Rainbow scattering under axial surface channeling from a KCl(001) surface

Fast He, Ne, Ar, and N atoms with projectile energies from 1 up to 60 keV are scattered under grazing polar angles of incidence from a flat and clean KCl(001) surface. For the scattering along low-index directions (axial surface channeling) we observe pronounced peaks in the angular distributions of scattered projectiles which can be attributed to rainbow scattering. From classical trajectory calculations based on universal and individual pair as well as density functional theory (DFT) potentials, we obtained corresponding rainbow angles for comparison with the experimental data. Fair agreement was found for DFT and individual pair potentials calculated from Hartree-Fock wave functions.

Figure 1

Potential energy as function of interatomic distance for (left) He-K, Ar-K, and N-K and (right) He-Cl, Ar-Cl, and N-Cl. Individual HF potentials are calculated in this work (blue circles) and by Kim and Gordon[24] (red triangles); blue and red solid curves show interpolation functions (for details, see text and Table ); green curves show OCB potential; black curves show ZBL potential. For calculation of individual HF potentials charge states of K${}^{+}$ and Cl${}^{-}$ ions were taken into account. (Note that the upper part of the potential-energy axis is scaled logarithm, whereas the lower part is linearly scaled.)

Figure 2

Equipotential lines of potential $V_{\mathrm{surface}}(x,z)$ for scattering of He atoms along $\langle 110\rangle$ of KCl(001) in an energy range 0.3–40 eV, where $V_{\mathrm{surface}}(x,z)$ is given by a sum of He-K and He-Cl string potentials. Contours are derived from individual HF potentials calculated (a) in this work, (b) by Kim and Gordon[24], and from (c) OCB and (d) ZBL potentials. For calculation of HF potentials charge states of K${}^{+}$ and Cl${}^{-}$ ions were taken into account.

Figure 3

Equipotential lines of potential $V_{\mathrm{surface}}(x,z)$ for scattering of (top) He and (bottom) Ar atoms along (left) $\langle 100\rangle$ and (right) $\langle 110\rangle$ of KCl(001) in an energy range 0.3–40 eV, where $V_{\mathrm{surface}}(x,z)$ is given by a sum of He-K${}^{+}$ and He-Cl${}^{-}$ and of Ar-K${}^{+}$ and Ar-Cl${}^{-}$ string potentials, respectively. Contours are derived from individual HF potentials calculated in this work, where charge states of K${}^{+}$ and Cl${}^{-}$ ions were taken into account. Projections of 50 calculated classical trajectories of He and Ar atoms with $E_{\perp }=1$ eV and 11 eV scattered along $\langle 110\rangle$ and $\langle 100\rangle$, respectively, are shown as gray curves. Rainbow angle ${\theta }_{\mathrm{rb}}$ is highlighted for scattering of Ar along $\langle 100\rangle$.

Figure 4

Equipotential lines of potential $V_{\mathrm{surface}}(x,z)$ for scattering of He atoms along (top) $\langle 100\rangle$ and (bottom) $\langle 110\rangle$ of KCl(001) in an energy range 0.3–11 eV. Contours are derived from DFT (solid curves) and individual HF (dashed curves) potentials calculated in this work, where charge states of K${}^{+}$ and Cl${}^{-}$ ions were taken into account.

Figure 5

Two-dimensional plots of angular distributions recorded by means of position-sensitive microchannel plate (MCP) detector for scattering of (top) 15-keV Ar atoms along $\langle 100\rangle$ under ${\phi }_{\mathrm{in}}=1.{53}^{\circ }$ with $E_{\perp }=10.7$ eV and (bottom) 7-keV He atoms along $\langle 110\rangle$ under ${\phi }_{\mathrm{in}}=0.{64}^{\circ }$ with $E_{\perp }=0.9$ eV from KCl(001). Annuli mark elastic scattered projectiles; solid and dashed lines mark rainbow angles ${\theta }_{\mathrm{rb}}$. Color code for two-dimensional angular distributions is as follows: red, high intensity; blue, low intensity.

Figure 6

Rainbow angles ${\theta }_{\mathrm{rb}}$ as function of normal energy $E_{\perp }$ for scattering of (a) He, (b) Ne, (c) Ar, and (d) N atoms from KCl(001) along $\langle 100\rangle$. Gray circles represent experimental data; curves represent results from classical trajectory calculations using individual HF potentials calculated in this work (black solid curve) and by Kim and Gordon[24] (red dashed curve), OCB (blue dash-dotted curve), and ZBL (green dotted curve) potentials.

Figure 7

“Inner” rainbow angles ${\theta }_{\mathrm{rb}}$ as function of normal energy $E_{\perp }$ for scattering of (a) He, (b) Ne, (c) Ar, and N atoms from KCl(001) along $\langle 110\rangle$ (same notation as in Fig. 6).

Figure 8

Rainbow angles ${\theta }_{\mathrm{rb}}$ as function of normal energy $E_{\perp }$ in a range 0.1–4.8 eV for scattering of He atoms from KCl(001) along (top) $\langle 100\rangle$ and (bottom) $\langle 110\rangle$ as shown in Figs. 6 and 7. Open gray circles represent experimental data, and the solid gray circles in the bottom panel represent experimentally determined values of the “outer” rainbow angle (not shown in Fig. 7; for details see text). Curves represent results from classical trajectory calculations using DFT potential (red solid and dashed curves) and individual HF potential (blue solid and dashed curves).