Table of contents

We investigate the possibilities for the generation of solitons and vortices in a degenerate gas of neutral fermionic atoms. In analogy with the already experimentally demonstrated technique applied to a gaseous Bose-Einstein condensate we propose the phase engineering of a Fermi gas as a practical route to excited states with solitons and vortices. We stress that solitons and vortices appear even in a non-interacting fermionic gas. For solitons, in a system with a sufficiently large number of fermions and appropriate trap configuration, the Pauli blocking acts as the interaction between particles.

We report on the results of the ¹S single differential cross section (SDCS) for electron impact ionization of atomic hydrogen at 4.0 eV above threshold using the `intermediate energy R-matrix method' in conjunction with a two-dimensional R-matrix propagation approach. The current approach employs a more densely packed pseudo-state basis and larger interaction volume than in previous close-coupling calculations. Using this, together with different numerical techniques for analysing the SDCS data, provides a greater understanding of the differences that have arisen between previous theoretical studies. The current results are in excellent agreement with recent time-dependent close-coupling and exterior complex scaling calculations.

The ground bound states in the H₂⁺, D₂⁺, HD⁺ and HT⁺ ions are determined to a high accuracy by using the multi-box strategy developed (Frolov A M 2001 Phys. Rev. E 64 036704) for high precision variational calculations in three-body systems. In this approach the ground state wavefunctions are represented as the variational sums of generalized exponents written in the relative inter-particle coordinates r₃₂,r₃₁ and r₂₁. Our present variational energies and bound state properties are determined without making use of the Born-Oppenheimer approximation. The computed expectation values for various properties in the H₂⁺, D₂⁺, HD⁺ and HT⁺ ions are significantly more accurate than values known for these systems from earlier computations. The observed agreement between the computed and predicted cusp values is very good for electron-nuclear cusps. In contrast with this, the computed nuclear-nuclear cusps and nuclear-nuclear delta functions differ significantly from the predicted values.

The physical meaning of the entanglement of two identical `two-level' atomic dipole oscillators is investigated. Using Schrödinger's equation, the development of entanglement from an initial product state in which one atom is in the upper state and the other in the lower state is exhibited. Examination of the correlation of the oscillations shows that complete entanglement leads to full phase correlation of unknown absolute phase. This property serves to explain the physical meaning of entanglement for the class of systems considered and the results of measurements conducted on them, without resort to the `action at a distance' concept associated with the Einstein-Podolsky-Rosen paradox. A recent experiment in which such entanglement was produced and cited as an illustration of the paradox is analysed and explained by the present theory. It is shown that the Bell inequalities, unlike in experiments on other entangled states, cannot in principle be tested in this type of experiment.

The excitation energies and oscillator strengths of the 1s-2p transitions from O IV low-lying terms belonging to the configurations 2s²2p, 2s2p² and 2p³ are calculated using configuration interaction (CI) wavefunctions. Reasonably good agreement is obtained between the length and velocity forms. To verify the correctness of the results, these data are further obtained by treating the 1s-2p excitations as resonances occurring in photoionization processes. The photoionization cross sections are computed using the close-coupling scheme implemented by the R-matrix method. The resonance energies and autoionization widths of the 1s-2p excited states are determined by analysing the resonances exhibited by the photoionization cross sections. The results show that the resonance energies obtained by the R-matrix method are systematically lower than those by the CI scheme by 0.1-0.2 Ryd. This shows that a strong CI effect exists between the K-shell excited and continuum states. This effect can also produce redistribution of the oscillator strengths, especially for the weak transitions.

Symmetry-resolved spectra for excitation to the C 1s^-12π_u Renner-Teller pair states A₁ and B₁ in CO₂ are simulated theoretically. Reliable ab initio potential energy surfaces of the core excited states are calculated at the level of multi-configuration self-consistent-field theory. The problem of two-dimensional symmetric stretching and bending vibrational motion in the excited states is solved numerically and then the vibrationally resolved excitation spectra are analysed in detail. The calculated spectrum for excitation to the B₁ state is in excellent agreement with a recent experimental result. The vibrational structures in the spectrum are found to originate from the symmetric stretching motion in the B₁ state. On the other hand, the present calculation reproduces global features of the experimental spectrum for excitation to the A₁ state except for the vibrational structures in the higher-energy region. The absence of vibrational structures in the present simulation is ascribed to no account being taken of a vibronic coupling between the A₁ and B₁ adiabatic states. A very simple analysis taking account of the vibronic coupling demonstrates that the vibrational structures in the A₁ spectrum also originate from the symmetric stretching motion in the coupled B₁ state.

