Dark soliton states of Bose-Einstein condensates in harmonic traps are studied both analytically and computationally by the direct solution of the Gross-Pitaevskii equation in three dimensions. The ground and self-consistent excited states are found numerically by relaxation in imaginary time. The energy of a stationary soliton in a harmonic trap is shown to be independent of density and geometry for large numbers of atoms. Large amplitude field modulation at a frequency resonant with the energy of a dark soliton is found to give rise to a state with multiple vortices. The Bogoliubov excitation spectrum of the soliton state contains complex frequencies, which disappear for sufficiently small numbers of atoms or large transverse confinement. The relationship between these complex modes and the snake instability is investigated numerically by propagation in real time. 03.75.Fi, 05.45.Yv,

Dielectronic capture processes in highly charged uranium ions are studied in the isolatedresonance, distorted-wave approximation.A fully relativistic Dirac-Fock method is employed to calculate resonant transfer and excitation cross sections for collisions of U + and U' + with H2 and dielectronic recombination cross sections associated with the 2p~2s stabilizing transition of U' +.A semirelativistic method based on the previously developed AUTOSTRUCTURE code is found to give cross sections in good agreement with the Dirac-Fock method in all cases. When the Dirac-Fock method is further extended to include the effect of the two-body Breit interaction, substantial changes are found in certain low-energy cross sections associated with E-shell resonant transfer and excitation, but little change is found in the hn =0 dielectronic recombination cross sections.

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We study the dynamics of a two-species Bose-Einstein condensate in a double well. Such a system is characterized by the intraspecies and interspecies s-wave scattering as well as the Josephson tunneling between the two wells and the population transfer between the two species. We investigate the dynamics for some interesting regimes and present numerical results to support our conclusions. In the case of vanishing intraspecies scattering lengths and a weak interspecies scattering length, we find collapses and revivals in the population dynamics. A possible experimental implementation of our proposal is briefly discussed.Comment: 7 pages, 5 figure

The double photoionization of a helium atom and a singly charged lithium positive ion enclosed in charged Cq60 fullerenes is studied using the time-dependent close-coupling method. Continuum raising and lowering effects are seen in the shift of the double-ionization threshold of the confined atom or ion. Confinement resonances in the double-photoionization cross section, previously observed for helium confined inside a neutral fullerene, persist for helium confined in both positively and negatively charged fullerenes and are found to be independent of the charge on the fullerene. The double photoionization of a confined singly positively charged lithium ion is found to exhibit similar behaviour to a confined neutral atom, with confinement resonances present in the double-photoionization cross section for confinement in neutral, positively and negatively charged fullerenes. In addition, the confinement resonances are shown to be sensitive to the width of the fullerene with the resonances having a smaller amplitude for larger fullerene widths.