Intermediate stages of the Rydberg-level population of multiply charged ions escaping solid surfaces

Abstract

We have investigated the intermediate stages of electron capture into Rydberg states of multiply charged ions ͑core charge Z 1, principal quantum number n A 1͒ escaping solid surfaces at low velocity. The timesymmetrized, two-state vector model of the process is proposed by using both initial and final states of the ion-surface system. The two conditions determine two wave functions and both are used to describe the system at intermediate stages. The appropriate probabilities and rates are defined and calculated from the corresponding mixed flux. Taking into account both the surface polarization and the polarization of the electronic cloud of the ionic core, the probabilities and rates are obtained in a simple analytical form; the population of the Rydberg levels of the ions Ar VIII, Kr VIII, and Xe VIII interacting with an Al surface is considered as an example. The quasiresonant character of the process is demonstrated, as well as the complementarity of the neutralization and ionization processes for the A Z+ ions escaping the surface and the A ͑Z−1͒+ ions approaching the surface, respectively. The neutralization distances for the ions finally detected in a given Rydberg state are obtained from the calculated rates. Although defined under different physical conditions, the results obtained are in agreement with the coupled-angular-mode theoretical predictions.

Population dynamics of the ions SVI, ClVII and ArVIII interacting with solid surfaces

“…We point out that in Ref. [31] only the ions ArVIII, KrVIII and XeVIII (all with core charges Z ¼ 8) have been concerned.…”

“…The mentioned theoretical studies [28][29][30] were focused on the final population probabilities P fin . Recently [31], the model has been adapted to the intermediate stages of the population dynamics in the low-velocity region. The TVM represents a form of the time-symmetric formulation of quantum mechanics; namely, the state of a single electron is described by two state vectors jC 1 ðtÞi and jC 2 ðtÞi.…”

“…We use the simple TVM analytical expressions for the normalized rates obtained in Ref. [31] to analyze the intermediate stages of the process. We point out that in Ref.…”

“…We consider the electron capture from the initial parabolic state jm M i, corresponding to the continuous energy parameter g M , into the low-l A Rydberg states with m A ¼ 0. During the neutralization, both the polarization of the solid, and the polarization of the electronic cloud of the ionic core are taken into account [31]. For description of the intermediate stages of the process [31] we use the normalized probabilityP n A ðtÞ ¼ P n A ðtÞ=P fin n A and the corresponding rateG n A ðtÞ, where P n A ðtÞ is defined as a ''sum'' over the initial per unit g M , T m M ;n A ðtÞ.…”

“…During the neutralization, both the polarization of the solid, and the polarization of the electronic cloud of the ionic core are taken into account [31]. For description of the intermediate stages of the process [31] we use the normalized probabilityP n A ðtÞ ¼ P n A ðtÞ=P fin n A and the corresponding rateG n A ðtÞ, where P n A ðtÞ is defined as a ''sum'' over the initial per unit g M , T m M ;n A ðtÞ. By definition, the quantityP n A ðtÞ represents the neutralization probability at the time t under the condition that the state jn A i is populated at the time t !…”