In high-energy atomic collisions between bare high-$Z$ projectiles and low-$Z$ target atoms, an electron may be captured radiatively into the ground state or, alternatively, into an excited projectile state, which subsequently decays by x-ray emission. These processes are the inverse of a single-step or a two-step ionization, in which the first photon resonantly excites an electron from the hydrogenic ${1s}_{1/2}$ ground state and a second photon ionizes the excited electron. In this paper, we present a theoretical analysis with a particular emphasis on a detailed multipole decomposition of the photon wave function. This treatment is suitable for connecting angular correlations with alignment studies of the excited state. The anisotropy factors for angular correlations beween the beam axis and the decay x rays following radiative electron capture (REC) into the ${2p}_{3/2},\hspace{0.5em}\hspace{0.5em}{3p}_{3/2},\hspace{0.5em}\hspace{0.5em}{3d}_{3/2},$ and ${3d}_{5/2}$ levels of bare ${\mathrm{Xe}}^{54+},\hspace{0.5em}\hspace{0.5em}{\mathrm{Au}}^{79+},\hspace{0.5em}\hspace{0.5em}{\mathrm{Pb}}^{82+},$ and ${\mathrm{U}}^{92+}$ projectiles with energies ranging from 10 MeV/u to 10 GeV/u are explicitly presented and the connection with the alignment is given. It is predicted that REC occurs predominantly into states with the minimal magnetic quantum number $\pm \frac{1}{2}$ indicating a strong alignment perpendicular to the beam axis.

A pulsed laser investigation is performed to study the detailed effects of electronic angular-momentum alignment on the cross section for the energy-transfer process $\mathrm{Ca}\left(4s4p{}^3{P}_1\right)+\mathrm{Ca}\left(4s4p{}^3{P}_1\right)\to \mathrm{Ca}\left(4s4p{}^1{P}_1\right)+\mathrm{Ca}{(4s}^2).\mathrm{}$ A uniform magnetic field imposed by a set of Helmholtz coils is used to systematically precess the initial state orbitals with a well-defined period, allowing different alignments to be sampled at different time delays after the pulsed laser excites and aligns the $\mathrm{Ca}\left(4s4p{}^3{P}_1\right)$ states. The polarization effects in this collision process are striking. For example, the cross section for two atoms both in the $m_j=0\mathrm{}$ magnetic substrate is 13 times larger than the cross section for two atoms that are both in the $m_j=1\mathrm{}$ (or -1) substrate, where the quantization axis is taken to be along the relative velocity vector of the collision. The initial m-sublevel dependence of this three-vector correlation process can be completely described with eight fundamental parameters, five of which are accurately obtained. In addition, the coarse energy dependence of these parameters is deduced.

Inversion relations expressing inclusive cross sections as linear combinations of exclusive cross sections are derived within the independent electron approximation without exchange. Both binomial and multinomial probability distributions are used. No particular model is used for $P\left(\overrightarrow{b}\right).\mathrm{}$ A criterion for applicability of the multinomial probability distribution to describe second-order transitions for the different collision channels, also independent of $P\left(\overrightarrow{b}\right),$ is presented. The coupling of ionization and capture of outer-shell electrons is discussed and the inversion relations derived are applied to the analysis of coincidence measurements of projectile and target charge states. Parametrization and scaling laws for single and double ionization of outer-shell electrons of many-electron atoms are considered by studying the influence of the electron capture channel.

In the light of the generalized Sturm-Liouville theorem, the Levinson theorem for the Dirac equation in two dimensions is established as a relation between the total number $n_j$ of the bound states and the sum of the phase shifts ${\eta }_j(\pm M)$ of the scattering states with the angular momentum $j$: ${\eta }_j\mathrm{}\left(M\right)+{\eta }_j\left(-M\right)=\{\left(\{{(n}_j+1)\pi ,\mathrm{when}\mathrm{}\mathrm{a}\mathrm{}\mathrm{half}\mathrm{}\mathrm{bound}\mathrm{}\mathrm{state}\mathrm{}\mathrm{occurs}\mathrm{}\mathrm{at}\hspace{0.5em}E=M\hspace{0.5em}\hspace{0.5em}\mathrm{and}\hspace{0.5em}\hspace{0.5em}j=3/2\mathrm{}\hspace{0.5em}or\hspace{0.5em}-1/2\left\}\right\{{(n}_j+1)\pi ,\mathrm{when}\mathrm{}\mathrm{a}\mathrm{}\mathrm{half}\mathrm{}\mathrm{bound}\mathrm{}\mathrm{state}\mathrm{}\mathrm{occurs}\mathrm{}\mathrm{at}\hspace{0.5em}E=-M\hspace{0.5em}\hspace{0.5em}\mathrm{and}\hspace{0.5em}\hspace{0.5em}j=1/2\mathrm{}\hspace{0.5em}or\hspace{0.5em}-3/2\}\{n_j\pi \hspace{0.5em},\mathrm{the}\mathrm{}\mathrm{remaining}\mathrm{}\mathrm{cases}.\}\right)$The critical case, where the Dirac equation has a finite zero-momentum solution, is analyzed in detail. A zero-momentum solution is called a half-bound state if its wave function is finite but does not decay fast enough at infinity to be square integrable.

