Grazing incidence collisions of multiply charged ions on solid surfaces. Influence of the formation of intermediate Rydberg states

Abstract

We elaborate the quantum-mechanical analysis using the two-state vector model to investigate the formation of intermediate Rydberg states of multiply charged ions (core charge Z ≫ 1, principal quantum number nA ≫ 1) interacting with solid surfaces in the grazing incidence geometry. For the fixed initial and final states of the active electron, the two wavefunctions are used to describe the transitional electron state at the time t. Considering the projectile motion classically, the effect of projectile velocity is taken into account in accordance with Galilean invariance. The population probabilities of the intermediate Rydberg states are obtained in the analytical form, which enables an analysis of the localization and the selectivity of the process, for various ion–surface parameters. Ions ArZ+, KrZ+ and XeZ+ with Z ∈ [5, 35] interacting with Al-surface are considered as an example. The results are compared with the classical overbarrier predictions and the measured kinetic energy gain due to the image acceleration of the ions. It is demonstrated that the ionic velocity influences the ion–surface distance at which the formation of the particular intermediate Rydberg state is mainly localized, as well as the probability for this formation.

Effect of the cascade neutralization energy on the surface modification by the impact of slow highly charged ions

“…The first state evolves from the initial state |Ψ 1 (t in ) (electron in metal) towards the future, and the second state evolves towards the fixed final state |Ψ 2 (t f in ) (electron captured by the ion). The states of the active electron at the time t (at ion-surface distance R) between the initial time t in and the final time t f in are expressed via intermediate eigenstates |µ M (R) and |ν A (R) of the in-HamiltonianĤ 1 (R) and the out-HamiltonianĤ 2 (R), respectively (Nedeljković et al, 2012;Nedeljković et al, 2016). By the ap-propriate expressions of the HamiltoniansĤ 1 (R) andĤ 2 (R) we take into account the polarization of the metal surface and the polarization of the ionic core, respectively, as well as the effect of the dielectric film (Majkić et al, 2017).…”

“…The effect of the arbitrary collision geometry is taken into account by the Galilean invariance, i.e. by the translation factor in the function |Ψ 2 (t) (Nedeljković et al, 2012;Nedeljković et al, 2016) expressed via perpendicular velocity component v ⊥ , and the energy shift…”

“…The mixed flux we calculate through the fictive Firsov plane S F (Demkov & Ostrovskii, 1975;Nedeljković & Majkić, 2007), which separates the metal surface and the ionic region. The S F plane is positioned sufficiently far both from the surface and on the ionic core so that we use the asymptotic expressions of the wavefunctions Ψ 1 (r, t) and Ψ 2 (r, t) for the calculation of the mixed flux (Nedeljković et al, 2012). For an arbitrary collision geometry and moderate ionic velocities the electrons are captured quasi-resonantly from the overall metallic states |µ M into the ionic Rydberg state |ν A through the potential barrier formed between the surface and the ionic core.…”

“…For very low ionic velocities the population process is resonant. In the more general velocity case, the intermediate population probability is given by (Nedeljković et al, 2016), where T ν A (t) is calculated by the integration of the transition probability density T µ M ,ν A (t) (Nedeljković et al, 2012):…”

“…at ion-surface distance R we have γ M = γ A (R); the influence of the energy levels with γ M γ A (R) is expressed via E (Nedeljković et al, 2016). The quantity f Ω k represents the angle-averaged Fermi-Dirac distribution of the electron momenta in solid (Nedeljković et al, 2012). The parametersα andβ in (2) are defined byα = Z/γ A − 1/2 + 1/4γ M andβ = γ M + (γ A − γ M )/2, respectively.…”