IONIZATION DISTANCES OF RYDBERG ATOMS APPROACHING SOLID SURFACES IN THE PRESENCE OF WEAK ELECTRIC FIELDS

The ionization distances R_c^I of slow hydrogenlike Rydberg atoms approaching solid surfaces in the presence of a weak external electric field are calculated. The ionization is treated as resonant electron tunneling in the very vicinity of the top of the potential barrier, created between the ionic core and polarized solid. We obtain both the complex energies and the ionization distances by solving the energy eigenvalue problem under the outgoing wave boundary condition towards the solid. The eigenvalue problem is studied in parabolic coordinates within the framework of an etalon equation method adapted to include the confluence of turning points. It is demonstrated that in a critical region R≈R_c^I≫1 a.u. of ion-surface distances R, parabolic quantum numbers n₁, n₂, and m can serve as approximate, but “sufficiently good” quantum numbers, at least for lower n₁ values. The method offers asymptotically exact analytical expressions for the ionization rates and energies, which follow the theoretical predictions of the complex scaling method (CSM). It is also found that the resulting ionization distances R_c^I are in very good agreement with the results of CSM. The implications of using obtained results in analyzing the recent xenon experimental data for R_c^I are briefly discussed.

IONIZATION DYNAMICS VIA ION-COLLECTION FIELD OF RYDBERG ATOMS APPROACHING METAL SURFACES

 

The ionization dynamics of slow hydrogenlike Rydberg atoms (principal quantum number n≫1) approaching solid surfaces is considered via an ion-collection electric field, using an appropriate etalon equation method. The complex energy eigenvalue problem is solved in the critical region R≈R_c≈R_c^I of the ion-surface distances R in which the ionization process is mainly localized and the parabolic symmetry is preserved. The relatively simple analytical forms for the parabolic rates enable us to elucidate the main features of the self-consistent ionization dynamics of the projectiles with the time-dependent charges. The ionization distances R_c^I are calculated and an agreement of the averaged probability (for the atomic beam) with the corresponding experimental results is discussed for the relevant parameters of the ion-surface system. The formulas are suggested for the simulation of the experimental signal and for deducing the R_c^I values from this signal.

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THE EFFECT OF CORE POLARIZATION ON THE POPULATION

OF THE RYDBERG STATES OF ArVIII IONS

ESCAPING SOLID SURFACES

 

The appearance of maxima at  n_A = n_max  in the population distributions for the

Rydberg states of multiply charged ions ArVIII escaping solid surfaces at intermediate velocities

(v ≈ 1 a.u.) is discussed. Within the framework of the time-symmetrized two-state

vector model, in which the state of a single active electron is described by two wave functions

y₁  and  y₂, the regular maxima appear as a consequence of the electron tunneling

through the potential barrier created between the ionic core and the polarized solid. The

pronounced peaks (resonances) in the population distributions are addressed to the electron

tunneling in the vicinity of the potential barrier top. The appropriate etalon equation method

is used in the calculation of the function y₁ ; the effect of core polarization is expressed

via the function  y₂ .

NEUTRALIZATION OF MULTIPLY CHARGED RYDBERG IONS

INTERACTING WITH SOLID SURFACES UNDER

THE GRAZING INCIDENCE GEOMETRY

 

We elaborated the time-symmetric, two-state vector model to investigate the

intermediate stages of the electron capture into the Rydberg states of multiply charged

ions interacting with solid surface under the grazing incidence geometry. The neutralization

distances for the ions  Xe^Z+ interacting with Al-surface are calculated, for core

charges  ZÎ[5,30] . The corresponding mean neutralization distances are in agreement

with the data deduced from the measured kinetic energy gain due to the image acceleration

of the ions.

SURVIVAL OF LARGE-l RYDBERG STATES OF HIGHLY

CHARGED IONS IN THE VICINITY OF METAL SURFACES

 

The probabilities for ionization of large-l multiply charged Rydberg ions approaching

metallic surfaces at thermal velocities in the normal incidence geometry were

calculated. The ionization process was treated within the framework of decay model using

the appropriate etalon equation method for solving the complex energy eigenvalue problem.

It is shown that, in contrast to corresponding low-l states, the large-l Rydberg states

exhibit non-zero survival probabilities.

