Three dimensional classical theory of rainbow scattering of atoms from surfaces

In this work, we extend to three dimensions our previous stochastic classical theory on surface rainbow scattering. The stochastic phonon bath is modeled in terms of linear coupling of the phonon modes to the motion of the scattered particle. We take into account the three polarizations of the phonons. Closed formulae are derived for the angular and energy loss distributions. They are readily implemented when assuming that the vertical interaction with the surface is described by a Morse potential. The hard wall limit of the theory is derived and applied to some model corrugated potentials. We find that rainbow structure of the scattered angular distribution reflects the underlying symmetries of the surface. We also distinguish between “normal rainbows” and “super rainbows”. The latter occur when the two eigenvalues of the Hessian of the corrugation function vanish simultaneously.