Using a recently derived extension of the Friedel sum rule to finite velocities we calculate the energy loss of helium ions in aluminum. The model includes the contribution due to the excitation of valence electrons according to a quantum-mechanical picture based on scattering theory (transport cross-section approach) and gives a self consistent representation of the velocity-dependent screening for swift ions. The method provides a direct evaluation of the nonlinear effects in the more complex range of energies around the stopping power maximum. In the corresponding limits, the present results converge to the existing low- and high-velocity approximations. The stopping power values calculated with this method are in good agreement with various experimental results.

We investigated the hybridization of ${\mathrm{He}}^{+},$ ${\mathrm{Li}}^{2+},$ and ${\mathrm{Be}}^{3+}$ ionic levels and the creation of surface resonances for nuclear charges $Z=2,3,$ and $4$ near an Al surface. Starting from a two-center basis set expansion with hydrogenic wave functions on the ion site and jellium wave functions in the metal half space, we calculate the self-energy for ion-surface system in the fixed-ion approximation. We obtain convergence by using a rather small set of bound ionic states. This ideally suits this method for the generation of adiabatic basis states that can be used in time-dependent close-coupling calculations for slow ion-surface collisions. We compare our resonance energies and widths with other theoretical approaches, discuss electronic density profiles, and analyze resonances in terms of Stark states.

We present a theoretical study of the transmission of relativistic ${\mathrm{H}}^{-}$ ions through thin carbon foils for a broad range of beam energies. Our study is based on a Monte Carlo solution of the Langevin equation describing electronic excitations of the atoms during the transport through the foil. We present calculations for the subshell populations of outgoing hydrogen atoms and we show that there exists a propensity for populating extreme Stark states. Our results are found to be in good agreement with recent experimental data. We analyze the effect of a laboratory magnetic field on the population dynamics.

We study the effects on the electronic stopping power of large clusters in solids, resulting from multiple elastic scattering of each particle in the cluster by the target atoms, in the small-angle approximation. Evaluation of the cluster vicinage self-energy at the entrance of the target shows that large clusters may stabilize against the Coulomb explosion for a range of cluster sizes and speeds, so that the change of the cluster structure, due to multiple scattering, may have a noticeable influence on the vicinage, or interference, energy losses of clusters due to collective electronic excitations in the target. Stopping power calculations are presented for ${\mathrm{C}}_{60}$ and $({\mathrm{H}}_2{)}_{50}$ clusters in an Al target, together with the results on stabilization conditions against the Coulomb explosion for $({\mathrm{H}}_2{)}_{N_m}$, based on self-energy considerations.

We have used all-electron local (LDA) and nonlocal (GGA) approximations to the density-functional theory to determine binding energies, equilibrium geometries, vibrational frequencies, and magnetic properties of ${\mathrm{Rh}}_N$ clusters $(N<~6).$ We present careful tests on the ${\mathrm{Rh}}_2$ dimer that compare results as calculated with a large (18-single Gaussian) and a very large (23-single Gaussian) basis sets. While the smaller set of Gaussians leads to underconverged results, we find that the large basis set leads to converged results that are also in excellent agreement with the experimental data available for ${\mathrm{Rh}}_2.$ The ground state of ${\mathrm{Rh}}_2$ is confirmed to be a quintuplet, the trigonal ${\mathrm{Rh}}_3$ is predicted to be a sextuplet, ${\mathrm{Rh}}_4$ in its tetrahedral configuration is a singlet, ${\mathrm{Rh}}_5$ sextuplet is a square pyramid, and ${\mathrm{Rh}}_6$ septuplet is the octahedron. Results from several excited states are calculated and presented as well. It is found that LDA overestimates the binding energy but that GGA corrects this deficiency and predicts longer bond lengths.

