This study is devoted to the general properties of pole strings and string curves of the eigenvalues of complex scaled Hamiltonians; in detail, it is our aim to correlate parameters of the Hamiltonian (mass and parameters of the potential) to the shape and location of the corresponding string curve. In the present contribution, which considers one-dimensional Hamiltonians, we show that every string curve can be decomposed into a few, very simple ‘‘primitives.’’ The latter are associated with certain subunits (or parts) of the potential in such a way that each subunit gives one and only one string curve. If a potential under investigation contains more than one subunit, then one will find multiple or composite string curves. The corresponding Hamiltonian will possess an additional symmetry that can be expressed by introducing a combined index (n,m), where n numbers the subunit and m the resonant eigenvalue belonging to the subunit. Furthermore we show in this contribution phenomenologically which kind of string curve emerges from which type of subunit; one is able to predict the general shape of the string curve and some of its inherent information. The mass dependence (or nondependence) of the string curves is explicitly discussed and parallels with the semiclassical WKB theory are addressed. In addition we present material concerning the possible ‘‘wiggly’’ behavior of pole strings; we show explicitly on the semiclassical level why certain potential features wiggle while others do not. Employing semiclassical concepts, we are even able to ‘‘explain’’ the corresponding string curves in terms of simple integrals. We also give a condition—depending only on the zeros of the function E-V(z)—for the possible emergence of wiggles. Numerical experiments that are partly reported here show that all potentials with a Gaussian damping factor possess wiggles, while those with exponential damping (${\mathit{e}}^{\mathrm{-}\mathit{x}}$) do not.

The anisotropy of resonant Auger decay of photo-excited Kr 3${\mathit{d}}_{3/2,5/2}^{\mathrm{-}1}$5p and Xe 4${\mathit{d}}_{3/2,5/2}^{\mathrm{-}1}$6p states has been studied by multiconfiguration Dirac-Fock method. The calculations account for the configuration interaction both in the initial and in the final states of the Auger decay. For the nonresolved ${\mathit{nd}}^{\mathrm{-}1}$(n+2)p(J=1) resonances (n=3 for Kr and n=4 for Xe) the average intensities and anisotropies of Auger lines were calculated by weighing each partial rate by the pertinent Dirac-Fock photoexcitation probabilities. Our results show that, in addition to the initial- and final-state correlation, both the relaxation and the exchange interaction have a substantial effect on the anisotropy of these Auger spectra. For most Auger lines there is good agreement between our calculated β parameters and experimental values for the Kr and Xe ${\mathit{nd}}_{5/2}^{\mathrm{-}1}$(n+2)p photoexcitation resonances; there is also satisfactory agreement for the Kr 3${\mathit{d}}_{3/2}^{\mathrm{-}1}$5p and Xe 4${\mathit{d}}_{3/2}^{\mathrm{-}1}$6p resonant Auger spectra. However, the remaining notable discrepancies between theory and experiment indicate that important correlation effects are still omitted in our calculations. Discrepancies between different experimental results stress the need for further improvements on the experimental side.

To describe the rearrangment channels for three-particle atomic reactions and for three-particle muonic processes a semiclassical formalism of the Faddeev-Hahn equations is applied. The relative motion of heavy particles is treated from the classical point of view while the motion of the lighter particle is described from the quantum-mechanical point of view. To find correct trajectories of heavy particles the self-consistent Pechukas method, based on the Feynman path-integral theory, is employed.

