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We have employed the concept of the surface wake field to model the formation of the circular Rydberg states in the beam-foil experiments. The experimental studies of atomic excitation processes show the formation of circular Rydberg states either in the bulk of the foil or at the exit surface, and the mechanism is explained by several controversial theories. The present model is based on the interesting fact that the charge state fraction as well as the surface wake field depend on the foil thickness and it resolves a long-standing discrepancy on the mechanism of the formation of circular Rydberg states. The influence of exit layers is twofold. Initially, the high angular momentum Rydberg states are produced in the last layers of the foil by the Stark switching due to the bulk wake field and finally, they are transferred to the circular Rydberg states as a single multiphoton process due to the influence of the surface wake field.

We report the measurement of surface wakefield on the lifetime of He-like Ti (1s2s ³S1) during the time-of-flight measurements in the beam-foil experiment. Quenching in the lifetime of 1s2s ³S1 state from 26.6 ns to 67.11 ps has been observed due to blending with short-lived 1s2p ³ states in the presence of wakefield present near the target surface. The measured and theoretical lifetime of unperturbed He-like Ti (1s2s ³S1) and (1s2p ³) has been used to calculate the blending parameter ε (3.74 × 10⁻²). The surface wakefield for 110 MeV Ti⁺⁸ passing through 80 μg/cm² thick carbon foil is found to be 9.15 × 10⁷ V/cm. The measured stark mixing parameter can be used to determine the surface wakefield as well as the wake stopping power of an ion through a solid target.

We have measured the stopping powers and straggling of fast, highly-ionized atoms passing through thin bi-layer targets made up of metals and non-conductors. We were surprised to find that the energy losses as well as the straggling depend on the ordering of the target and have small but significantly different values on bi-layer reversal. We ascribe this new energy-loss to the SELF (the Surface Energy Loss Field) effect to the differing surface wake fields as the beam exits the target in the two cases. This finding is validated with experiments using several different projectiles, velocities and bi-layer targets. Both partners of diatomic molecular ions also display similar results. Comparison of the energy loss results with those of previous theoretical predictions for the surface wake potential for fast ions in solids supports the existence of self-wake..

Selective Rydberg-level population of multiply charged ions (e.g., Z=6, 7, and 8) at solid surfaces is treated in normal emergence geometry. For the intermediate ionic velocity region (between v≊1 and 3 a.u.) a molecular-dynamics-type model of the electron pickup process from the solid valence band into low-angular-momentum ionic states (l=0, 1, and 2) is proposed. Specific features of the Rydberg states and ions (large size, high degeneracy with respect to l, high value of Z) are included in the model. The electron transition amplitude is calculated as a mixed electron-density flux through a moving Firsov plane, whose kinematics is determined by a variational requirement. A multichannel character of the process is taken into account in the framework of a statistical treatment of decoupled channels, based on the approximation of small transition probabilities. The population probability Pnl=Pnl(v,Z) of the (n,l) state is in sufficiently good agreement with available beam-foil experimental data (S VI, Cl VII, Ar VIII) not only as a function of the principal quantum number n, but also as a function of l and v. An ‘‘anomalous’’ peak at n=11 in the population probability of Ar VIII is briefly discussed from the standpoint of the developed formalism. The predicted maxima in the v dependence of Pnl(v,Z) in the intermediate velocity region calls for further more refined experimental studies.

Processes of formation and decay of the Rydberg states of multiply charged ions escaping solid surfaces with intermediate velocities (v ≈ 1 a.u.) represent complex quantum events that require a detailed quantum description. We have developed a two-state vector model for the population process, with the functions Ψ1 and Ψ2 for definition of the state of a single active electron. The electron exchange between the solid and the moving ion is described by a mixed flux through a plane positioned between them. For the low values of the angular momentum quantum numbers l the radial electronic coordinate ρ can be neglected, whereas for the large-l values a wide space region around the projectile trajectory was taken into account. The reionization of the previously populated states is considered as a decay of the wave function Ψ2. The corresponding decay rates are obtained by an appropriate etalon equation method: in the large-l case the radial electronic coordinate ρ is treated as a variational parameter. The theoretical predictions based on that population-reionization mechanism are compared with the available beam-foil experimental data, as well as the experimental data obtained in the interaction of multiply charged ions with micro-capillary foil. Generally, the model reproduces the experimentally observed non-linear trend of the l distributions from l = 0 to lmax = n − 1.