We present a numerically efficient algorithm for multiphoton dissociation of molecules with light pulses in the infrared frequency regime. The shape of the external electric field can be arbitrary. The method is essentially based on discretizing the continuum; dissociation is simulated by a coordinate-dependent cutoff function. A substantial reduction of the computer time required for solving the large set of first-order differential equations in time $\left(N\approx 2000\right)$ can be achieved if the interaction with the field can be separated according to $Ŵ\mathrm{}\left(t\right)=E\left(t\right)\mathrm{}{\hat{\mu }}_{\mathrm{eff}},$ where ${\hat{\mu }}_{\mathrm{eff}}$ is an effective coordinate-dependent dipole moment function. We applied this method to the excitation and dissociation of the triatomic molecule HCO including all three vibrational degrees of freedom. Comparison with calculations based on the propagation of a wave packet on a three-dimensional grid yields good agreement, provided the rate of excitation is not too large. The accuracy of classical trajectory calculations is also tested.

We present a general expression for the field ionization probability of atoms and ions under a quasistatic external electric field. While the treatments available as yet are only for the case of a single electron in the outer $\mathrm{nl}$ subshell, the expression obtained here is applicable to atoms and ions with any number of electrons in the outer subshell and with partially filled inner subshell(s). We also present a more accurate method to determine the prefactor in the expression for the field ionization probability. Ionization probabilities are calculated using the WKB approximation; therefore, the results become exact in the weak-field limit. It is shown that in certain cases the field ionization probability depends significantly on the projection of the total orbital angular momentum in the direction of the field. A proper way to normalize the optical-electron wave-function asymptotics is explained and the difficulties in the use of Hartree-Fock routines for that purpose are discussed. The general expression obtained is used to calculate field ionization probabilities for several states of some atoms and ions that are of special interest for spectroscopic diagnostics: $\mathrm{C}\mathrm{}I$, $\mathrm{Li}\mathrm{}I$, and $\mathrm{Ba}\mathrm{}\mathrm{II}$. We also discuss the case of a significant spin-orbit interaction, treating the ionization of the $\mathrm{Ba}\mathrm{}\mathrm{II}\hspace{0.5em}6p$ level as an example. For the $\mathrm{Li}\mathrm{}I$ $2p$ level, the present calculations disagree with previously published calculations based on the use of Hartree-Fock wave functions; possible reasons for the discrepancy are discussed. For this level and the $3d$ level of $\mathrm{Li}\mathrm{}I$, our results are compared with experimental data available in literature and are found to be in agreement.

Electron-atom scattering at small scattering angles $(0\mathrm{}°–25°)$ in the presence of an intense radiation field is investigated employing second Born approximation. We perform exact numerical calculation of differential cross sections of electron-He scattering with one-, two-, and three-photon exchange and compare our results with the Kroll-Watson approximation (KWA) results and the recent experiments; our results are much better than KWA’s for small angle scattering compared with experiments.

The evolution of Rydberg states of hydrogen and alkali-metal atoms subject to short half-cycle pulses is studied. The convergence of the numerical solutions of the time-dependent Schrödinger equation based on an expansion of the electronic wave function in a finite basis set of Sturmian functions is analyzed in detail. It is shown that the accuracy of such calculations can be established by investigating the stabilization of the transition probabilities with respect to the parameters that define the basis set. The dependence of the quantum and classical ionization thresholds on the pulse shape is investigated. The calculations are compared with experimental data for various pulse profiles, which feature slow or fast rise times. The results show that the ionization thresholds for long pulses are very sensitive to the rise time of the electric field.

We present a simple and efficient method for the broadband laser excitation of ions in a fast beam by optical rapid adiabatic passage. The method relies on the frequency chirp affecting the ions in continuous-wave fixed-frequency laser light as a result of the Doppler effect when they are accelerated in local electrostatic fields. We have studied this excitation scheme at the Heidelberg Test Storage Ring and demonstrated its particular application to overcome collisional losses in laser cooling of fast stored ion beams.

