Ionization distances of multiply charged Rydberg ions approaching solid surfaces

Abstract

The ionization distances ${R}_{c}^{I}$ as well as the ionization rates and eigenenergies of one-electron multiply charged Rydberg ions (core charge $Z⪢1$, principal quantum number $n⪢1$) approaching solid surfaces are calculated. Within the framework of a nonperturbative \'etalon equation method (EEM), these quantities are obtained simultaneously. The complex energy eigenvalue problem for the decaying eigenstates is solved within the critical region $R\ensuremath{\approx}{R}_{c}\ensuremath{\approx}{R}_{c}^{I}$ of the ion-surface distances $R$. This region is characterized by the energy terms localized in the vicinity of the top of an effective potential barrier, created between the ion and polarized solid. We take into account that the parabolic symmetry is preserved for $R\ensuremath{\approx}{R}_{c}$ and that the parabolic quantum numbers can be taken as approximate but sufficiently good quantum numbers. The parabolic rates, energies, and corresponding ionization distances are presented in relatively simple analytical forms. The ionization distances are compared with the results of a classical overbarrier model. Comparison of the obtained energies and rates with the available theoretical predictions of the coupled angular mode method shows good agreement. The use of the EEM for an estimation of the upper limit of the first neutralization distance in the subsequent neutralization cascade is briefly discussed.