We use a formalism of integral operators to present a unified approach to variational R-matrix methods for many-electron systems described by the Dirac Hamiltonian. Variational principles for eigenvalues and matrix elements of many-electron integral operators ${\mathcal{B̂}}^{(\pm )}\mathrm{}\left(E\right)\mathrm{}$ and ${\mathcal{R̂}}^{(\pm )}\mathrm{}\left(E\right),$ which are the central objects in the approach, are listed. The Rayleigh-Ritz linear trial functions are used in these principles, yielding second-order variational estimates of eigenvalues, matrix elements, and kernels of these operators. A multiconfiguration Dirac-Hartree-Fock approach to the relativistic R-matrix method is proposed.

An approximate symmetry of the three-body Coulomb problem which reveals itself via approximate separability of the hyperspherical adiabatic (HSA) eigenvalue problem in hyperspherical elliptic (HSE) coordinates $(\eta ,\xi )$ and thus is intimately related to the HSA approximation is discussed. The additional integral of motion responsible for this separability is specific to the Coulomb interaction and generalizes the Laplace-Runge-Lentz vector known from the two-body Coulomb problem and the integral of separation constant of the two-center Coulomb problem. In the zeroth approximation, this symmetry leads to a completely separable representation of the three-body wave function, where each state is labeled by a pair of HSE quantum numbers ${(n}_{\eta }{,n}_{\xi })$ that generalize the spheroidal quantum numbers for diatomic molecules, on the one hand, and the Herrick-Lin quantum numbers for two-electron atoms, on the other. This approximation is illustrated by calculations for a number of three-body Coulomb systems for states with zero total angular momentum. Taking into account the nonadiabatic couplings as well as the nonseparable part of the Coulomb potential by mixing a few separable states permits one to obtain accurate results for systems with arbitrary masses and charges of particles and for a wide spectrum below the three-body breakup threshold.

The validity of a δ-function approximation for the electromagnetic interaction of relativistic heavy ions is investigated. The production of $e^{+}{e}^{-}$ pairs, with electron capture, is used as a test of the approximation.

Absolute cross sections have been measured for single and double charge exchange and x-ray line emission for highly charged ions of C, N, O, and Ne colliding with He, ${\mathrm{H}}_2,$ ${\mathrm{CO}}_2,$ and ${\mathrm{H}}_2\mathrm{O}$ at collisions energies of $7q\mathrm{keV}.$ Present results of charge exchange in He and ${\mathrm{H}}_2$ compare favorably with previous results. For ${\mathrm{CO}}_2$ and ${\mathrm{H}}_2\mathrm{O},$ where prior work is scarce, the classical overbarrier model is found to overestimate results by up to a factor of 3. An analysis of the relative intensities of the observed Lyman x-ray transitions indicates that capture into l states is not statistical, as collision velocities are insufficient to populate the highest angular-momentum states. The importance of autoionization following multiple capture is highlighted, and enhanced radiative stabilization following double capture is observed and compared to other studies. Present results are also discussed in terms of mechanisms likely to generate x-ray emission in comets.

A systematic development of the relativistic J-matrix theory of scattering is presented. The reference Hamiltonian includes the Coulomb interaction, and the short-range perturbing potential may include spin-dependent coupling. The nonrelativistic limit is obtained and shown to be identical to the familiar nonrelativistic J matrix.

Time-dependent close-coupling calculations of the electron-impact ionization of lithium are presented and compared to experiment and other recent theoretical calculations. Total integral cross sections are found to be in excellent agreement with the previous converged close-coupling calculations of Bray [J. Phys. B 28, L247 (1995)], but are substantially lower than the only low-energy region experimental results of Zapesochnyi and Aleksakhin [Sov. Phys. JETP 28, 41 (1969)]. Ejected-energy differential cross sections are presented for incident energies of 10 eV, 15 eV, 20 eV, and 25.4 eV. At 25.4 eV, the time-dependent close-coupling results are found to be in only moderately good agreement with the converged close-coupling results of Bray et al. [J. Phys. B 32, 4309 (1999)]. A study is also made of the convergence of the spin asymmetry parameter as a function of orbital angular momentum. The final time-dependent result for the spin asymmetry parameter at an incident energy of 15 eV is found to be in excellent agreement with the converged close-coupling results of Bray [J. Phys. B 28, L247 (1995)], but is slightly lower than the experiment of Baum et al. (1985).

A systematic description of coherent ultrafast x-ray spectroscopies in terms of nonlinear response functions and susceptibilities is developed. Correlation-function expressions of charge and current densities provide a unified treatment and classification of information content of the various possible techniques and connect them with their optical counterparts. Applications to pump-probe and four-wave mixing measurements are discussed.

We present new results on the coherent control of a four-wave mixing signal in rubidium vapor involving Rydberg levels. By varying the relative polarizations of the laser beams responsible for the nonlinear process, we control atomic excitation routes and thus quantum interference in the medium. We observed interference fringes as a function of the relative polarizations and further developed a theoretical model based on the density-matrix formalism that is in very good agreement with our experimental results.