A technique of differential intracavity phase spectroscopy is introduced. The measured beat frequency between the two counterpropagating fields in a ring laser directly yields the differential phase shift due to the presence of an atomic vapor. In an unstabilized laser cavity, phase differences near ${10}^{-6}$ are measured. This technique is used to study the nonlinear dispersion associated with a three-level $\Lambda$ system in atomic samarium. Sub-Doppler resonances and population trapping are observed, both of which are attributed to the coherences between the two lower levels of the $\Lambda$ level structure. Solutions of the density matrix describing the system are also presented, and good qualitative agreement is found between the calculations and the measurements.

We present a detailed experimental study of the frequency-modulated excitation of a two-level atom, using a microwave field to drive transitions between two Rydberg Stark states of potassium. In the absence of a modulation the interaction is the standard model of the Rabi problem, producing sinusoidal oscillations of the population between the two states. In the presence of a frequency modulation of the interacting field, however, the time evolution of the system is significantly modified, producing square wave oscillations of the population, sinusoidal oscillations at a different frequency, or even sinusoidal oscillations built up in a series of stair steps. The three responses described above are each found in a different regime for the frequency of the modulation with respect to the unmodulated Rabi frequency: the low-, high-, and intermediate-frequency regimes, respectively.

The dynamics of atoms subject to laser light propagating between perfectly conducting parallel plates is investigated. In the semiclassical approximation the motion of atoms in this context is governed by a van der Waals–type potential, together with a dynamic dipole potential that comes into play as soon as a cavity mode is excited. In addition, the atoms become subject to an average dissipative (spontaneous) force associated with the cavity mode that always acts parallel to the plates. We show that, by a suitable choice of field intensity and detuning, the total transverse potential can be used to confine atoms in transverse vibrational states, while their motion in the parallel direction is controlled by the dissipative force. Significant variations of the characteristics of the system with atom velocity, dipole orientation, and type of excited cavity mode are emphasized. These features are illustrated using typical parameters for the case of sodium atoms between parallel plates with subwavelength separations.

We present a detailed experimental analysis of Rb-polarization imaging in high-pressure gas cells. The Rb vapor in these cells is optically pumped by high-power diode-laser arrays. We present images for high (35 G) and low (4 G) magnetic fields and for different He and Xe buffer-gas mixtures. We demonstrate that high-field imaging provides an absolute measurement of the Rb-polarization distribution in the cell, based on the fact that a spin-temperature distribution of the hyperfine magnetic sublevels is established in high-pressure buffer gases. A survey of various mechanisms that broaden the Rb magnetic-resonance lines is presented. These broadening mechanisms determine the limits of the spatial resolution achievable for images of the Rb-polarization distribution.

This paper analyzes the extension of the three-state process of stimulated Raman adiabatic passage to chainwise-connected multistate systems. A necessary condition for such a process is the existence of an adiabatic-transfer state, which connects adiabatically the initial state of the chain to its final state. Various counterintuitive pulse sequences are examined, in all of which the pulse that drives the last transition of the chain precedes the pulse driving the first transition, while the pulses driving the intermediate transitions may have different timings. The paper demonstrates some important qualitative differences and similarities between the systems with odd and even number of states. In the on-resonance case, an adiabatic-transfer state always exists for an odd number of states while it never exists for an even number of states. In the off-resonance case, however, the two types of systems behave in a very similar manner and the condition for existence of an adiabatic-transfer state is essentially the same. This condition, which imposes certain limitations on the laser parameters, is derived in a simple and compact form. It is also shown analytically that, besides by large detunings, the populations of the intermediate states (which are generally nonzero during the transfer) can be damped by large intermediate couplings. It is concluded that for an odd number of states, the optimal case is the on-resonance one, with equal and large intermediate couplings. For an even number of states, the optimal (off-resonance) case is when the intermediate couplings and the detunings have similar values. Various numerical examples of success and failure of multistate population transfer confirm the analytic conclusions.

In this paper we present a detailed treatment of the ac Stark effect of a three-level atom driven by two strong laser fields in a cascade scheme. We consider two situations where there is a weak laser field probing a new transition starting from one of the three levels to a fourth level. In one case the initial level of the probed transition is the ground state and in the other case the initial level is the intermediate state. For both situations we derive an analytical expression for the absorptive and dispersive responses of the weak probe field and present the spectrum obtained from numerical calculation. The general feature of the spectrum has a three-peak structure. The positions and relative intensities of the three spectral components are affected strongly by the driving field intensities and detunings. An account of the spectrum is given in terms of the dressed-state formalism.