Table of contents

Accurate relativistic coupled-cluster studies with basis sets up to h-functions result in a static dipole polarizability of 9.11 au = 1.35 ųfor Rb⁺ . Relativistic effects are of the same size as correlation contributions although small compared to the non-relativistic Hartree-Fock limit (9.14 au).

An explanation is suggested for the experimental fact that positronium formation in positron-impact double ionization is strongly suppressed for helium and neon, but less so for the other noble gases. Positronium is assumed to be formed in the collision but it may then break up as a result of the recapture of the electron by the residual ion. The probability of break up is expected to increase with the magnitude of the energy liberated to the positron in the recapture process, and this is consistent with the experimental data. The proposed mechanism also explains certain features of positronium formation in single ionization.

We present a quantum mechanical, classical and semiclassical study of the energy spectrum of a Rydberg hydrogen atom in the instantaneous van der Waals potential for the L_z= 0 case. The semiclassical results are in good agreement with the results of the quantum mechanical calculations within the first-order perturbation theory as well as with the quantum mechanical calculations of other authors. The classical analysis shows that the phase space of the system is separated into the regions of vibrational and rotational motions, which are connected, respectively, with the lower-lying energy levels of doublet symmetry, and with the non-degenerate higher-energy levels. Finally, we compare the classical (eigen)trajectories with the corresponding eigenstates and find that both of them show the same symmetry patterns.

The multiconfiguration Dirac-Fock model is employed to compute the hyperfine interaction constants of the 5p⁴ 5d ⁴ D_7/2 , 5p⁴ 6p ⁴ P_5/2 , 5p⁴ 6p ² D_5/2and 5p⁴ 6p ⁴ D_7/2levels of the xenon ion. The wavefunctions are obtained with the active space expansion method, where configuration state functions of a specific parity and Jvalue are generated by substitutions from the reference configurations to an active set of orbitals. The active set is then increased in a systematic way, allowing the convergence of the expectation values to be monitored. The calculated electric field gradients are combined with experimentally determined electric quadrupole hyperfine constants in order to extract the nuclear electric quadrupole moment of isotope 131 of Xe, for which the value Q= -0.117(6) barn is found.

We present a new extended version of the R -matrix method for the calculation of continuum properties in which non-orthogonal orbitals are extensively used for describing both the target states and the R -matrix basis functions. In particular, a B -spline basis is used for the description of continuum states in the inner region and the target states may be obtained from independent calculations. This leads to a generalized eigenvalue problem but has the advantage of requiring much smaller bases for accurate representation of target wavefunctions and to achieve convergence in the close-coupling expansion. The present approach and its code are both applicable to a general atom and their efficiency for low-energy scattering processes is demonstrated by calculating the photoionization of Li. A detailed analysis of the resonance structure is given. Very good agreement with experimental data has been obtained, and considerable improvement in the description of resonances has been achieved in comparison with the standard R -matrix calculations.

This paper explores the utility of a discrete singular convolution (DSC) algorithm for solving the Schrödinger equation. DSC kernels of Shannon, Dirichlet, modified Dirichlet and de la Vallée Poussin are selected to illustrate the present algorithm for obtaining eigenfunctions and eigenvalues. Four benchmark physical problems are employed to test numerical accuracy and speed of convergence of the present approach. Numerical results indicate that the present approach is efficient and reliable for solving the Schrödinger equation.

Absolute measurements of single- and double-electron-capture cross sections by C³⁺projectiles on atomic and molecular hydrogen targets were performed for projectile energies between 1.0 and 3.5 MeV for the single- and 1.0 and 2.0 MeV for the double-capture processes. The ^H /^H₂cross section ratios were measured using an absolutely calibrated tungsten-tube furnace for the production of atomic hydrogen. The single-capture data are compared with calculations based on the boundary-corrected first Born approximation, the eikonal approximation and a semiclassical model, presenting a good overall agreement. Calculations for the double capture using an analytical expression, obtained within the independent electron approximation and based on the same semiclassical model, give a reasonable qualitative description of the data.

The use of Brillouin-Wigner perturbation theory in describing many-body systems is critically re-examined.

