formulation, the bound state resonance scattering method of the atom–surface system was presented within the framework of Feshbach internal excitation approach. Our emphasis here is the role of the phonon transitions in the selective adsorption and desorption. Our method is adoptable again to arbitrary and flexible input potentials and yields ab initio calculational procedures from which the resonance energies, the energy shift and width functions, the line shapes, and the intensities of the simultaneous diffraction and phonon transitions can be obtained. Among other effective calculational schemes, we discussed a method where the bound state resonance scattering amplitude is computed from simplified wave functions which are obtained as products of the spatial wave function generated from the elastic diffraction potential and that of the phonon state. The nonresonant potential scattering amplitude in the method is obtained from CCTM approach within the open channels. Finally, a method of obtaining the quantal adsorption rates and sticking probabilities, which deals with the half-collision processes, was presented as another application of our scattering formulation.