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... The electron capture into the Rydberg states of highly charged ions can be achieved under different geometrical conditions. Consequently, there are three large classes of experiments: the interaction of a highly charged ions with a metallic microcapillary foil [24], the grazing incidence [25] and the beam-foil experiments [26][27][28][29]. The experimental data for transmission of highly charged ions through microcapillaries [30] have been analyzed theoretically [31] by a classical trajectory simulation based on the COB model. ...

... A strictly, quantummechanical explanation of this process depends on a huge number of parameters such as ionic charge Z, principal quantum number n, orbital quantum number l, velocity region of the ionic projectile, etc. The normal escaping geometry is particularly adopted to the beam-foil experiments, which have recently become actual [27]. Taking into account the developed techniques of the optical spectroscopy, we are able to establish a connection between the population of a certain Rydberg state and the number of photons emitted during deexitation of this state but in the outgoing part of the ionic trajectory. ...

... In our effort to realize the electron capture probability distributions, registered in the beam-foil experiments [26][27][28][29], as functions of principal n A and orbital l A quantum number of the final populated Rydberg states, we analyzed the mechanism of the electron transfer between solid surface and ion. The consideration of intermediate stages, i.e. the investigation of the probability distributions as functions of the ion-surface distance at fixed values n A and l A , is very important for better description of charge exchange process. ...

The theoretical research of the electron capture dynamics is essential for describing a variety of ion-surface processes. We analyze the intermediate stages of the population of the Rydberg states (n A ≫ 1, l A = 0 - 2) of highly charged ions escaping metal surface in the normal geometry by using the two-wave-function (TWF) method. Within the framework of the proposed time-symmetrized quantum model, the state of a single active electron is described by two wave functions and , evolving continuously and causally from a fixed initial state of the past (t = t in ) and from a fixed final state of the future (t = t fin ), respectively. A TWF method of the single active electron in the ion-surface system has been extended and applied to analyze the population of the highly charged Rydberg ions at intermediate ionic velocities (v ≈ 1 a.u.). The obtained rates demonstrate that the neutralization is unstable near the surface, indicating that additional reionization process is very active and completely destroy previously populated states. At larger ion-surface distances the population process is stabilized and allows estimation of the neutralization distances. The results are compared with the coupled-angular-mode method as well as with the values calculated by using the first-order transition rates and the classical over-the-barrier predictions.

... Certain peaks become more prominent with the delay such as the lines at 5.4, 6.5, and 7.5 keV marked as d1, d2, and d3. Such kind of features has been observed recently with H-like ions of projectile [21][22][23]and projectile-like ions [24] owing to the formation of circular Rydberg states. The excited states corresponding to the maximum orbital quantum number (l max ) as well as magnetic quantum numbers (|m|) for a particular principal quantum number (n) satisfying the relation l max = |m| = n − 1 have exactly a circular path and are called the circular Rydberg states [25], which decay via the resonance state through the cascading chain leading to the E2 transitions. ...

... Therefore, the delayed transitions observed in present study are expected to originate from the circular Rydberg states. The circular Rydberg states can be observed either through the resonances appearing on the lifetime decay curve of a certain metastable state [22] or the current technique involving the prompt and the delayed measurements. If the time-of-flight is selective, the resonance will be missing in the measurement and one measures only the decay of the metastable level [26]. ...

... The beam energy used in the experiment surpasses the Coulomb barrier energy, and therefore , the projectile like ions [24] can be produced from the α and 2α transfer reactions of the binary system [29] Table 1). Although these E2 transitions are fast decaying, they are still observed at the delays because of the circular Rydberg states cascading through the yrast chain [21,22,24] . Since the 2p 2 P 3/2, 1/2 –1s 2 S 1/2 transitions from the circular Rydberg states evolve with the delay, a little intensity contribution in the spectra at t = 0 must be due to the M1 transition 2s 2 S 1/2 –1s 2 S 1/2 . ...

... Recently, Mishra et al. [1] studied in detail the effect of cascade through circular orbits ðl ¼ n À 1Þ on the decay of unresolved 2p; 2s-1s transitions of H-like Fe at very large times (50-3000 ps) after the excitation. At such large times, intensity enhancements were observed as humps riding on the decay curve of the beam-foil-excited 2s state. ...

