In this work we investigate fluorescence decay of low-lying $(n<~8)$ resonances with odd parity and total angular momentum $J=1\mathrm{}$ below the $N=2\mathrm{}$ threshold of helium. After discussing the photoabsorption cross section for creation of such states, we estimate the probability for the primary fluorescence transition to $1snl$ states below the first ionization threshold. The subsequent fluorescence cascade decay brings helium into the ground state or into one of the two long lived $1s2s{}^{1,3}S$ states. We discuss the time scale of the cascade and combine all the calculated transition probabilities to determine branching ratios for singlet and triplet metastable production. Finally, we estimate the angular distribution of the emitted uv photons and perform a comparison with the recent experimental data of Penent et al. [Phys. Rev. Lett. 86, 2758 (2001)].

Thermal energy collisions of two p-excited alkali-metal atoms have been examined, taking into consideration the fine-structure splitting of atomic energy levels. Collisional-induced transitions between fine-structure levels and energy-pooling processes have been investigated by means of combined semiclassical approximation (CSA). The operator of evolution was constructed with the aid of a numerical solution of a time-dependent quantum electronic equation with appropriate asymptotic Hamiltonian and single trajectory approximation for nuclear motion at large internuclear separations R. Generalized multichannel Landau-Zener model with adiabatic phase averaging for small R has been included in CSA. Numerical results for cross sections in case of scattering of two $3p$-excited sodium atoms in a collision energy range of 300–2000 K have been obtained. The estimation of results accuracy was carried out. The propensity rule for detailed collisional-induced fine-structure transitions has been established.

We have theoretically studied the influence of K-shell ionization of Li-like Fe on the circular polarization of the ${\mathrm{}\left(1s2s\right)\mathrm{}}_1\to {(1s}^2{)}_0$ or $1s2s{\hspace{0.5em}}^3{S}_1\to {1s}^2{\hspace{0.5em}}^1{S}_0$ forbidden line of the heliumlike ${\mathrm{Fe}}^{24+}$ ion, when the incident electron beam is assumed to be longitudinally polarized. The required cross sections for ionization to the ${\mathrm{}\left(1s2s\right)\mathrm{}}_1{M}_J=-1,$ 0, and $+1\mathrm{}$ magnetic sublevels were calculated in a relativistic distorted-wave approximation for incident electron energies up to 2000 Ry. New cross sections were used for excitation of the ${\mathrm{Fe}}^{24+}$ ion from the ground level to each magnetic sublevel of the upper line level as well as the higher cascading levels. These were computed in a relativistic distorted-wave method that includes the generalized Breit interaction between the bound and free electrons. Our calculations show that for a relatively large range of impact energies above the ionization threshold, the inner-shell ionization populates more preferentially the $M_J=+1\mathrm{}$ sublevel relative to the $M_J=-1$ sublevel than does the combination of direct collisional excitation and radiative cascades, and its inclusion results in an increase of the circular polarization degree of the line, depending on the Li- to He-like abundance ratio. However, at higher impact energies, the inner-shell ionization has the effect of decreasing the degree of circular polarization.

A family of orbiting resonances in molecular scattering is globally described by using a single pole moving in the complex angular momentum plane. The extrapolation of this pole at negative energies gives the location of the bound states. Then a single pole trajectory, which connects a rotational band of bound states and orbiting resonances, is obtained. These complex angular momentum singularities are derived through a geometrical theory of the orbiting. The downward crossing of the phase shifts through $\pi /2,$ due to the repulsive region of the molecular potential, is estimated by using a simple hard-core model. Some remarks about the difference between diffracted rays and orbiting are also given.

There have recently been several relative measurements of triple differential cross sections for the double photoionization of helium by a number of various experimental groups. In response to these measurements, we present theoretical calculations of total integral, single differential, and triple differential cross sections for this process using the time-dependent close-coupling method. This approach has previously given excellent agreement with absolute experimental measurements [see Colgan et al., J. Phys. B 34 L457 (2001)]. Detailed comparisons with the experimental measurements are made, where possible, and, in general, very good agreement is found with the relative experiments over a wide range of excess energies and ejected electron energies and angles.

