The nonmonotonic energy dependence of the $\mathrm{L}{\mathrm{i}}^0$ fraction on high-work-function surfaces has not been understood so far. To further study this phenomenon, in this work, efficient neutralization of $\mathrm{N}{\mathrm{a}}^{+}$ ions has been reported on various surfaces, instead of $\mathrm{L}{\mathrm{i}}^{+}$ ions. The nonmonotonic energy dependence of the $\mathrm{N}{\mathrm{a}}^0$ fraction becomes more and more obvious with the increase of the surface work function. For Cu(111) and Cu(110) at the scattering angle of 7°, the energy dependence of the neutral fraction is still nonmonotonic as compared to the scattering angles of 135° and 53°. For the scattering angle of 53°, the nonmonotonic angle dependence has been observed for these surfaces. The essences of the nonmonotonic angle and energy dependences are the same. The quantum-mechanical calculations reveal that the width and position of the atomic level below the Fermi level at short ion-surface distances are responsible for high neutral fractions at large exit energies, and that the neutral fraction at much smaller exit energies is probably related to the neutralization at large distances. For the exit angle dependence, the competition between neutralization at short and large distances strongly depends on the surface work function. In particular, the neutralization is enhanced by the relatively large parallel velocity.

Negative-ion fractions depending on incident energies and angles have been measured for keV-energy fluorine negative ions scattering on a graphite surface at a scattering angle of 38°. For specular scattering, the fraction increases monotonously with increasing incident energy. A specific feature is the nonmonotonic angular dependence of the fraction with the variation of incident angles. It strongly indicates the interaction-time-dependent electron transfer process. The incident-velocity effect has been taken into account to analyze the experimental results, in which an exponential scaling is found.

The jellium model of free electron gas and its extended version have been widely used to understand the neutralization of alkali-metal ions on metal surfaces. We report an unexpected deviation from its prediction that we observed in the neutralization of $\mathrm{N}{\mathrm{a}}^{+}$ ions scattering from an Al(111) surface. We find that the neutralization probability decreases monotonically with increasing ion velocity for the specular scattering condition, which is consistent with the well-known parallel velocity effect. However, the neutralization probability exhibits an unexpected bell shape with the variation of outgoing angle for a given incident energy. Calculations based on the jellium model using the rate equation and including the dynamic parallel velocity effect are presented. Their results agree with the velocity dependence of the neutral fraction, but completely fail in reproducing the angle dependence. This anomalous angle dependence could be due to the appearance of inelastic processes, corresponding to inner $2p$ electron promotion in hard encounters with Al atoms for large incidence angles, when the interatomic distances become small. This can lead to the formation of autoionizing Na states that result in the formation of extra $\mathrm{N}{\mathrm{a}}^{+}$ ions, not accounted for in the jellium model.

The Demkov model fails to explain the formation of negative ions in grazing scattering of atoms from insulator surfaces at relatively high velocities, since the electron detachment process is not included in the model. In this work, the well-known quantum tunneling effect for electrons through the repulsive Coulomb barrier has been proposed to describe electron detachment from the formed negative ions. The combination of these two models results in excellent agreement with the experimental data in the overall impact velocity range.