Excitation of molecular hydrogen has been studied in 1.8-keV collisions with molecular projectile ions ${\mathrm{H}}_2^{+}$, ${\mathrm{N}}_2^{+}$, ${\mathrm{CO}}^{+}$, ${\mathrm{O}}_2^{+}$, and ${\mathrm{CO}}_2^{+}$ by means of energy-loss spectrometry using a high-resolution ion translational-energy spectrometer. Excitation of the target ${\mathrm{H}}_2$ is observed only in the case of collisions with ${\mathit{H}}_2^{+}$. Oscillator strengths for electronic transitions to various electronic states are determined by simulating the measured energy-loss spectra with calculations using calculated Franck-Condon overlap integrals. Excitation of the projectile ions is observed in the case of collisions with ${\mathrm{N}}_2^{+}$ and ${\mathrm{CO}}^{+}$ projectiles. Neither projectile excitation nor target excitation is observed when experiments are carried out with ${\mathrm{O}}_2^{+}$ and ${\mathrm{CO}}_2^{+}$ projectiles. The results obtained in the present study are interpreted as a manifestation of wave-function-overlap effects involving the highest occupied molecular orbitals of the target and projectile ions.

We present the results of an extensive classical trajectory Monte Carlo (CTMC) simulation of the ejected electron spectrum in collisions of 1.5-MeV/u ${\mathrm{F}}^{9+}$ with helium. Excellent agreement is found with the measurements of Lee et al. [Phys. Rev. A 41, 4816 (1990)] for ejection to 0°. In particular, the simulation reproduces extremely well the shape and magnitude of the electron-capture-to-the-continuum and binary peaks. We contrast this agreement with calculations utilizing various quantum-mechanical perturbation theories. Also, a continuum-distorted-wave–eikonal-initial-state approach, which describes the interaction between the outgoing electron and the residual target ion through a model potential, has been utilized. This approach is shown to be an improvement over conventional calculations based on the use of effective charges. We draw conclusions regarding the proper representation of the collision dynamics leading to electron ejection in the low-energy, electron-capture-to-the-continuum, and binary peak regimes. Calculations of the doubly differential ionization cross section for non-0° ejection are displayed as well.

Recent accurate measurements of the stopping powers of eleven halogenated hydrocarbon compounds for protons and α particles in the respective energy intervals of 0.5–2.1 MeV and 1.6–3.0 MeV have been analyzed in the context of Bethe theory, modified by inclusion of Barkas-effect and Bloch terms. The values of various parameters of the formulation were ascertained through two- and three-parameter fits to the data. The results were generally consistent with anticipated deviations from the additivity rule.

Energy losses of 1-MeV ${\mathrm{H}}_2^{+}$ ions passing through carbon foils of 2–8 μg/${\mathrm{cm}}^2$ thickness have been measured. The observed energy loss increases linearly with the target thickness and shows an offset, 0.4 keV, at zero thickness. The stopping power derived from the observed energy losses is 1.15 times as large as the sum of the stopping powers for two single ${\mathrm{H}}^{+}$ of the same velocity. Stopping powers for ${\mathrm{H}}_2^{+}$ ions and diprotons are calculated with the first Born approximation. The calculated stopping power for the diproton agrees quite well with the one observed. This indicates that the observed ${\mathrm{H}}_2^{+}$ ions traverse the target as diprotons after the loss of the binding electrons upon entrance into the foil and recapture target electrons at the exit surface. The observed energy-loss offset at zero thickness also supports this scenario.

Electron capture from surfaces by grazing heavy projectiles is studied with a fully quantum treatment. The collision is considered in the high-energy regime where the projectile velocity is larger than the Fermi velocity of the free-electron gas of the solid. Some approximations commonly used in atomic collision theory, such as the first-order Born, the impulse, and the Vainstein-Presnyakov-Sovelman approximations, are adapted to the present geometry and interactions. The surface-electron and surface-projectile interactions are represented according to the jellium model and the Molière and Lindhard potentials. Detailed calculations are made for protons on an Al(111) surface and compared with recent experiments. No agreement is found; the theory largely underestimates the experiments at high energies. This disagreement shows that the high-energy-tail data cannot be explained as a capture process from the free-electron gas. Other neutralization mechanisms should take place to account for the experiments.