... This unusual behavior was explained as due to the sequential cascading of circular orbits to 2p state, which modifies the time-dependent photon intensity, IðtÞ, of the 2p-1s transition from an exponential to hump-like structures for t c τ 2p . Although the presence of surface electric field, which ranges from 10 6 to 10 8 V/cm, in beam-foil spectroscopy is known for a long time [2][3][4][5], in their study Mishra et al. [1] did not consider the effect of electric field on the lifetime of the metastable 2s state. In the present work we use the experimental data of Ref. [1] to study the combined effect of cascade through circular orbits and surface electric field on the decay of unresolved 2p; 2s-1s transitions of H-like Fe. ...

... Although the presence of surface electric field, which ranges from 10 6 to 10 8 V/cm, in beam-foil spectroscopy is known for a long time [2][3][4][5], in their study Mishra et al. [1] did not consider the effect of electric field on the lifetime of the metastable 2s state. In the present work we use the experimental data of Ref. [1] to study the combined effect of cascade through circular orbits and surface electric field on the decay of unresolved 2p; 2s-1s transitions of H-like Fe. It is found that the lifetime of the 2s state reduces to $222 ps (from its natural lifetime of 350.6 ps) due to Stark quenching. ...

... For z p ≈ 25, the Auger or radiative decay rates are comparable. In contrast, for z p ≥ 47, radiative decay rates are many orders of magnitude higher than Auger rates and the high lying states so formed are termed as circular Rydberg states, possessing highest magnetic quantum number as observed in several experiments [9,36]. These states undergo neither Auger transition nor fast radiative decay because of restriction on the dipole selection rules ∆l = ±1. ...

We have employed x-ray spectroscopy to probe the charge changing process only in the bulk of the foil when swift heavy ions pass through it. In contrast, the electromagnetic methods take into account integral effect of the charge changing process in the bulk as well as the charge exchange phenomenon at the surface of the foil. Thus, the difference between the mean charge states so measured from the two methods disentangles the charge exchange phenomenon at the surface from the charge changing process in the bulk and, provides opportunities to refine the understanding of ion-surface interactions. Very surprisingly, up to tens of electrons per event participate in the charge exchange phenomenon during swift heavy ion-surface interactions. This finding has been validated with a series of experiments using several ions (z = 22-35) in the energy range of 1.5-3.0 MeV/u and also verified theoretically with Fermi-gas model. Interestingly, such unusual charge exchange phenomenon could play significant role in x-ray emission of many astrophysical environments, infrared emission bands from range of environments in galaxies, accelerator physics, ion energy losses in solids, heavy ion cancer treatments, inner shell ionization by heavy ions, and surface modifications in nano scale.

The review covers the dynamics of different kinds of one electron Rydberg quasimolecules in various environments, such as being subjected to electric and/or magnetic fields or to a plasma environment. The higher than geometrical symmetry of these systems is due to the existence of an additional conserved quantity: the projection of the supergeneralized Runge–Lenz vector on the internuclear axis. The review emphasizes the fundamental and practical importance of the results concerning the dynamics of these systems.

The detailed description of electron terms in the field of two stationary Coulomb centers of charges Z and Z′ separated by a distance R is one of the most fundamental problems in quantum mechanics. When the charges Z and Z′ approach each other and share the only one electron that they have, they form a quasimolecule. Such quasimolecules are encountered in various kinds of plasmas and play an important role in theoretical and experimental studies of charge exchange. When the electron is in a highly-excited state, it is a one-electron Rydberg quasimolecule (OERQ). There are extensive analytical studies of the OERQ by the methods of classical mechanics (which are appropriate for Rydberg states). In one of our previous papers we studied the OERQ subjected to a laser field in the situation where the laser frequency was much smaller than the highest frequency of the unperturbed system. In the present paper we consider the situation where the OERQ is subjected to a laser field whose frequency is much greater than the highest frequency of the unperturbed system. For obtaining analytical results we use a generalization of the method of effective potentials. We show that as the amplitude of the laser field increases, in the case of the linearly-polarized laser field, the structure of the energy terms becomes more complex. Moreover the number of the energy terms increases in this case. We also calculated analytically the shift of the radiation frequency of OERQ caused by the laser field. As the amplitude of the laser field increases, so does the shift. The radiation frequency is shifted to the blue in the case of the linearly-polarized laser field, and to the red in the case of the circularly-polarized laser field. For a known amplitude of the laser field, by measuring the relative shift of the radiation frequency it should be possible to determine experimentally the distance of the orbital plane of the electron from the nucleus of the smaller nuclear charge.