The elastic $2\overrightarrow{s}2s$ and inelastic $2\overrightarrow{l}{3l}^{\prime }$ laser-assisted collision of hydrogen with fast incident electrons is studied, by applying the nonperturbative Born-Floquet theory. The embedding monochromatic or “3 + 1” bichromatic linearly polarized field of moderate intensity tunes the $n=2\mathrm{}$ and $n=3\mathrm{}$ levels into one-photon resonances. A peculiarity of the laser-assisted $e-\mathrm{H}$ collision involving levels with $n>~3$ is that cross sections corresponding to no photon exchange with the field do not reduce to the field-free cross sections in the $\overrightarrow{I}0$ limit. In addition, structures in the cross sections like two separate peaks in the resonance vicinity are observed, resulting from interferences between different resonant excitation virtual pathways from an initial to the final state. An increase of intensity of the monochromatic field by two orders of magnitude has the consequence of attenuating resonant structures in the cross sections. For rather moderate intensities of both components of the bichromatic field, narrow multiphoton resonances induced by the lower-frequency field appear, superimposed on wings of broad resonances brought in by the higher-frequency field. The overall effect on the cross sections for $e-\mathrm{H}$ scattering resulting from relative-phase variation of the resonant moderate-intensity bichromatic field is small.

A solenoid consisting of two interwound helical coils carrying equal but opposite currents can act as a guide for neutral atoms. In this paper we develop the theory of such a guide and report on its performance in guiding laser-cooled cesium atoms. Our guide is a useful tool for transporting cooled atoms since it prevents ballistic expansion of the atomic cloud after it is released from a magneto-optical trap. In contrast to atom-guide designs using permanent magnets, our guide can be switched off by switching the currents; hence it can be placed close to a magnetic trap without adversely affecting the trapping efficiency. One of the unique features of this guide is that, except in the immediate neighborhood of the walls of the guide, the atoms are not magnetically perturbed to any appreciable extent by the guide field. This opens up the possibility of a system for cooling atoms.

A Lie transformation is developed to study the structure of classical phase space for a perturbed Penning trap. In general, perturbations may result from imperfections or may be deliberately introduced into the system by the application of fields. We study the lowest-order nontrivial perturbation in the trap, which is octupolar, using classical perturbation methods. The original three-degree-of-freedom problem is reduced to a single degree of freedom by (i) symmetry arguments, (ii) generation of apt action-angle variables, and (iii) computation of the classical normal form. The phase-space structure of the resulting normalized Hamiltonian, in the 1:1 resonance, is then analyzed. In the process we discover a saddle-node bifurcation. This approach provides for a global view of the reduced phase space, and, thereby, allows for a systematic study of the impact of several simultaneously applied perturbations.

The dynamics of collapsing and exploding Bose-Einstein condensates caused by a sudden switch of interactions from repulsive to attractive are studied by numerically integrating the Gross-Pitaevskii equation with atomic loss for an axially symmetric trap. We investigate the decay rate of condensates and the phenomena of bursts and jets of atoms, and compare our results with those of the experiments performed by E. A. Donley et al. [Nature (London) 412, 295 (2001)]. Our study suggests that the condensate decay and the burst production is due to local intermittent implosions in the condensate, and that atomic clouds of bursts and jets are coherent. We also predict nonlinear pattern formation caused by the density instability of attractive condensates.

We propose a mechanism to change the interaction strengths of a two-component condensate. It is shown that the application of $\pi /2\mathrm{}$ pulses allows us to alter the effective interspecies-interaction strength as well as the effective interaction strength between particles of the same kind. This mechanism provides a simple method to transform spatially stable condensates into unstable ones and vice versa. It also provides a means to store a squeezed spin state by turning off the interaction for the internal states and thus allows to gain control over many-body entangled states.

In this paper imaginary- and real-time versions of an equation for the condensate density, which describe dynamics and decay of any spherical Bose-Einstein condensate (BEC) within the mean-field approach, are presented. We obtain quantized energies of collective, finite-amplitude radial oscillations, and exact numerical instanton solutions, which describe quantum tunneling from both the metastable and radially excited states of the BEC of ${}^7\mathrm{Li}$ atoms. The mass parameter for the radial motion is found different from the Gaussian value assumed hitherto, but the effect of this difference on decay exponents is small. The collective breathing states form a slightly compressed harmonic spectrum, $n=4\mathrm{}$ state lying lower than the second Bogoliubov (small amplitude) mode. The decay of these states, if excited, may simulate a shorter-than-true lifetime of the metastable state. By scaling arguments, results extend to other attractive BECs.

