Differential and total cross sections for the dipole excitation of valence electrons in alkali-metal-like ions by electron impact well above the threshold energy are calculated in the generalized Born approximation and in a semiclassical approximation. The angular distribution is peaked at an angle which is essentially defined by energy-momentum-matching conditions on the classical Coulomb trajectory; around this angle, the semiclassical description is in excellent agreement with the quantal description. Deviations from the mean-field electron screening are weak and manifest themselves only in backward scattering. Semiclassical total cross sections are practically equal to the Coulomb-Born predictions. This near equality is explained within the WKB approximation. The practical equivalence between the semiclassical, WKB, and Coulomb-Born approximations applies also for other multipoles in a wide range, of energy transfer, and ionic charge.

We have measured Δn≥1 dielectronic-recombination cross sections for the heliumlike ions ${\mathrm{Ni}}^{26+}$, ${\mathrm{Mo}}^{40+}$, and ${\mathrm{Ba}}^{54+}$. We observed the x rays emitted during dielectronic recombination by ions in an electron-beam ion trap and obtained cross sections from a calibration based upon radiative recombination. The results generally agree well with theoretical predictions.

The energy losses of 0.7-MeV He ions which have surface channeled along atomic rows on a clean (100) surface of SnTe are studied. An energy spectrum of the surface-channeled ions shows a few peaks whose energies and heights depend on the angle of incidence of He ions, ${\mathrm{\theta }}_{\mathit{i}}$. From the ${\mathrm{\theta }}_{\mathit{i}}$ dependence of the energy losses, position-dependent stopping powers of the (100) surface for the He ions are determined at the [001] and [011] surface channeling. The contribution of collective excitation of surface valence electrons to the stopping powers is extracted from the obtained position-dependent stopping powers. This agrees well with the theories where the dynamical response of valence electrons to the fast-moving ions is taken into account.

The x-ray-absorption spectra of gaseous HBr and ${\mathrm{Br}}_2$ at the Br K edge have been studied in order to evidence the contribution of double-electron excitation channels to the atomic-absorption background. Evident features due to the simultaneous excitations of 1s4p, 1s4s, 1s3d, and 1s3p electrons, named ${\mathit{KN}}_{2,3}$, ${\mathit{KN}}_1$, ${\mathit{KM}}_{4,5}$, and ${\mathit{KM}}_{2,3}$ channels, respectively, have been identified in both spectra. The data analysis takes proper account of the structural signal of the neighboring atom in the molecules calculated including the ${\mathrm{\chi }}_2$ single-scattering signals and the ${\mathrm{\chi }}_4$ triple-scattering contribution in the case of ${\mathrm{Br}}_2$. Comparisons of energy positions with self-consistent atomic calculations are in excellent agreement with the observed energy onsets. An empirical model function for the double-electron-channel cross section was found to reproduce accurately the observed shapes, the threshold region included. The proper account of both double-electron channels and structural signals allows the correct explanation of the experimental spectra. The fit of the experimental spectra provided a determination of the structural parameters in excellent agreement with the known molecular values. These results are of general importance for structural studies at the Br K edge.

We propose an algebraic model for bent triatomic molecules and discuss its geometrical interpretation. We solve the model analytically for the special case of bent symmetric triatomic molecules in the mean-field approximation and study water as an example.

The equilibrium properties of small MgO clusters (MgO, ${\mathrm{Mg}}_2$O, ${\mathrm{MgO}}_2$, and ${\mathrm{Mg}}_2$${\mathrm{O}}_2$) are calculated to obtain their dependence on computational constraints such as the basis set and level of computation. The results have led to the suggestion that the inclusion of the correlation correction at the second-order Moller-Plesset level is necessary for the atomization energy although the configuration parameters may be obtained at the Hartree-Fock level. Based on this suggestion, the calculated properties of the neutral and single-ionized MgO monomer are in excellent agreement with the experimental data and available values from very accurate calculations. For the triatomic clusters, ${\mathrm{Mg}}_2$O is found to be more stable than ${\mathrm{MgO}}_2$, whose geometrical structure is determined by the strong O-O interaction. The optimum configuration of ${\mathrm{Mg}}_2$${\mathrm{O}}_2$ is a slightly distorted square with a ${\mathit{D}}_{2\mathit{h}}$ symmetry. Upon ionization, these clusters undergo structural modifications, but these effects are softer than in alkali halide clusters due to the delocalized character of the hole. Our results show that the evaporization of a neutral oxygen atom provides the most favorable fragmentation channel for the neutral and single-ionized stoichiometric dimers.