We describe measurements of the lifetimes of metastable states in one- and two-electron nickel ions. The 2 [sup 2][ital S][sub 1/2] level in one-electron nickel was found to have a lifetime of 217.1(1.8) ps, in agreement with a theoretical calculation of 215.45 ps. The lifetimes of the 2 [sup 1][ital S][sub 0] and 2 [sup 3][ital P][sub 2] levels in two-electron nickel were found to be 156.1(1.6) and 70(3) ps, respectively, in agreement with the theoretical results of 154.3(0.5) and 70.6 ps. We also studied the phenomenon of hyperfine quenching of the He-like 2 [sup 3][ital P][sub 0] level by comparing decay curves for the isotopes [sup 61]Ni and [sup 58]Ni. The lifetime of the 2 [sup 3][ital P][sub 0] level in [sup 61]Ni[sup 26+] was found to be 470(50) ps, in agreement with a theoretical prediction. The measurements were carried out using the beam-foil time-of-flight technique with a fast beam of highly charged nickel ions. We discuss the handling of systematic effects in the measurements, including the study of yrast cascades following the beam-foil interaction.

In the recent beam-foil experiment, resonances have been observed in decay of the beam-foil excited 2p and 2s states of H-like Fe ions at very large times. Qualitatively, the resonances were explained as a consequence of cascading down from the Rydberg states (n⪢1,l=n−1)(n⪢1,l=n−1) to 2p state. Full explanation requires the theoretical values of the population probabilities Pn,lPn,l of the large-l Rydberg states of multiply charged ions of core charges Z⪢1Z⪢1 a.u. escaping the solid surfaces at velocities v⪢1v⪢1 a.u. The resonances observed in the time dependent photon intensity indicate the existence of resonances (pronounced maxima at several n=nres)n=nres) in the Pn,lPn,l distributions. Considering the population process within the framework of the time-symmetrized two-state vector model, with dynamically generalized interaction Hamiltonian, we found that the nonresonant electron pick up from the foil conduction band into the field of ionic core when the ion leaves the surface represents an important population mechanism. The obtained population distributions have the resonance-like structure like the ones simulated from the experimental signal, and the overlap shape and magnitude in accordance with the wake field model estimations.

Processes of formation and decay of the Rydberg states of multiply
charged ions escaping solid surfaces with intermediate velocities ( v
Ë1 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 coresponding ionization rates are
obtained by an appropriate etalon equation method: in the large- l case
the radial electronic coordinate ? 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.

The appearance of resonances (pronounced maxima at nA = nres) in the probability distributions for the population of the Rydberg state (nA, lA, mA) 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 functions Ψ1 and Ψ2, 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 transitions into the model, the appropriate etalon equation method is used in the calculation of the function Ψ1. 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 Ψ2. The population probabilities for nA ≈ nres are complemental to those obtained recently for nA < nres, 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).

The alignment of HeI 3d1D after the interaction of fast He ions of 30–310 keV energy with thin carbon foils is found to depend strongly on energy and beam current density of the incoming ions. The current dependence of the polarization is linear, but for small currents a pronounced deviation from this linearity is found.

A diagrammatic procedure is described, by which the time dependence of the population of any level in a decay scheme of arbitrary complexity can be prescribed directly in terms of transition probabilities and initial populations, without specifically solving the determining differential equations.