Yield spectra of the multiply charged ions Kr²⁺, Kr³⁺, Kr⁴⁺ and Kr⁵⁺ in coincidence with threshold electrons (E_k⩽0.03 eV) have been measured near the 3p-shell ionization region of Kr. Profiles of post-collision interaction (PCI) effects induced by Auger cascades following 3p-shell threshold ionization are derived from these coincidence spectra. On the basis of the PCI profiles, the number of Auger cascade steps for each of the decay channels leading to the formation of the multiply charged ions in 3p_3/2- and 3p_1/2-shell threshold ionization of Kr was determined, and the branching ratios of the decay channels were estimated.

Fragment ion-photon coincidence (FIPCO) spectra by 120 eV electron impact on carbon dioxide (CO₂) have been observed, in which optical emission in the 250-600 nm region has been detected. There are a dominant CO₂⁺ peak and a weak, broad CO⁺ peak in the FIPCO spectra. The kinetic energy distribution of CO⁺ correlated with the CO⁺(A ²Π-X ²Σ⁺) emission has been estimated on the basis of the Monte Carlo simulation of the CO⁺ band shape. This CO⁺(A ²Π) ion is produced through the dissociation process, CO₂ + e^-→CO₂^+*[MET I ²Π_u] + 2e^-→CO⁺(A ²Π) + O(³P) + 2e^-, where MET refers to multiple electron transitions. The production of CO⁺(B ²Σ⁺) is negligible compared with that of CO⁺(A ²Π). The produced CO⁺(A ²Π) ion is in vibrationally excited levels, and there is little population in the vibrational levels, v'⩽3.

A complete calculation of the mα⁶ contribution to the helium ionization energy of 2 ³P_J states is presented. The result, beyond the previously known radiative corrections, amounts to 0.4046 MHz and significantly reduces theoretical uncertainties. The computational method is based on the effective Hamiltonian derived from relativistic quantum electrodynamic theory. The current status of theoretical predictions is summarized and a comparison with the latest experimental results is performed.

We have performed a number of experiments with a Bose-Einstein condensate (BEC) in a one-dimensional optical lattice. Making use of the small momentum spread of a BEC and standard atom optics techniques, a high level of coherent control over an artificial solid-state system is demonstrated. We are able to load the BEC into the lattice ground state with a very high efficiency by adiabatically turning on the optical lattice. We coherently transfer population between lattice states and observe their evolution. Methods are developed and used to perform band spectroscopy. We use these techniques to build a BEC accelerator and a novel, coherent, large-momentum-transfer beam-splitter.

Recently measured radiative lifetimes of the Rydberg series 6pns (n = 8-13) and 6pnd (n = 6-11) J = 1 states of Pb I (Li Z S, Svanberg S, Biémont E, Palmeri P and Zhankui J 1998 Phys. Rev. A 57 3443) have been compared with theoretical values obtained by multichannel quantum defect theory analyses. The channel admixture coefficients were obtained from experimentally determined energy levels and are used to evaluate the theoretical lifetimes. The lifetime values for highly excited Rydberg states have also been predicted.

Theoretical differential and integral cross sections are reported for inelastic scattering of electrons by neon atoms for incident electron energies in the range of 20-100 eV. Transitions from the ground state to forty states associated with the 3s, 3p, 3d, 4s, and 4p manifolds were considered. The methods employed were the distorted wave approximation and first-order many-body theory, where the distorting potential includes the static-exchange potential. A comparison of our results with experimental data and other theoretical results are shown and discussed.