The performance of approximate theories for the collective nonlinear optical response of assemblies of interacting molecules is investigated by comparing their predictions to exact calculations. To this end, the nonlinear absorption coefficient of linear molecular aggregates with energetic disorder is studied with the aid of Monte Carlo simulations. It is shown that the well-known local-field approximation (LFA) cannot describe the near-resonance nonlinear absorption spectrum for disorder values up to the nearest-neighbor intermolecular interactions; surprisingly, it is found that the validity of the LFA does not at all improve with growing disorder. By contrast, the ‘‘excitonic two-level system’’ approximation, in which each collective one-photon transition (Frenkel exciton) of the assembly is treated as an independent two-level system, turns out to describe the collective nonlinear response of the aggregates in a much better way and, moreover, rapidly improves for growing disorder values. It is shown that both models correctly describe the linear optical response and that, within the framework of the LFA, a close connection exists between the rotating-wave approximation and the Heitler-London approximation.

The theory of time-resolved laser-induced fluorescence (LIF) in a static magnetic field is reformulated by means of the graphical method of angular momentum theory. Invariant general geometrical relations of the time-resolved fluoresence signal are obtained in an explicit form for arbitrary polarization and propagation directions of the primary and secondary radiation and for any direction of the magnetic field. On this basis an extensive experimental study was carried out to find general conditions for lifetime experiments using laser-induced fluorescence, under which the direction of polarization in the excitation and the observation channel and the influence of external magnetic fields does not change the time evolution of the fluorescence signal. It is shown that besides the well-known ‘‘magic-angle’’ excitation also measurements at very low pressures (p≊${10}^{\mathrm{-}4}$ mbar) provide conditions where laser-induced alignment is negligible and does not disturb the time evolution of the decay signal. Furthermore the experiments confirm that the magnitude of laser-induced alignment depends very sensitively on the chosen transition scheme, on the value of the cross section for alignment destroying collisions, and on the geometry of the experiment. Interferences on the time-resolved fluorescence signal by external magnetic fields are also discussed. It is shown that the presence of a strong magnetic field can lead to lifetime results systematically too short under conditions typical for LIF lifetime experiments.

A single two-level atom, with quantized center-of-mass motion, is constrained to move in a one-dimensional harmonic potential while interacting with a single-mode classical traveling-wave light field. When the classical light field is tuned to the atom’s lower vibrational sideband, cooling can occur. The strong-sideband and Lamb-Dicke perturbation regimes for the system are defined. The steady-state and time-evolution behaviors in the strong-sideband regime are discussed and, in particular, it is shown that the steady-state average trap number saturates when spontaneous emission is weak and that the steady-state average trap number depends more strongly on the trap frequency in the saturated regime than previously predicted. Finally, the possibility of observing quantum jumps between trap levels is discussed.

We have investigated the effect of the dipole force and its fluctuation on the motion of Li atoms in an intense, one-dimensional, near-resonant standing light wave. The duration of the interaction of the atoms with the standing wave was varied from several tens of spontaneous-emission lifetimes to several hundreds. For a standing-wave frequency blue detuned from resonance, diffusive heating can dominate the time-averaged dissipative dipole force so that there is no steady-state momentum distribution. However, for sufficiently large blue detunings, the rate of diffusion is so slow that the resulting distribution approaches a quasisteady state. For red detunings, the diffusion is balanced with the force and a true steady state is achieved. We apply a Monte Carlo method based on the density-matrix equations in the dressed-state representation to simulate the atomic motion. The dynamics of atom channeling is discussed.

