Effects of the surface Miller index on the resonant neutralization of hydrogen anions near Ag surfaces

We compare the resonant neutralization dynamics of hydrogen anions in front of plane Ag surfaces of symmetries (100) and (111) using a Crank–Nicholson wave-packet propagation method. For the $\text{Ag}\left(100\right)$ surface, the surface state, degenerate with the valence band, rapidly decays while being populated by the ion. For $\text{Ag}\left(111\right)$, in contrast, the population of a quasi-local Shockley surface state inside the projected $L$-band gap impedes the electron decay into the bulk along the direction normal to the surface. This difference in the decay pattern strongly affects the survival of $1\text{keV}$ ions scattered from these surfaces. Scattering off the $\text{Ag}\left(111\right)$ surface results in about an order of magnitude higher ion-survival as a function of the exit angle with respect to the surface plane compared to that off $\text{Ag}\left(100\right)$. Results for $\text{Ag}\left(111\right)$ show good agreement with measurements [Guillemot and Esaulov, Phys. Rev. Lett. 82, 4552 (1999)].

Figure 1

(Color online) The projected density of states at the ion-surface separation $D=6\text{a.u.}$ for $\text{Ag}\left(100\right)$ and $\text{Ag}\left(111\right)$ surfaces. The band gaps corresponding to each of the surfaces are indicated as horizontal double-headed arrows. The origin of the energy scale is defined by the vacuum energy.

Figure 2

(Color online) Same as Fig. 1, but for $D=1\text{a.u}$.

Figure 3

(Color online) Energies of various resonances as a function of the ion-surface distance for $\text{Ag}\left(100\right)$ and $\text{Ag}\left(111\right)$ surfaces.

Figure 4

(Color online) Widths of various resonances as a function of the ion-surface distance for $\text{Ag}\left(100\right)$ and $\text{Ag}\left(111\right)$ surfaces.

Figure 5

(Color online) Percentage survival probability [Eq. (12)] of ${\mathrm{H}}^{-}$ scattered from $\text{Ag}\left(100\right)$ and $\text{Ag}\left(111\right)$ surfaces as a function of the exit angle (= incidence angle for the present case of specular scattering condition) with respect to the surface plane. Initial normal velocities $v_{\text{nor}}^{\text{in}}$, constant parallel velocities $v_{\text{par}}$, and distances of closest approach $D_{\text{cls}}$ are given along the upper $x$-axis. For the description of trajectory-I and trajectory-II, see the text.

Figure 6

(Color online) ${\mid A\left(t\right)\mid }^2$ as a function of the distance of the $1\text{keV}$ ion from the corresponding distance of closest approach $D_{\text{cls}}=0.184\text{a.u.}$ along trajectory-I; negative and positive distances are respectively the incoming and outgoing segment of the trajectory. The angle of incidence is $\Theta =40°$. Three regions of different interaction characters are identified.