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.

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.

Orbital-angular-momentum (l) distributions of ions in intermediate n and l states have been compared for 1.5-5-MeV carbon ions traversing C foils and He gases by projectile Auger spectroscopy. The degree of high-l enhancement in C targets is quantitatively established. A picture involving multiple collisions between target atoms and the entrained electrons which accompany the ions explains the results.

E1, M1, E2, M2, E3, and M3 transition probabilities for hydrogen-like atoms are calculated with point-nucleus Dirac eigenfunctions for Z51 - 118 and up to large quan- tum numbers ,525 and n526, increasing existing data more than a thousandfold. A critical evaluation of the accuracy shows a higher reliability with respect to previous works. Tables for hydrogen containing a subset of the results are given explicitly, listing the states involved in each transition, wavelength, term energies, statistical weights, tran- sition probabilities, oscillator strengths, and line strengths. The complete results, includ- ing 1 863 574 distinct transition probabilities, lifetimes, and branching fractions are avail- able at http://www.fisica.unam.mx/research/tables/spectra/1el © 2005 American Institute of Physics. @DOI: 10.1063/1.1796671#

We present a joint theoretical and experimental study of the time evolution of electronic states of highly charged hydrogenic ions formed by capture during transmission through solids as they undergo multiple collisions and radiative decay. For this transport problem we have developed an inhomogeneous nonunitary Lindblad master equation that allows for a description of open quantum systems with both sinks (electron loss) and source (capture) present. We apply this theoretical framework to study transient coherences created in electron capture by 13.6 MeV∕amu Ar18+ ions transmitted through amorphous carbon foils and decoherence during subsequent interaction with the foil. In the limit of thin targets we can directly probe electron capture cross sections under single collision conditions, while for thicker targets we follow the partially coherent dynamics of the open quantum system in interaction with the solid as a function of interaction time. The calculated results are in close agreement with experimental data obtained at the LISE facility in GANIL. Photon intensities from excited argon ions were determined through high resolution x-ray spectroscopy in which individual fine structure components were resolved. Measurements were performed for a wide range of carbon foil thickness to study the time development of the excited state populations.

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.

A complete experimental study on the production and transport of long lifetime excited states has been done for Ar18+ on solid C targets, at a velocity of 23 a.u. and for a range of thickness allowing to vary the transport conditions from single collision to equilibrium (3.5 to 201 µg/cm2). A systematic determination of Ar17+ Rydberg l and 2s state populations has been performed using X-ray spectroscopy technique. Results are compared with predictions of different transport simulations (either developed on a quantum or classical phase space), which take into account multiple collisions and the strong polarization induced by the incoming ion (the wake field). Using Continuum Distorted Wave approximation for modeling the initial capture process, very good agreement is found between experimental Rydberg state populations and theoretical approaches limited to the effect of multiple collisions. On the contrary, the transport of the metastable 2s exhibits strong sensitivity to Stark mixing induced by the wake field. Limitation of each theoretical approach is discussed with respect to the different experimental observables.

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).

Production of projectile Rydberg states in fast-ion-foil collisions is shown to exhibit a pronounced target-thickness dependence, proving that Rydberg states are not predominantly formed by direct capture of target electrons. Instead, it is proposed that ionized projectile electrons can undergo transition back to Rydberg states when the ion emerges from the foil.

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.

Radiative lifetimes (and f values) have been measured for the n=3 levels of the sodiumlike ion, Cu18+, using the beam-foil method. Strong cascade tails attributable to the decay of long-lived Rydberg or "yrast" levels were observed.

Explicit calculations demonstrate that cascade repopulation effects are
a possible explanation of the t$sup -1$.$sup 5$ dependence in the decay of Ly-
$alpha$ radiation at long times after excitation observed recently by
Braithwaite, Matthews, and Moore. Good agreement with all available experimental
data is obtained with reasonable population models; excitation proportional to
n$sup -$/subm/ with m=2.2--4 is indicated.