SELF-CONSISTENT PROCEDURE FOR TREATMENT OF THE

IONIZATION DYNAMICS OF RYDBERG ATOMS

APPROACHING SOLID SURFACES IN THE ELECTRIC FIELD

 

The self-consistent procedure for the analysis of the ionization dynamics of slow

hydrogenlike Rydberg atoms approaching solid surface in a weak electric field has been

developed. The complex energy eigenvalue problem is solved in the critical region of the

ion-surface distances R using an etalon equation method. The problem of motion of a

representative member of the atomic beam is resolved by including the R-dependent

expression for the perpendicular velocity into the expression for the ionization probability

iteratively. The results of the procedure were employed to calculate the averaged

ionization probabilities which were compared to the available experimental results.

DECAY RATES OF LARGE-l RYDBERG STATES OF MULTIPLY

CHARGED IONS APPROACHING SOLID SURFACES

 

We investigate the ionization of large-l multiply charged Rydberg ions approaching

solid surfaces within the framework of decay model and applying the etalon equation

method. The radial coordinate r of the active electron is treated as a variational parameter

and therefore the parabolic symmetry is preserved in this procedure. The complex eigenener-

gies are calculated from which the energy terms and the ionization rates are derived. We find

that the large-l Rydberg states decay at approximately the same ion-surface distances as the

low-l states oriented toward the vacuum and considerably closer to the surface comparing

to the low-l states oriented towards the surface.

l-DISTRIBUTIONS OF THE FIRST ELECTRON

TRANSFERRED TO MULTIPLY CHARGED

IONS INTERACTING WITH SOLID SURFACES

 

We analyze the angular momentum distributions of the electron transferred into

the Rydberg states of multiply charged ions escaping the solid surfaces. The population

probabilities are calculated within the framework of two-state-vector model; in the case of

large values of the angular momentum quantum numbers l the model takes into account

an importance of a wide space region around the projectile trajectory. The reionization of

the previously populated states is also taken into account. The corresponding ionization

rates are obtained by the appropriate etalon equation method; in the large-l case the radial

electronic coordinate  r  is treated as variational parameter. The theoretical predictions based

on the proposed population-reionization mechanism fit the available beam-foil experimental

data; the obtained large-l distributions are also used to elucidate the recent experimental

data concerning the multiply charged Rydberg ions interacting with micro-capillary foil.

NEUTRALIZATION DISTANCES OF Ar^Z+ RYDBERG

IONS INTERACTING WITH SOLID SURFACES

 

We apply the recently developed time-symmetrized, two-state vector model to

investigate the intermediate stages of the electron capture into the Rydberg states of multiply

charged Ar^Z+ ions (core charge Z ≫ 1, principal quantum number n_A ≫ 1) escaping Al-

solid surface at low velocity. The simple analytical formulae derived for the corresponding

neutralization rates enable us to analyze the neutralization distances for the low-l Rydberg

states (n_A; l_A;m_A), for diferent charge states Z of the ion. It is found that the inclusion

of core polarization significantly reduces the neutralization distances. The neutralization

distances for the highest Rydberg levels that can be populated in the vicinity of solid surface

are in agreement with the data deduced from experiments in which the kinetic energy gain

due to the image acceleration of the ions is measured.

FORMATION AND DECAY OF THE RYDBERG STATES

OF MULTIPLY CHARGED IONS INTERACTING

WITH SOLID SURFACES

 

Processes of formation and decay of the Rydberg states of multiply charged ions

escaping solid surfaces with intermediate velocities ( v ≈1 a.u.) are complex quantum

events that require a detailed quantum description. We developed a two-state vector model

of electron captures into lower-n, but high-l Rydberg states. The electron exchange process

is described by a mixed flux through a moving plane, positioned between the solid surface

and the ionic projectile. Generally, the lower-n model reproduced the experimentally observed

non-linear trend of the l distributions from l = 0 to lmax = n – 1. In the case of large

values of the angular momentum quantum numbers l , the model takes into account an importance

of a wide space region around the projectile trajectory. The reionization of the

previously populated states is also taken account and can be described as a decay process

of the electron wave function. The corresponding ionization rates are obtained by an appropriate

etalon equation method: in the large- l case the radial electronic coordinate r  is

treated as variational parameter. The theoretical predictions based on that population–

reionization mechanism fit the available beam-foil experimental data concerning the SVI,

ClVII and ArVIII ions, as well as the experimental data obtained in the interaction of multiply

charged ions with micro-capillary foil.

    Even at large distances from the surface, the state of the excited active electron of the ion-surface system can be strongly affected by the influence of the surface, leading to the formation of the molecular-like parabolic states. In the interaction with surface, the electron exchange (ionization-neutralization) between the ion-surface subsystems occurs. The available experiments are devoted both to the final stages of the processes (population probabilities in the beam/target experiments within the framework of optical spectroscopy), and, recently, to the intermediate stages (an ion signal determines the ionization distances, a projectile kinetic energy gain due to the surface image acceleration determines the neutralization distances, etc).