We present a theoretical study of resonances and thresholds, two specific features of Rydberg-state formation of multiply charged ions (Z=6, 7, and 8) escaping a solid surface at intermediate velocities (v≈1a.u.) in the normal emergence geometry. The resonances are recognized in pronounced maxima of the experimentally observed population curves of Ar VIII ions for resonant values of the principal quantum number n=nres=11 and for the angular momentum quantum numbers l=1 and 2. Absence of optical signals in detectors of beam-foil experiments for n>nthr of S VI and Cl VII ions (with l=0, 1, and 2) and Ar VIII for l=0 is interpreted as a threshold phenomenon. An interplay between resonance and threshold effects is established within the framework of quantum dynamics of the low angular momentum Rydberg-state formation, based on a generalization of Demkov-Ostrovskii’s charge-exchange model. In the model proposed, the Ar VIII resonances appear as a consequence of electron tunneling in the very vicinity of the ion-surface potential barrier top and at some critical ion-surface distances Rc. The observed thresholds are explained by means of a decay mechanism of ionic Rydberg states formed dominantly above the Fermi level EF of a solid conduction band. The theoretically predicted resonant and threshold values, nres and nthr of the principal quantum number n, as well as the obtained population probabilities Pnl=Pnl(v,Z), are in sufficiently good agreement with all available experimental findings.

We have investigated the electron capture into large-l Rydberg states of multiply charged ionic projectiles (e.g., the core charges Z=6, 7, and 8) escaping solid surfaces with intermediate velocities (v≈1a.u.) in the normal emergence geometry. A model of the nonresonant electron capture from the solid conduction band into the moving large angular-momentum Rydberg states of the ions is developed through a generalization of our results obtained previously for the low-l cases (l=0, 1, and 2). The model is based on the two-wave-function dynamics of the Demkov-Ostrovskii type. The electron exchange process is described by a mixed flux through a moving plane (“Firsov plane”), placed between the solid surface and the ionic projectile. Due to low eccentricities of the large-l Rydberg systems, the mixed flux must be evaluated through the whole Firsov plane. It is for this purpose that a suitable asymptotic method is developed. For intermediate ionic velocities and for all relevant values of the principal quantum number n≈Z, the population probability Pnl is obtained as a nonlinear l distribution. The theoretical predictions concerning the ions S VI, Cl VII, and Ar VIII are compared with the available results of the beam-foil experiments.

Numerical calculations of the 2E1 and M1 decay rates of the 2s1/2 metastable states of the hydrogen isoelectronic sequence are presented. The 2E1 rates are found to be in good agreement with recent calculations of Goldman and Drake, but substantially different from the earlier numerical values of Johnson. Effects of nuclear finite size on the 2E1 rates are found to be insignificant, whereas finite-size effects reduce the M1 rate by about 1.1% at Z=92.

One of the simplest, and most completely treated, fields of application of quantum mechanics is the theory of atoms with one or two electrons. For hydrogen and the analcgous ions He+, Li++, etc., the calculations can be performed exactly, both in Schrödinger’s nonrelativistic wave mechanics and in Dirac’s relativistic theory of the electron. More specifically, the calculations are exact for a single electron in a fixed Coulomb potential. Hydrogen-like atoms thus furnish an excellent way of testing the validity of quantum mechanics. For such atoms the correction terms due to the motion and structure of atomic nuclei and due to quantum electrodynamic effects are small and can be calculated with high accuracy. Since the energy levels of hydrogen and similar atoms can be investigated experimentally to an astounding degree of accuracy, some accurate tests of the validity of quantum electrodynamics are also possible. Finally, the theory of such atoms in an external electric or magnetic field has also been developed in detail and compared with experiment.

We observed the circular Rydberg states populating H-like Fe ions during fast ion-solid collisions. Time-resolved X-ray spectra obtained with 164 MeV 5626Fe ions colliding with a carbon foil do not show any lines due to H-like Fe ions at small delay times until 600 ps. However, Lyα and Lyβ transitions appear after a while and attain maximum intensity at a delay of 920 ± 5 ps. Such a delay is attributed to successive cascading from the circular Rydberg levels, which has important implications for understanding the origin of radio recombination lines from interstellar space.

