Friction-Induced Energy-Loss Rainbows in Atom Surface Scattering

The rainbow is due to extrema of the angular deflection function of light impinging on water drops. Generically, extrema of suitably defined deflection functions lead to rainbows. These include angular and rotational rainbows in surface scattering and more. Here we introduce the concept of an “energy-loss deflection function” for scattering of particles from a periodic surface whose extrema lead to a new form—the “energy-loss rainbow” which appears as multiple maxima in the final energy distribution of the scattered particle. Energy-loss rainbows are caused by frictional phonon effects which induce structure in the energy-loss distribution instead of “washing it out.” We provide evidence that they have been observed in Ne scattering on self-assembled monolayers.

Figure 1

$T=0\mathrm{K}$ theoretical computation of the energy loss to the bath as a function of the impact parameter for the scattering of Ar from a LiF(100) surface. The solid (black), dashed (red), dotted (green) and dot-dashed (blue) lines correspond to incident angles of 0°, 15°, 45°, and 60°, respectively. Note the multiple extrema of the “energy-loss deflection functions”.

Figure 2

Theoretical final energy distributions of Ar scattered on a LiF(100) surface at incidence angles of 0°, 15°, 45°, and 60° displayed in panels (a)–(d). The (green) dots, (red) circles, and (blue) squares correspond to the numerical distributions calculated at $T=0.5$, 30, and 90 K, respectively. The solid lines show the analytic distributions calculated from Eq. (2) using the modified form of the variance.

Figure 3

Theoretical joint energy loss and angular distribution for Ar scattered from LiF at $T=30\mathrm{K}$ and incident energy of 3 eV. Also shown are the integrated angular and energy-loss distributions. Note the relation between the angular rainbows and the energy-loss rainbows.

Figure 4

Comparison of theoretical (crossed lines) and experimental [16] (solid lines) energy-loss distributions for the scattering of Ne from a SAM of 1-decanethiol on Au(111).