We describe a cesium atomic beam (${10}^{14}$ atoms ${\mathrm{s}}^{\mathrm{-}1}$, 6×${10}^{16}$ atoms ${\mathrm{sr}}^{\mathrm{-}1}$ ${\mathrm{s}}^{\mathrm{-}1}$) spin polarized using light from two diode lasers. Of the atoms, 95% may be placed into either the 6${\mathit{S}}_{1/2}$(F,${\mathit{m}}_{\mathit{F}}$)=(3,3) or (4,4) state, with less than 2×${10}^{\mathrm{-}4}$ of the atoms left in the depleted hyperfine level. The latter fraction rises linearly with atomic beam intensity because of reabsorption of light scattered during the optical pumping process. This and other effects limiting complete hyperfine pumping are discussed.

Wave equations—nonrelativistic and relativistic—describing the motion of a charged particle in a multimode laser field are considered and solutions are derived that may serve as asymptotic wave functions in the evaluation of amplitudes for laser-assisted scattering and multiphoton ionization. Unlike the well-known Volkov solutions that can be used only for fields of the plane-wave type, the wave functions obtained here are appropriate for the wider class of fields for which the different modes need not all have the same direction of propagation. This generalization allows in principle for the construction of wave packets, fields that are localized in space as well as time and hence capable of providing a more realistic description. The treatment of the nonrelativistic case is essentially exact, in the sense that errors introduced, of order (v/c${)}^2$, are comparable to those inherent in the nonrelativistic approximation. As an illustration, a low-frequency approximation for potential scattering in a multimode field is derived based on the use of the generalized Volkov solutions as asymptotic wave functions. Generalized Volkov solutions of the Klein-Gordon and Dirac equations are derived as well, though here in an approximation requiring a limitation on the strength of the external field.

We develop a radiation diffusion equation for an infinite slab geometry where the slab may have different reflectivities on either surface, and for conditions where complete frequency redistribution is valid. Additionally we consider the effect of two competing trapped transitions. Specifically we consider the emission from the thallium 7 ${}_{}{}^2{}_{}{}^{}$${\mathit{S}}_{1/2}$ state to either the 6 ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{3/2}$ (metastable state) at 535 nm or 6 ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}_{1/2}$ (ground state) at 378 nm. High densities of the long-lived metastable level can be produced in a number of ways. The escape factors (which are simply related to the decay rates) and excited-atom spatial profiles are calculated for a variety of conditions for the first several natural modes of the system. The spatial modes for this system are asymmetric. The asymmetry can vary dramatically with only small changes in either of the two lower-state densities. The correct description of the spatial modes is critical in order to determine the overall excited-atom profile accurately. For the simpler systems (i.e., a single transition and nonreflective boundaries) usually considered the mode profiles do not change appreciably as the optical depth is changed (given conditions of high optical depth and a single-line broadening mechanism). The fundamental mode decay rate is shown for a fixed metastable-state density as a function of the ground-state density.

The dependence of the fundamental mode escape factor for the first resonance transition on the optical depth (or ground-state density) is in general more complicated than for the case of a single trapped transition. For conditions considered here a simple power rule cannot be used to scale the decay rates as a function of line-center optical depth. Also shown is the fundamental mode escape factor as a function of buffer gas pressure for fixed ground- and metastable-state densities. The calculations presented here allow us to model the narrow-bandwidth thallium fluorescence filter. This filter will be discussed in more detail in a separate paper. A thorough review of atomic resonance filters was done by Gelbwachs [IEEE J. Quantum Electron. 24, 1266 (1988)]. We have considered a much broader range of ground- and metastable-state densities than would be practical for efficient filter operation. This is done to illustrate several aspects of the radiation trapping processes.