The capture of electrons bound to the atoms of a crystal surface by grazing heavy projectiles is studied in the high-energy regime. The eikonal impulse approximation is used to calculate the capture atomic probabilities, which are then folded with the distance-to-the-surface distribution given by planar channeling theory. Good agreement is found with experiments at high energies. We also study the influence of the rugosity or surface irregularities formed by adsorbed atoms. It is concluded that, in the high-energy tail, the capture of bound electrons is more important that capture from the free-electron gas. It is found that the closest distance to the surface and the rugosity play decisive roles.

Atom de Broglie–wave interference fringes are revealed by their selective destruction. A thermal potassium beam is transmitted through a Talbot-Lau atom interferometer. Different fringe Fourier components resonate in the interferometer at different atomic velocities. The thermal velocity distribution averages and washes out the high-frequency components. ac-modulated laser light passes through the interferometer, is scattered by atoms at one velocity, and destroys, and thereby reveals via the ac modulation, the associated high-frequency fringe contribution.

The absorption profiles of left-hand and right-hand circularly polarized laser light propagating through sodium vapor are asymmetric and considerably frequency shifted if small static magnetic fields are present. Using an analytical model we show how optical pumping ‘‘enhances’’ the laser-induced light shift from the kilohertz to the gigahertz range. We compare the analytical results with experimental data obtained from the homogeneously broadened Na ${\mathit{D}}_1$ transition.

Atomic mirrors and beam splitters based on adiabatic following by delayed laser pulses in a three-level Raman configuration are analyzed. We show that in a pure three-level system of two ground states and one excited state, laser pulses tuned precisely on resonance with the excited state do not produce any accumulated phase shifts due to ac Stark shifts even if the process is nonadiabatic. A numerical simulation suggests that multiple delayed laser pulses are attractive for precision interferometry since high transfer efficiencies (up to 98.7% per pulse for the cesium D1 line) and low ac Stark shifts are expected. A possible application to optical two-photon spectroscopy for an optical clock is discussed.

The light-induced drift velocity of optically active atoms immersed in a buffer gas sometimes changes sign at some temperature. It is pointed out that the density of the active atoms and the temperature of the system form a nonlinear dynamical system that may exhibit instabilities. These may show up as an oscillatory behavior of these quantities as a function of time. A possible realization in the case of alkali-metal atoms is discussed.

The electron polarization of hydrogen (H) and deuterium (D) atoms in a spin-exchange optical-pumping apparatus has been measured as a function of H (D) density and magnetic-field strength. The atomic density was varied between 4×${10}^{13}$ and 2.6×${10}^{14}$ atoms/${\mathrm{cm}}^3$ and the magnetic-field strength from 120 to 400 mT. The results suggest that the atoms approach spin-temperature equilibrium even though the magnetic fields are large compared to the critical fields of the atoms.

The role played by the quadratic term of the interaction Hamiltonian -αA(t)⋅p+1/2${\mathrm{\alpha }}^2$${\mathbf{A}}^2$(t) in the velocity gauge is examined in both the semiclassical and the quantized theory. It is shown that this term cannot be eliminated in every case via standard contact transformations. For second-order processes a special transformation is proposed that eliminates the noncontributing parts of ${\mathbf{A}}^2$(t), and leads to the right expressions for the Stark shift and the resonance-fluorescence probability. The generalization to arbitrary order of these results is done in a fully quantized theory by resorting to diagram summation. One finds that the contributions of diagrams displaying double-photon absorptions and emissions sum to zero. The only effect of the quadratic term is to shift the whole atomic spectrum by an intensity-dependent amount.

We present an alternative method for changing atomic alignment to orientation through interactions with orthogonal static electric and magnetic fields. Experimental results demonstrating this effect in the 5d6p ${}_{}{}^1{}_{}{}^{}$P state of atomic barium and the F=4 hyperfine level of the ground state of atomic cesium are presented. The theory of this effect for a j=0 to j=1 electric dipole transition is discussed in detail. The tensor polarizability of the 5d6p ${}_{}{}^1{}_{}{}^{}$P state of Ba is determined to be 1.31(15) MHz/(kV/cm${)}^2$, in good agreement with the results of van Leeuwen and Hogervorst [Z. Phys. A 310, 37 (1983)].