We report on the measurement of the wakefield of an ion moving through a beam–foil plasma using an indirect experimental method. The standard beam–foil time-of-flight technique is used to measure the lifetime of the perturbed H-like V 2s2S1/2 state due to its passage through the wakefield. This measured lifetime along with the theoretical lifetimes of pure H-like V 2s2S1/2 and 2p2P1/2 states has been used to determine the Stark mixing parameter of H-like 2s2S1/2 and 2p2P1/2 states, which is further exploited to determine the wakefield at the surface of the exit foil. The wakefield intensity during the passage of 160 MeV 5123V ion through thin C-foil as well as Au-foil is found to be as high as 3.2 ± 0.07 × 107 V cm−1.

A theoretical study of the two-photon emission rate from the 1s2s 1S state of two-electron ions is presented. High-precision values of the nonrelativistic emission rate for ions with nuclear charge Z up to 36 are obtained by use of correlated variational wave functions of the Hylleraas type. Summations over intermediate states are performed by finite-basis-set methods. The results are used to obtain an accurate extrapolation formula and to study the convergence characteristics of a 1/Z expansion for the decay rate. The leading hydrogenic term is calculated to an accuracy which substantially exceeds Klarsfeld’s, and the next term is obtained for what is believed to be the first time. Relativistic effects are taken into account by means of a screened hydrogenic approximation. The predicted decay rate for two-electron Kr34+ is (2.993±0.012)×1010 s-1, where the error is the uncertainty in the relativistic correction. This lies significantly higher than the value (2.934±0.030)×1010 s-1 recently measured by Marrus et al.

DOI:https://doi.org/10.1103/PhysRevA.35.3168

Based on the correspondence principle, a simple semiclassical derivation of a universal formula for the radiative mean lifetime tau(n,l) of hydrogenlike states is presented. (The possibilities of stimulated emission and collisional deexcitation are neglected.) Within the nonrelativistic dipole approximation the mean lifetime for an electron in a state characterized by quantum numbers n and l in the field of a nucleus of charge Z is given by tau(n,l)~=tau0n3l(l+1)/Z4, where tau0= 3h/(2alpha5muc2)~=93.42×10-12 s and mu is the reduced mass. The formula is accurate to at least 6% for the lowest states and to a much higher degree of accuracy for highly excited states. The semiclassical result is expected to be valid to leading order in n and l. However, the very simple derivation yields results of an accuracy comparable to several approximate quantum-mechanical and semiclassical results that have been published. The approach is based primarily upon a treatment of the rate of loss of angular momentum, not of energy. A clear physical interpretation of some aspects of the radiative decay process, which is somewhat obscure in the quantum evaluation, emerges naturally from the angular momentum approach.

We investigate the validity of the surface electric-field interaction model in beam-foil experiments where the polarization of the emitted light is measured. After summarizing the theory for expanding the density operator into state multipoles and linking these to the Stokes parameters of the light, we show also how to use symmetries to reduce the size of the calculations. A very simple model is chosen for the electric field: it is perpendicular to the foil and constant over a finite distance, then zero. This model is used to find the initial density matrix for the n=3 singlet states of He i and the electric-field parameters from tilted-foil experiments. Reasonable results are obtained given the unrealistic electric-field model used.

NIST Atomic Spectra Database (ver.4.1.0) [Online]. National Institute of Standards and Technology Available: 〈http://physics. nist.gov

- Ralchenko Yu
- Ae Kramida
- J Reader
- Nist
- Team

Ralchenko Yu, Kramida AE, Reader J. NIST ASD Team, NIST Atomic
Spectra Database (ver.4.1.0) [Online]. National Institute of Standards
and Technology, Gaithersburg, MD; 2011. Available: 〈http://physics.
nist.gov/asd3〉 [2013, November 10].