The diffraction theory of a reflection grating for atoms based on a standing light wave is developed in a particular dressed-state approximation. The basis states take into account internal and external atomic degrees of freedom simultaneously and correspond to diffraction orders in the asymptotic region. In this basis the atom is described as an effective multilevel system. In an adiabatic approximation for the motion perpendicular to the grating, these levels serve as position-dependent potentials. An incoming de Broglie wave is coupled to higher diffraction orders by nonadiabatic transitions near avoided crossings of the potentials. Numerical results confirm the qualitative predictions following from the physical picture of the diffraction process and lead to an improved description of experiments.

Even with incoherent driving, coherence effects may show up in the spontaneous emissions of an atom. We derive a general master equation and predict that for both the three-level V and Λ systems the intensity correlation function ${\mathit{g}}^{\mathrm{}\left(2\right)\mathrm{}}$(τ) may exhibit pronounced oscillations with frequency δω if the level separation ħδω is small. We obtain a marked difference in the beat amplitude for a single Λ system as compared to a beam or gas. If δω is much smaller than the natural linewidth we find dark and light periods in the spontaneous emission.

Laser cooling a trapped ion damped by an electromagnetic reservoir in a squeezed-vacuum state is investigated. The cooling rate and the final temperature are given for the case in which the ion is located at the node of a laser standing wave, on resonance with its internal transition. In particular, we find that the ion can have final temperatures below the Dopper limit.

The problem of adiabatic amplification of nonlinear guided waves is solved analytically using two different approaches. The amplitude approach allows us to calculate fields and shows how they are reshaped during the amplification. It is closely related to the problem of stability of nonlinear guided waves. The second approach is in terms of energy. A general energy-balance equation is derived for nonlinear guided waves in an arbitrary layered structure. The growth rate parameter is calculated using both the energy-balance equation and a direct amplitude approach. It is shown that the quasistationary solution, in the presence of gain, smoothly changes its shape, propagation constant, and energy, while remaining close to stationary solutions if these solutions belong to a stable branch of the energy dispersion diagram.

A different set of the Maxwell-Bloch equations describing optical bistability in a dye ring cavity has been derived. A complete linear stability analysis including propagation effects is given. The corresponding numerical simulations show that the bistable regions are functions of both the frequency detuning and the band-structure parameters such as the bandwidth and the distribution of the dipole moments.

By utilizing amplifiers in a modified interferometer, both particlelike and wavelike characteristics of single input photons are analyzed theoretically. Quantum theory predicts that proposed measurements on the amplified field will indicate that the single input photon exhibits extremes of both wavelike and particlelike characteristics. The evidence for wavelike behavior is fringe visibility at the output of the interferometer. Anticorrelation between the outputs of the two legs of the interferometer provides the evidence for particlelike behavior. Although quantum noise degrades both the particle-sensitive and the wave-sensitive measurement, no trade-off between the wavelike and the particlelike characteristics takes place. Complementarity, however, is maintained by the quantum noise added during amplification.

An approximate solution is given for the Jaynes-Cummings model with cavity losses, i.e., the problem of a two-level atom interacting with a single mode of the quantized radiation field, in the rotating-wave approximation, when the field is damped by a reservoir at zero temperature. The approximate solution is derived for initial coherent field states with moderately large numbers of photons. It is simpler in form than earlier results derived by other authors and, over the appropriate parameter range, substantially more accurate than some of them, as shown by direct numerical integration of the master equation. In particular, it is found that an earlier treatment of this problem based on a secular approximation is seriously flawed, in that the conditions for its validity are much more restrictive than was previously believed. Among the results derived it is shown that, just as for the lossless case, when the atom is initially prepared in one of the semiclassical eigenstates the evolution is very simple, with the field and the atomic dipole drifting together in phase. For moderate losses this leads, as in the lossless case, to a ‘‘state preparation’’; i.e., to a good approximation, the state of the atom at a specific time can be made independent of its initial state. The effect of losses on the recently discovered ‘‘Schrödinger cat’’ state of the field is also analyzed. It is found that, although the dissipation destroys the coherence of the macroscopic superposition very rapidly, preparation and observation of the ‘‘cat’’ should be possible with the cavity quality factors reported in recent micromaser experiments.