The visibilities of second-order (one-photon) and fourth-order (two-photon) interference have been observed in a Young’s double-slit experiment using light generated by spontaneous parametric down-conversion and a photon-counting intensified charge-coupled device camera. Coherence and entanglement underlie one- and two-photon interference, respectively. As the effective source size is increased, coherence is diminished while entanglement is enhanced, so that the visibility of one-photon interference decreases while that of two-photon interference increases. This experiment demonstrates the complementarity between one- and two-photon interference (coherence and entanglement) in the spatial domain.

Continuous-wave generation of the anti-Stokes Raman laser is demonstrated in the new $\Lambda$ scheme $\mathrm{Ar}$ II ${3d}^{\prime }{}^2{G}_{9/2}\to {4p}^{\prime }{}^2{F}_{7/2}\to {4s}^{\prime }{}^2{D}_{5/2}$ with quasimetastable initial and final levels. Red pump radiation with wavelength ${\lambda }_p=611\mathrm{}\hspace{0.5em}\mathrm{nm}$ from a dye laser that excites transition ${3d}^{\prime }{}^2{G}_{9/2}\to {4p}^{\prime }{}^2{F}_{7/2}$ is converted into the blue radiation at $\lambda =461\mathrm{}\hspace{0.5em}\mathrm{nm}$ ${(4p}^{\prime }{}^2{F}_{7/2}\to {4s}^{\prime }{}^2{D}_{5/2})$ with efficiency of about $30\%.$ The tunability range spans more than 20 GHz around exact resonance, which is five times broader than the Doppler contour. The output frequency $\omega$ is found to depend linearly on the frequency ${\omega }_p$ of the pump field: $\omega \simeq {\omega }_p{\lambda }_p/\lambda .$ A sharp peak of output power is observed in the spectral profile at the exact resonance instead of the well-known two-photon dip. The model is proposed that includes ionic scattering in plasma and interaction of the running pump and standing output waves. The theory offers an interpretation of the observed peak.

We present a theoretical and experimental study of preparing maximally entangled two-photon polarization states, or Bell states, using femtosecond-pulse-pumped spontaneous parametric down-conversion (SPDC). First, we show how the inherent distinguishability in femtosecond-pulse-pumped type-II SPDC can be removed by using an interferometric technique without spectral and amplitude postselection. We then analyze the recently introduced Bell-state preparation scheme using type-I SPDC. Theoretically, both methods offer the same results, however, type-I SPDC provides experimentally superior methods of preparing Bell states in femtosecond-pulse-pumped SPDC. Such a pulsed source of highly entangled photon pairs is useful in quantum communications, quantum cryptography, quantum teleportation, etc.

High-resolution resonant Auger-electron spectra of NO measured at the $\mathrm{N}1\overrightarrow{s}2\pi$ core excitations are presented. The open-shell ground-state electronic configuration of the molecule results in four excited electronic states, three of which are populated in the photoabsorption spectrum, ${}^2\Delta ,$ ${}^2{\Sigma }^{-},$ and ${}^2{\Sigma }^{+}.$ Electron emission spectra obtained at different vibrational levels of the three $\mathrm{N}1s$ core-excited states of NO are reported. Recent ab initio calculations [J. Chem. Phys. 106, 4038 (1997)] are used to generate theoretical spectra for comparison with the experimental results taking lifetime vibration interference and Auger resonant Raman effects into account. The Auger-electron spectra are decomposed into contributions from different final ionic states for comparison of the calculated and experimental partial Auger decay rates. Revised values for the core-hole lifetime width and Morse potential of the ${}^2\Delta$ excited state, and for the adiabatic ionization energy of the ${}^1\Delta$ ionic state are given.

We present results of the application of the Schwinger multichannel method using effective configurations [Azevedo et al., Phys. Rev. A 61, 042702 (2000)] to study special features of low-energy electron-molecule scattering, such as (i) the shape resonance in $e^{-}-{\mathrm{N}}_2$ scattering; (ii) the Ramsauer-Townsend minimum in $e^{-}-{\mathrm{CH}}_4$ scattering; and (iii) a Feshbach resonance in $e^{-}-{\mathrm{H}}_2$ scattering (in a two-channel coupling calculation including polarization effects). In all cases, we find that the use of effective configurations to describe polarization effects allows a substantial reduction of the configuration space, without any loss of quality of the results. The present applications (together with our previous study of nonresonant $\mathrm{electron}-{\mathrm{H}}_2$ scattering) indicate that this technique will be very useful in the analysis of more complex systems.

We investigate the time-frequency characteristics of high-order harmonics generated in atomic gases by intense femtosecond laser pulses, using the Wigner distribution function. The dynamically induced chirp of high harmonics is calculated both quantum mechanically and semiclassically, and a good agreement between them is reached as long as the tunneling effect is properly taken into account. Using the time-frequency analysis, we demonstrate that the large harmonic blueshift observed experimentally is due mainly to the single-atom effect.