Stimulated by a recent experiment [L. D. Noordam et al., Phys. Rev. Lett. 68, 1496 (1992)], we present a model of Rydberg-atom photoionization whose essential feature is the resonance between the initially populated Rydberg state and an additional state lying below Rydberg quasicontinuum. Despite the infinite number of discrete states involved in our model we have obtained the expressions for photoionization yield and discrete-state populations in completely analytical form. These expressions cover both short- and long-time scales, i.e., when laser-pulse duration is shorter or longer than the classical round-trip time of the Rydberg electron. The short-time scale corresponds to the conditions met in the experiment of Noordam et al. and, on the basis of our expressions, we have gained at least qualitative understanding of their observations. In the case of long pulses, which in our considerations are never longer than 54 ps, near resonance is shown to be the origin of a profound ionization suppression, particularly for some specific frequencies, which we identify as those ensuring the formation of a perfectly dark dressed state of zero width and thus unionizable. This dark state is shown to be populated with a probability increasing when laser gets stronger. We discuss the connection between stabilization and formation of this perfectly dark state as well as of additional dressed states, which are dark in the sense that they have the property of becoming very narrow as laser intensity increases. The undamped perfectly dark state, created at specific laser frequencies, has given us rise to introduce what we call the zero-pole approximation for ionization yield, which, as we have shown, works well if duration and intensity of laser pulse are appropriately combined.

The relaxation and generation of multipole orientations in a heavy-alkali-metal vapor in the presence of a weak static magnetic field are theoretically studied both for populations and for Zeeman coherences by taking into account the effects on the evolution of the atomic density matrix of the relaxation processes (by alkali-atom–buffer-gas, alkali-atom–alkali-atom with spin exchange and alkali-atom–cell-wall collisions) and of the optical pumping with any light polarization and spectral distribution. The dependence of the stationary-state multipole orientations on the pumping characteristic parameters is numerically analyzed. The detection process of these orientations is also studied.

We have measured the microwave ionization threshold electric fields for ns-state Na Rydberg atoms from n=24–33 as a function of the duration of the ionizing microwave pulse. Pulses as short as 2.8 ns were used, containing fewer than 25 cycles of 8.55-GHz radiation. While the fields required to produce the onset of ionization were independent of pulse duration and exhibited the ${\mathit{n}}^{\mathrm{-}5}$ scaling characteristic of ionization by diffusion through higher-energy states, the fields required to produce nearly complete ionization increased dramatically as the pulse was shortened. Additional measurements of the populations of bound states after the shortest microwave pulses showed that up to ∼10% of the atoms were excited to states above the initially populated ns state and the adjacent (n-1) manifold of higher angular momentum states, while most either ionized or remained in these states. From this observation we conclude that the rate-limiting process for ionization is the transition from the initially populated ns states or the adjacent manifold to the next higher manifold, not the diffusion through higher-lying states.

An ab initio approach has been applied to study multiphoton detachment rates for the negative hydrogen ion in the lowest nonvanishing order of perturbation theory. The approach is based on the use of B splines allowing an accurate treatment of the electronic repulsion. Total detachment rates have been determined for two- to six-photon processes as well as partial rates for detachment into the different final symmetries. It is shown that B-spline expansions can yield accurate continuum and bound-state wave functions in a very simple manner. The calculated total rates for two- and three-photon detachment are in good agreement with other perturbative calculations. For more than three-photon detachment little information has been available before now. While the total cross sections show little structure, a fair amount of structure is predicted in the partial cross sections. In the two-photon process, it is shown that the detached electrons mainly have s character. For four- and six-photon processes, the contribution from the d channel is the most important. For three- and five-photon processes p electrons dominate the electron emission spectrum. Detachment rates for s and p electrons show minima as a function of photon energy.