Dynamical effects as a window into van der Waals interactions in grazing-incidence fast He-atom diffraction from KCl(001)

In this paper we address, both experimentally and theoretically, the very grazing scattering of He atoms off KCl(001) with incidence along the $\langle 100\rangle$ channel. Our theoretical model combines a semiquantum description of the scattering dynamics and a high-precision interaction potential. By means of a thorough analysis of the quantum phase for in-plane scattering and rainbow trajectories, we are able to connect the presence of the physisorption well with the significant enhancements of the corrugation and rainbow angle, relative to the hard corrugated wall predictions. We trace this connection to dynamical effects on the incident and scattered beams due to their traversing of the physisorption well. Finally, we show that the inclusion of van der Waals interactions in the potential improves the theoretical accord with experiments for both the corrugation and the rainbow angle.

Figure 1

Sketch of the GIFAD geometry and sample pattern. He-KCl(001) system and incidence along $\langle 100\rangle$.

Figure 2

Two-dimensional diffraction charts, in terms of the normal energy $E_{\perp }$ and the azimuthal angle ${\phi }_f$ for impact energy $E=600$ eV. (a) Experiment and (b) SIVR simulation with the PBE PES.

Figure 3

Axial potential as a function of the He-surface distance $Z$ for fixed values of the coordinate $Y$ across the $\langle 100\rangle$ channel. Different exchange-correlation functionals are considered in each panel: (a) PBE, (b) vdW1, (c) vdW2, and (d) vdW3 (see text for the labeling of vdW approaches).

Figure 4

PBE equipotential curves of the axial potential along $\langle 100\rangle$ depicting the HCW (intrinsic) corrugation, the rainbow angle and in-plane $B$ and $M$ trajectories for a given $E_{\perp }$. Normal energy values are in meV. Nonlabeled curves correspond to values $-1,-2,-3,$ and $-4$ meV.

Figure 5

Surface corrugation as a function of the normal energy $E_{\perp }$ obtained from experimental GIFAD patterns, the PBE PES (HCW value) and SIVR simulations (with the PBE PES), the latter given by Eq. (4).

Figure 6

For border ($B$) and middle ($M$) trajectories, with $E_{\perp }=10$ meV and the PBE potential, we show (a) the phase ${\varphi }^{\left(\text{dyn}\right)}={\varphi }^{\left(\text{SIVR}\right)}-{\varphi }^{\left(\text{HCW}\right)}$ due to dynamical effects and (b) the axial potential along each trajectory. Both quantities are plotted as functions of Z.

Figure 7

Accumulated phase ${\mathrm{\Phi }}^{\text{(dyn)}}$ for border ($B$) and middle ($M$) trajectories (incoming path) as functions of $E_{\perp }$. Solid and dashed lines, respectively, correspond to ${\mathrm{\Phi }}^{\text{(dyn)}}$ evaluated in the attractive and the repulsive regions.

Figure 8

Rainbow angle as a function of $E_{\perp }$. Symbols and lines analogous to Fig. 5.

Figure 9

(a) SIVR trajectories deflected to ${\mathrm{\Theta }}_f\sim {\mathrm{\Theta }}_{rb}$, with $E_{\perp }=10$ meV and the PBE potential. (b) Axial potential along each of the depicted rainbow trajectories $z_t\left(y_t\right)$.

Figure 10

Corrugation as a function of $E_{\perp }$. Symbols and color lines analogous to Fig. 5 with (a) vdW1, (b) vdW2, and (c) vdW3 potentials. In all panels, red thin lines correspond to PBE-SIVR i (solid) and PBE-PES (dashed) results, and are meant to be used as a reference.

Figure 11

Rainbow deflection angle as a function of $E_{\perp }$. Symbols and lines analogous to Fig. 10.