The relative level populations in beam-foil-excited sodiumlike argon (Ar VIII) and copperlike krypton (Kr VIII) have been studied at 2-MeV projectile energy. In Ar VIII, the 3p and the 3d terms are strongly excited. The level population decreases rapidly with increasing value of the principal quantum number n, reaches a minimum for levels with n=5 or 6, but increases then and reaches a strong maximum for levels with n≃11. As an example, the 11d level is populated a factor of 2 more than the 3d level. Also the Kr VIII data show a population maximum for levels with n=11. The strong 3p and 3d level excitations in Ar VIII are explained as selective inner-shell processes which can be understood in the molecular-orbital electron-promotion picture. The preferential population of highlying Rydberg states is explained as resulting from a near-resonance electron transfer from the valence band of the carbon foil to the projectile. This process takes place when the projectile leaves the back of the foil, and the distribution of population upon different n levels will vary with charge state. The level population for levels with fixed n increases rapidly with increasing value of the orbital-angular-momentum quantum number for levels in Kr VIII, Kr X, Kr XI, and Kr XIII. The results are discussed, and their influence on decay curves as well as their relations to multiply charged ion-atom collisions are pointed out.

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 studied the relative level populations in beam-foil-excited C iv, N v, O vi, and F vii by optical spectrometry in the range n=3-12. These Li-like ions have the configuration 1s2nl. The population distribution curves are quite different, ranging from a sharp, approximately (n*)-3, decrease for C iv to flat maxima at n∼7 and 8 for O vi and F vii, respectively. This gradual change may be explained as resulting from a near-resonant charge transfer from the valence band of the carbon foil to the projectile. For fixed n, states with large l are preferentially populated. The consequences of these results in cascade analyses of lifetime data from beam-foil measurements are briefly discussed.

The differing results of previous analyses of the binding energy for particles trapped in the wake of fast-moving ions traversing a solid are reconciled, and the values given by Day are corrected at high velocities. A form of a variational calculation of these energies which permits comparison of various dielectric functions is presented, and used to deduce a possible form for the bound-particle wave function. This wave function is used in an analysis of processes occurring as the wake emerges from the surface.

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.

A complete experimental study of the production and transport of long-lifetime excited states has been done for Ar18+ on solid C targets, at a velocity of 23 a.u., and for a range of thickness allowing us to vary the transport conditions from single collision to equilibrium (3.5 to 201 μg∕cm2). A systematic determination of Ar17+ Rydberg ℓ- and 2s-state populations has been performed using the x-ray spectroscopy technique. Results are compared with predictions of different transport simulations (developed on either a quantum or a classical phase space), which take into account multiple collisions and the strong polarization induced by the incoming ion (the wakefield). Using the continuum distorted-wave approximation for modeling the initial capture process, very good agreement is found between experimental Rydberg-state populations and theoretical approaches limited to the effect of multiple collisions. On the contrary, the transport of the metastable 2s state exhibits strong sensitivity to Stark mixing induced by the wakefield. The limitation of each theoretical approach is discussed with respect to the different experimental observables.

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.

A facility for lifetime measurement of metastable states in highly charged ions using the beam-foil technique with a single-foil and a two-foil target has been developed. In the two-foil technique, one foil moves with respect to the other and the option of varying the thickness of the fixed foil online has been implemented. A holder with multiple foils is used as a fixed target, and moved along x, y, and θ, the angle of rotation with respect to beam direction along the z axis. Using this facility, the He-like 1s2p and Li-like 1s2s2p titanium lifetimes have been measured and compared with earlier values. In addition to this, the processes which occur when excited states collide with carbon foils of different thicknesses have also been investigated. Preliminary results suggest the scope of studying intrashell transitions during ion-solid collision using this setup. In this article, the setup is described in detail and representative results are briefly discussed.

We report collision-induced intra-shell transitions for the first time. It has been observed between two close by levels 1s2s 3S1 and 1s2p3Po2 in He-like Ti ions by the beam-two-foil time-of-flight technique. The mean collision-induced transition probability between these two levels is found to be quite large (0.72 ± 0.05/collision), which is attributable to the small energy splittings (32 eV) between them.

Using projectile-like ions instead of projectile ions in a beam–foil source, we have reconfirmed the formation of circular Rydberg states. The projectile-like 6028Ni and 6329Cu ions have been produced by a 5626Fe ion beam and 6230Zn ions by a 5828Ni ion beam, at beam energies above the Coulomb barrier, bombarding a thin carbon foil. Time-resolved x-ray transitions of these projectile-like ions attain their maximum intensities at different delays. Such delays are attributed to successive cascading through yrast transitions from the circular Rydberg levels, which find important implications in understanding the origin of radio recombination lines from interstellar space.

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.

