The physical interaction potential of gas atoms with single-crystal surfaces, determined from gas-surface diffraction experiments

A comprehensive survey and data collection of experimental results achieved from diffracting beams of light gases like H, D, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, and ${\mathrm{H}}_2$ from single-crystal surfaces (alkali halides, oxides, and graphite) is given, and it is shown that gas-surface diffraction is a valuable tool to get detailed information on the physical gas-surface potential: (a) From comparison of diffracted beam intensities with calculations in a corrugated hardwall approximation the periodic structure of the interaction potential is obtained together with information on the atomic structure at the surface. (b) From bound-state resonance investigations one gets information on the different terms of the gas-surface potential in Fourier expansion $v\left(r\right)\mathrm{} ={\Sigma }_G v_G\mathrm{}\left(z\right)\mathrm{}\exp \left(iG·R\right)$: the achieved spectrum of binding energies {$E_j$} can be used to construct the main term $v_{00}\mathrm{}\left(z\right)\mathrm{}$, whereas observed splitting of degenerate bound states allows evaluation of the strength of the periodic terms $v_{\mathrm{G}}\mathrm{}\left(z\right)\mathrm{}$. (c) from $E_j$ levels near the dissociation limit the constant $C_3$ of gas-surface long-range dispersion attraction can be determined. Finally, regarding the experimental results on $C_3$ and the potential well depth $D$, two semiempirical rules are established: $C_3=K_C·\alpha \frac{(\epsilon -1)}{(\epsilon +1)}$ and $D=K_D·\alpha \frac{(\epsilon -1)}{(\epsilon +1)}$. These rules allow the calculation of $C_3$ and $D$ from the static electric polarizability $\alpha$ of the atom, the optical dielectric constant $\epsilon$ of the solid, and the system-independent constants $K_C$, $K_D$ given in the text. Calculated values of $D$ for several gas-surface systems are given in a table.