Charge transfer due to collisions of ground-state S⁴⁺(3s^2 1S) ions with helium is investigated for energies between 0.1 meV u^-1 and 10 MeV u^-1. Total and state-selective single electron capture (SEC) cross sections and rate coefficients are obtained utilizing the quantum mechanical molecular-orbital close-coupling (MOCC), atomic-orbital close-coupling (AOCC), classical trajectory Monte Carlo (CTMC) and continuum distorted wave methods. The MOCC calculations utilize ab initio adiabatic potentials and nonadiabatic radial coupling matrix elements obtained with the spin-coupled valence-bond approach. Previous data are limited to a calculation of the total SEC rate coefficient using the Landau-Zener model that is, in comparison to the results presented here, three orders of magnitude smaller. The MOCC SEC cross sections at low energy reveal a multichannel interference effect. True double capture is also investigated with the AOCC and CTMC approaches while autoionizing double capture and transfer ionization (TI) is explored with CTMC. SEC is found to be the dominant process except for E>200 keV u^-1 when TI becomes the primary capture channel. Astrophysical implications are briefly discussed.

We study the formation of cusps in the double differential cross section for ion-atom ionization collisions by means of a classical trajectory Monte Carlo calculation. The use of an `importance sampling' algorithm allows us to improve the efficiency of the method. We show that the overall shape of the cusp is decided during the collision stage, while its divergence builds up asymptotically as the result of a two-body process, in complete accordance with the general framework of the final state interaction theory.

The method of selective photoionization of individual subshells by monochromatized synchrotron radiation has been employed to measure independently all Coster-Kronig and fluorescence yields of Er L subshells. Fitting the measured fluorescence intensities versus primary energy with the photoelectric cross sections derived the Coster-Kronig coefficients and fluorescence yields. The obtained yields were compared with tabulated data and a very good agreement among them was found.

Multiconfiguration Dirac-Fock and relativistic configuration interaction calculations with the inclusion of Breit interaction, quantum electrodynamics and finite nuclear mass corrections have been carried out in the extended optimal level scheme on the spin-forbidden electric dipole transitions of highly ionized argon. The calculations have been carried out in jj coupling with a single electron in the K shell, varying degrees of ionization in the L shell and open outer shells. The radiative transition rates have been calculated in Coulomb and length gauges. The sensitivity of the orbital wavefunctions and the effect of configuration interaction on the transition rates are analysed in some detail.

Angular distributions of photoelectrons from both C and O K-shells of a fixed-in-space CO molecule have been calculated using a continuum multiple scattering method with partially overlapping spheres. The calculations have been performed at several photon energies from the ionization thresholds up to about 30 eV above them, where the σ* shape resonances occur. Comparison with recently published experimental results (Motoki S et al 2000 J. Phys. B: At. Mol. Opt. Phys.33 4193) shows that this simple method gives a rather reliable description of the most sophisticated experimental data.

We study the tunnelling properties of a cigar-shaped Bose-Einstein condensate by using an effective 1D nonpolynomial nonlinear Schrödinger equation (NPSE). First we investigate a mechanism to generate periodic pulses of coherent matter by means of a Bose condensate confined in a potential well with an oscillating height of the energy barrier. We show that it is possible to control the periodic emission of matter waves and the tunnelling fraction of the Bose condensate. We find that the number of emitted particles strongly increases if the period of oscillation of the height of the energy barrier is in parametric resonance with the period of oscillation of the centre of mass of the condensate inside the potential well. Then we use NPSE to analyse the periodic tunnelling of a Bose-Einstein condensate in a double-well potential which has an oscillating energy barrier. We show that the dynamics of the Bose condensate critically depends on the frequency of the oscillating energy barrier. The macroscopic quantum self-trapping (MQST) of the condensate can be suppressed under the condition of parametric resonance between the frequency of the energy barrier and the frequency of oscillation through the barrier of the very small fraction of particles which remain untrapped during MQST.

A crossed-beam apparatus was used to measure the relative differential cross sections for O²⁺(2s²2p²³P) + He(1s²¹S) → O⁺(2s²2p³²P) + He⁺(1s ²S) + 5.52 eV, below E_lab = 50 eV. The significant undulations observed in the differential cross sections are interpreted qualitatively by a two-state model (Olson R E and Kimura M 1982 J. Phys. B: At. Mol. Phys.15 4231) as due to the `inelastic rainbow' effect and the quantum mechanical interference effect, Stückelberg oscillation.