Long-lived states in atom--surface collisions: Reciprocal lattice vector poles

The resonance energies of long-lived states in elastic scattering of atoms by solid surfaces are related to the trajectories of poles of the scattering matrix in the planes of the complex components of the reciprocal vector G. Resonance trajectories, similar to Regge-pole trajectories, are discussed for scattering of He by LiF(001) at fixed angle and varying wavelength. This approach gives insight into the ordering of resonances. A construction is described in the plane of the G vector components to identify possible resonance energies and to discuss their high-energy behavior