Interaction of atomic systems with solid surfaces

    We investigate the following subjects:

 

   1. neutralization of multiply charged Rydberg ions

        a)  under the grazing incidence on the surface,

        b)  for the normal emergence geometry

For 1 the appropriate theoretical models are developed within the framework of the time-symmertized (teleological) quantum model (two-state vector model, TVM),

 

    2. ionization of Rydberg atoms impinging a solid surface in the presence of a weak electric field 

    3. survival of the Rydberg ions under the normal incidence on the surface

For 2. and 3 the decay model and the etalon equation method, EEM, are developed.

FINAL RYDBERG STATE POPULATION PROBABILITIES OF MULTIPLY CHARGED IONS ESCAPING SOLID SURFACES

 

The two-state vector model is used to investigate the final population of the Rydberg states (n_A ≫ 1, l_A = 0-3, m_A) of multiply charged ions escaping solid surfaces at intermediate velocities (v ≈ 1 a.u.). Within the framework of the proposed time-symmetrized quantum model, the electron capture is a non-resonant, velocity dependent process, characterized by the selective population of the ionic Rydberg states. The final population probabilities are obtained in a relatively simple analytical form, which enable us to elucidate the role of the ionic core polarization and to analyze the n_A, l_A and v   probability distributions. We consider the ions SVI, ClVII and ArVIII with core charges Z = 6, 7 and 8, respectively, and the ions KrVIII and XeVIII with Z = 8. The results are obtained for two type of surfaces and compared with available beam-foil experimental data.

POPULATION DYNAMICS OF THE IONS SVI, ClVII AND ArVIII INTERACTING WITH SOLID SURFACES

 

We used the recently developed time-symmetrized, two-state vector model to investigate the intermediate stages of the electron capture into the Rydberg states (n_A ≫ 1, l_A= 0−3, m_A = 0) of multiply charged ions SVI, ClVII and ArVIII, with polarized core charges Z = 6, 7 and 8, respectively, escaping solid surfaces at low velocities. Within the framework of the model, the two wave functions are used to describe the system at intermediate stages; the corresponding probabilities and rates are based on the calculation of the mixed flux. The simple analytical formulae derived for the neutralization rates enable us to analyze the localization of the process and to calculate the neutralization distances. In the pointlike core approximation, the rates are comparable with the available coupled-angular-mode results. The neutralization distances follow the classical predictions for all considered Rydberg states with exception of the states with critical quantum numbers n_A = n_C mainly populated via tunneling mechanism; the corresponding values are larger than it is predicted by the classical overbarrier model. Inclusion of core polarization significantly reduces the neutralization distances.

INTERMEDIATE STAGES OF THE RYDBERG LEVEL POPULATION OF MULTIPLY CHARGED IONS ESCAPING SOLID SURFACES

 

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≫1) escaping solid surfaces at low velocity. The time-symmetrized, 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−1)+ 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.

IONIZATION DISTANCES OF MULTIPLY CHARGED RYDBERG IONS APPROACHING  SOLID SURFACES

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 étalon equation method (EEM), these quantities are obtained simultaneously. The complex energy eigenvalue problem for the decaying eigenstates is solved within the critical region R≈R_c≈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 ≈ 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.

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RESONANCES IN THE FINAL RYDBERG STATE POPULATION OF MULTIPLY CHARGED IONS ArVIII, KrVIII, AND XeVIII ESCAPING SOLID SURFACES

 

The appearance of resonances (pronounced maxima at n_A=n_res) in the probability distribution for the population of the Rydberg state (n_A, l_A, m_A) of multiply charged ions (Z≫1) escaping solid surfaces at intermediate velocities (v ≈ 1 a.u.) is discussed. Within the framework of the time-symmetrized two-state vector model, in which the state of a single active electron is described by two wave function Y₁ and Y₂ , the resonances are explained by means of an electron tunneling in the very vicinity of the ion-surface potential barrier top. To include this specific feature of electron transition into the model, the appropriate etalon equation method is used in the calculation of the function Y₁. We consider the ions ArVIII, KrVIII, and XeVIII with the same core charges Z=8 a.u., but with different core polarizations. The effect of the ionic core polarization is associated with the function Y₂. The population probabilities for n_A ≈ n_res are complemental to those obtained recently n_A < n_res , and in sufficiently good agreement with available beam-foil experimental data. The pronounced resonances in the final population distributions are recognized only in the case of ArVIII ion and for the lower values of the solid work function (argon anomaly).