Decoherence of molecular vibrational wave packets in hot alkaline dimers due to the vibration-rotation coupling is considered. The focus is on the study of observable manifestations of the decoherence process in molecular emission tomography. Criteria are presented for control over decoherence by means of driving molecular transitions with suitably shaped ultrafast laser pulses.

We theoretically investigate the use of Bessel light beams generated using axicons for creating optical dipole traps for cold atoms and atomic waveguiding. Zeroth-order Bessel beams can be used to produce highly elongated dipole traps, allowing for the study of one-dimensional trapped gases and realization of a Tonks gas of impenetrable bosons. First-order Bessel beams are shown to be able to produce tight confined atomic waveguides over centimeter distances.

The ac Stark shift of the resonance frequency of the nonlinear magneto-optic effect (NMOE) results in a fundamental broadening of this resonance which limits the precision of optical magnetometry based on NMOE. We have studied the dependence of the ac Stark shift versus frequency of the probing laser for the $D_1$ and $D_2$ lines of ${}^{87}\mathrm{Rb},$ and have shown that there exists a frequency where the shifts from different hyperfine components of the upper level cancel each other. This holds promise for an in-principle increase in the sensitivity of optical magnetometers. The influence of buffer gas on Faraday rotation and ac Stark shifts is also considered.

We propose a spatiotemporal interferometric scheme based on near-field diffraction of Bose-Einstein condensates confined in a one-dimensional hard wall potential. The scheme is closely related to the phenomenon of intermode traces recently studied for noncondensed wave packets; we show how the scheme may be used in the detection of weak forces.

Recently x-ray photoabsorption in $\mathrm{KLL}$ resonances of O VI was predicted [A. K. Pradhan, Astrophys. J. Lett. 545, L165 (2000)], and detected by the Chandra X-Xay Observatory [J. C. Lee et al., Astrophys. J. Lett. (to be published)]. The required resonance oscillator strengths $f_r$ are evaluated in terms of the differential oscillator strength $df/d\epsilon$ that relates bound and continuum absorption. We present the $f_r$ values from radiatively damped and undamped photoionization cross sections for Li-like C, O, and Fe calculated using relativistic the close-coupling Breit-Pauli R-matrix method. The $\mathrm{KLL}$ resonances of interest here are ${1s2p(}^3{P}^o\left)2s{[}^4{P}_{1/2,3/2}^o{,}^2{P}_{1/2,3/2}^o\right]$ and ${1s2p(}^1{P}^o\left)2s{[}^2{P}_{1/2,3/2}^o\right].$ The $\mathrm{KLL}$ photoabsorption resonances in Fe XXIV are fully resolved up to natural autoionization profiles. It is demonstrated that the undamped $f_r$ independently yield the resonance radiative decay rates, and thereby provide a precise check on the resolution of photoionization calculations in general. The predicted photoabsorption features should be detectable by the x-ray space observatories and enable column densities in highly ionized astrophysical plasmas to be determined from the calculated $f_r.$ The dielectronic satellites may appear as redward broadening of resonance lines in emission and absorption.

As a step towards constructing nonlocal energy density functionals, the leading term in the so-called $1/Z$ expansion for closed-shell atomic ions is the focus here. This term is characterized by the properties of the bare Coulomb potential $(-{\mathrm{Ze}}^2/r),$ and for an arbitrary number of closed shells it is known that $\partial \rho \mathrm{}\left(r\right)/\partial r=-{(2Z/a}_0\left){\rho }_s\mathrm{}\right(r),$ where $\rho \mathrm{}\left(r\right)\mathrm{}$ is the ground-state electron density while ${\rho }_s\mathrm{}\left(r\right)\mathrm{}$ is the s-state $\mathrm{}(l=0\mathrm{})\mathrm{}$ contribution to $\rho \mathrm{}\left(r\right).$ Here, the kinetic-energy density $t\left(r\right)\mathrm{}$ is also derived as a double integral in terms of ${\rho }_s\mathrm{}\left(r\right)\mathrm{}$ and Z. Although the exchange energy density ${\epsilon }_x\mathrm{}\left(r\right)\mathrm{}$ is more complex than $t\left(r\right),$ a proof is given that, in the Coulomb limit system, ${\epsilon }_x$ is indeed also determined by s-state properties alone. The same is shown to be true for the momentum density $n\left(p\right),$ which here is obtained explicitly for an arbitrary number of closed shells. Finally, numerical results are presented that include (a) ten-electron atomic ions $(K+L$ shells), (b) the limit as the number of closed shells tends to infinity, where an appeal is made to the analytical r-space study of Heilmann and Lieb [Phys. Rev. A 52, 3628 (1995)], and (c) momentum density and Compton line shape for an arbitrary number of closed shells.