Third-harmonic generation using a single medium receives theoretical analysis and the results are applied to ${\mathrm{CsLiB}}_6{\mathrm{O}}_{10}$ crystals. From the solutions for a full set of coupled-amplitude equations, comprehensive expression of overall-effective third-order nonlinear optical susceptibility is derived, including the contributions of direct third-order and cascaded second-order processes. The overall-effective third-order nonlinear optical susceptibility shows peculiar behaviors, such as oscillatory dependence on propagation distance and dependence on azimuthal and polarization angles with inversion symmetry. The optimum conditions for efficient third-harmonic generation are predicted at the phase-matching angles of second-harmonic generation, sum-frequency generation, and third-harmonic generation.

We present a time-dependent quantum calculation of the scattering of a few-photon pulse on a single atom. The photon wave packet is assumed to propagate in a transversely strongly confined geometry, which ensures strong atom-light coupling and allows a quasi-one-dimensional treatment. The amplitude and phase of the transmitted, reflected, and transversely scattered part of the wave packet strongly depend on the pulse length (bandwidth) and energy. For a transverse mode size of the order of ${\lambda }^2,$ we find nonlinear behavior for a few photons already, or even for a single photon. In a second step we study the collision of two such wave packets at the atomic site and find striking differences between the Fock state and coherent state wave packets of the same photon number.

We propose a simple scheme for highly efficient nonlinear interaction between two weak optical fields. The scheme is based on the attainment of electromagnetically induced transparency simultaneously for both fields via transitions between magnetically split $F=1\mathrm{}$ atomic sublevels, in the presence of two driving fields. Thereby, equal slow group velocities and symmetric cross coupling of the weak fields over long distances are achieved. By simply tuning the fields, this scheme can either yield giant cross-phase modulation or ultrasensitive two-photon switching.

We report an experimental, numerical, and analytical study of the near resonant propagation of a laser pulse through an atomic vapor. In the nonlinear regime probed, the light pulse develops frequency sidebands whose positions are, in first approximation, solely dependent on the maximum Rabi frequency of the system, in a fashion very similar to that observed in optical fibers. This modulational instability dictates the temporal reshaping of the laser field and finally results in pulse splitting.

In a recent paper, Maitra and Burke [Phys. Rev. A 63, 042501 (2001); 64, 039901(E) (2001)] have given an interesting and instructive example that illustrates a specific feature of the time-dependent density-functional theory—the dependence of the reconstructed time-dependent potential not only on the electron density, but also on the initial state of the system. However, a concise form of its presentation by these authors is insufficient to reveal all its peculiarities. Our paper represents a very detailed study of this valuable example, intended to facilitate a better understanding and appreciation.

When orthopositronium collides with a closed-shell atom or ion the “pick-off” process is the dominant process for positron annihilation. In pick-off annihilation the positron annihilates with electrons in the target but not with the electron that is part of the positronium atom. The rate for pick-off annihilation, expressed in terms of the dimensionless parameter ${}^1{Z}_{\mathrm{eff}},$ for orthopositronium scattering from ${\mathrm{Li}}^{+},{\mathrm{Na}}^{+},$ and ${\mathrm{K}}^{+}$ was computed with an $L^2$ variant of the fixed-core stochastic variational method. The threshold ${}^1{Z}_{\mathrm{eff}}$ for ${\mathrm{Li}}^{+}$ and ${\mathrm{Na}}^{+},$ which can form a stable bound state with Ps were found to be 0.067 and 0.73, respectively, while that for ${\mathrm{K}}^{+},$ which does not bind Ps, was 0.064.

It is shown that the wave function recently found by Guedes [Phys. Rev. A 63, 034102 (2001)] is a special case of the well-known Volkov solution to the time-dependent Schrödinger equation describing a nonrelativistic charged particle moving in an electromagnetic field.

It is shown that virtual ${\mathrm{H}}^{-}$ formation has a profound effect upon low-energy $\mathrm{Ps}\mathrm{}\left(1s\right)\mathrm{}-\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ scattering, yet ${\mathrm{H}}^{-}$ formation only accounts for about 10% of the total cross section just above threshold. Infinite series of Rydberg resonances converging on to the ${\mathrm{H}}^{-}$ formation threshold are seen.