Delayed emission of prompt Ly-α and Ly-β radiation has been used to investigate the initial population of excited states of fast H-like oxygen and sulfur ions emergingfrom foil targets. We can distinguish between low- and high-angular momentum states and identify ions with orbital dimensions of ≈1000 a0. It is shown that electron pick-up known from single ion-atom collisions is not sufficient to explain foil-induced excitation of high-angular momentum states and additional mechanisms must be considered. Capture due to last layer interaction is commented on.

Theory for the generation and decay of high-lying Rydberg states in beam-foil experiments is presented. Our theory is designed to check the assumption that electron capture in the foil proceeds via a direct transition from a free state. The success of the theory in explaining the observed (primary and secondary) oscillatory structure and underlying smooth background of the ionization signal, as a function of additional variable electric fields, justifies this assumption. In addition, existence of asymmetry with respect to sign change of the variable fields is predicted to be detectable at high field values. Generation of Rydberg atoms in beam-foil experiments is shown to be a sensitive probe of the state distribution prepared during the beam's passage through the foil. Our theory substantiates the claim that Rydberg atoms produced in the beam-foil encounter exit the foil in a pure superposition state.

The decay curves for 2p-1s and 3p-1s transitions in 32-MeV H-like oxygen projectiles excited by a thin carbon foil have been measured and compared with the results of a cascade computer program which calculates the intensities of these transitions for an assumed initial distribution of excited states as a function of decay time. The measured decay curves agreed best with those predicted by the cascade program using an l-independent population probability proportional to n/sup -4/ for each state.

Equilibrium charge distributions have been measured for 18 kinds of ions passing through a carbon foil in the energy region of 1-6 MeV/u for light ions and of 0.2-1 MeV/u for heavy ions. By combining the data obtained at present with those reported for other energies or ion species, an attempt is made to find the systematics for charge fraction F(q), mean charge q¯, and distribution width d over the wide range of ion species Z and energy E. Strong correlation has been found between the shell structure of ions and the variation of q¯ or d with Z or E. The analysis for this correlation enables the evaluation of rather reliable values of q¯, d, or F(q) for ion species 4

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.

The experimentally observed high-{ital l}-state population of ions excited in ion-solid interactions differs sharply from {ital l}-state populations produced in ion-atom collisions. We have studied the population dynamics of electronic excitation and transport within the framework of a classical transport theory for O{sup 2+} (2-MeV/u) ions traversing C foils. The resulting delayed-photon-emission intensities are found to be in very good agreement with experiment. Initial phase-space conditions have been obtained from both classical-trajectory Monte Carlo calculations and random initial distributions. We find evidence that the very-high-{ital l}-state populations produced in ion-solid collisions are the result of a diffusion to high-{ital l} states under the influence of multiple scattering in the bulk of the solid.

The first comparison of core-state populations of initially bare Kr36+ ions emerging from gaseous and solid targets is presented. Another new important feature of this experiment lies in the fact that for such fast heavy ions, the single-collision condition is fulfilled even in solid targets. Our results can be explained by a wake-field-induced Stark mixing of the substates in a solid. Further coherence angles and field strength measurement are discussed.

Projectile-centered Rydberg states of highly charged fast ions traversing thin solid targets show an unexpected abundance of high-l states. We present a theory for the production of high-l states based on classical stochastic dynamics. Diffusion into high-l states is shown to be universal for single-particle orbits in three dimensions under the influence of a stochastic perturbation, i.e., largely independent of the details of the interaction potentials. Monte Carlo simulations using a Langevin equation for stochastically perturbed electrons in a dynamically screened Coulomb field yield quantitative agreement with experimental data.

Angular momentum distribution of autoionizing states produced by 1.5-5-MeV C þ ions in carbon foils Theory of the coherent decay of high-lying Rydberg states in beam-foil encounters

- Y Yamazaki
- N Stolterfoht
- Pd Miller
- Hf Krause
- Pl Pepmiller
- S Datz

Yamazaki Y, Stolterfoht N, Miller PD, Krause HF, Pepmiller PL, Datz S, et al. Angular momentum distribution of autoionizing states produced by 1.5-5-MeV C þ ions in carbon foils. Phys Rev Lett 1988;61:2913–6. [12] Seideman T, Shapiro M, Vager Z. Theory of the coherent decay of high-lying Rydberg states in beam-foil encounters. Phys Rev A 1987;35:87–102.