Linear combination of atomic orbitals calculation of the Auger neutralization rate of He+ on Al(111), (100), and (110) surfaces

We develop a theory of the Auger neutralization rate of ions on solid surfaces in which the matrix elements for the transition are calculated by means of a linear combination of atomic orbitals technique. We apply the theory to the calculation of the Auger rate of ${\mathrm{He}}^{+}$ on unreconstructed Al(111), (100), and (110) surfaces, assuming ${\mathrm{He}}^{+}$ to approach these surfaces on high symmetry positions and compare them with the results of the jellium model. Although there are substantial differences between the Auger rates calculated with both kinds of approaches, those differences tend to compensate when evaluating the integral along the ion trajectory and, consequently, are of minor influence in some physical magnitudes like the ion survival probability for perpendicular energies larger than $100\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. We find that many atoms contribute to the Auger process and small effects of lateral corrugation are registered.