On the “quantum rainbow” in surface scattering

In this letter we propose a new method to compute the scattering amplitudes of atoms from a corrugated wall model of a crystal surface. The method method requires reasonable computing time and converges rapidly to the solution of the scattering amplitudes (within 0.01% in each beam and satisfying unitarity) for any corrugation such that kζ₀ < 4.5 and ζ₀ < 0.35 Å, where k is the magnitude of the incident wave vector and ζ₀ the amplitude of the corrugation. These conditions for kζ₀ and ζ₀ are satisfied for any crystal surface and light scattering atoms (H and He) at thermal energies which makes the method appropriate for the system He, LiF for which results are presented comparing them with recent experimental data.