Evolution Operator And Energy Spectrum Of A Quasiclassical Particle Interacting With Bosons: Application To Atom Surface Scattering

We investigate the properties of the interaction of a particle with a boson field describing the response of a solid in the limit in which the interaction matrix elements may be considered as quasiclassical and the particle-boson coupling linear but not necessarily weak. We start by expressing the evolution operator of the system in a convenient form of an exponentiated nested commutator expansion in powers of the interaction potential. From this we are able to estimate under which conditions on the particle motion the contributions of the higher order expansion terms become small, irrespective of the coupling strength. Neglecting such small terms in the exponent of the evolution operator, we can calculate the energy excitation spectrum characteristic of the coupled system or of any of its constituents (particle or boson field). These spectra have the appearance of an exponentiated Born approximation (EBA) which contains and interpolates smoothly between the more frequently used distorted wave Born approximation (DWBA) and the trajectory approximation (TA), thereby covering a wide range of the parameter space for the description of the particle-boson interaction dynamics. The shape of the spectra and their characteristics (the weight of the elastic line or the Debye-Waller factor (DWF), the mean number of excited bosons, and the mean energy transfer in the course of the interaction) are discussed and shown to be very sensitive to the (non)adiabaticity of the switching of the interaction and the magnitude of the particle mass M. In the case of nonadiabatic switching on (as e.g. in photoemission) and linear bosonic density of states, we retrieve in the limitM→∞the familiar infrared threshold divergences in the spectrum of the system. In the opposite case of adiabatic switching rates typical of scattering, the spectra exhibit a well-defined elastic line and a finite DWF. The case of surface scattering is discussed in more detail for the example of neutral atom scattering from dispersionless surface phonons in atomic adlayers.