Spectra from the Rydberg series 1s-n p for the principal quantum numbers n 8 of Cl¹⁶⁺are observed on the JET tokamak. Individual lines up to n= 15 are resolved. The line intensity of n= 10 is enhanced, relative to the underlying 1/n³scaling, due to charge exchange collisions with neutral deuterium in the ground state. The observations are compared with predictions based on available partial charge exchange cross section data. There is generally good agreement, however, some details of the predicted n -shell distribution are different from those observed in the experiment.

Relativistic tunnelling ionization of atoms by intense, elliptically polarized light is considered. The relativistic version of the Landau-Dykhne formula is employed. The general analytical expression is obtained for the relativistic photoelectron spectra. The most probable angle of electron emission, the angular distribution near this angle, the position of the maximum and the width of the energy spectrum are calculated. In the weak-field limit we obtain the familiar non-relativistic results. For the case of circular polarization our analytical results are in agreement with recent derivations of Krainov (1999 J. Phys. B: At. Mol. Opt. Phys.321607).

The laser-synchrotron radiation combination technique has recently been incorporated into an apparatus for two-dimensional photoelectron spectroscopy of atoms and molecules in order to investigate photoionization dynamics of polarized atoms. Ground state Ar atoms are excited with linearly polarized synchrotron radiation to Rydberg states lying below the first ionization potential. The aligned atoms thus formed are ionized by irradiation of a laser which is also linearly polarized. Photoelectrons emitted in the direction of the electric vector of the synchrotron radiation are sampled and energy analysed. The photoelectron angular distribution is measured with respect to the electric vector of the laser. Expressions which correlate the asymmetric coefficients for the angular distribution with theoretical dynamic parameters involving transition dipole matrix elements are derived. The anisotropy of the present angular distribution can be reasonably explained, assuming that the matrix elements and phase shift differences are essentially independent of the total angular momentum quantum number of the final state and that the spin-orbit interaction in the continuous spectrum is small.

Multiphoton ionization rates have been calculated for He at the KrF laser wavelength of 248 nm and for laser intensities up to 6 × 10¹⁴W cm^-2using the R -matrix Floquet method. For intensities above that at which channel closing takes place it is found that intermediate five-photon resonances with bound states strongly influence the total rate. In particular, the resonance between the ground state and the 1s2p ¹ P^ostate is found to occur at a laser intensity of 5 × 10¹⁴W cm^-2 . This resonance is investigated at several neighbouring wavelengths and its prominent nature, which is discussed in terms of a proposed nearby laser-induced degenerate state, should enable it to be observed experimentally.

The problem of a hydrogen atom in an impenetrable spherical cavity of small radius Ris considered on the basis of the first-order perturbational treatment of the electron-nucleus interaction taking explicit account of the boundary condition. An approximate analytic expression is derived for the electronic energy as a function of the shift of the nucleus off the centre. The estimations obtained are in good qualitative and semiquantitative agreement with the results of the finite-difference calculations. Some general features of the energy dependences are discussed qualitatively.

We perform time-dependent quantum calculations on the ionization dynamics of helium in intense ultrashort laser fields. A linear model of the atom is used to extract single- and double-ionization yields for a 780 nm excitation. For an intensity of 10¹⁵W cm^-2clear evidence is found for a direct double-ionization process which is caused by rescattering of an electron from the core in the presence of the field. A momentum-space analysis of the wavefunctions shows that in this case both electrons are preferentially emitted in the same direction and with different momenta.

Electron-collision excitation cross sections of inelastic transitions among the 28 LSterms of the 2s² 2p³ , 2s2p⁴ , 2s² 2p² 3s, 2s² 2p² 3p, 2s² 2p² 3d and 2s² 2p² 4s configurations of singly-ionized oxygen are calculated using the R -matrix method. The target states are represented by fairly extensive configuration-interaction wavefunctions which yield excitation energies, oscillator strengths and radiative lifetimes of excited states that agree well with available calculated and measured values. To assess the importance of electron correlation and coupling to higher excited states in the scattering calculation, the present 28-state calculation is compared with the earlier 11-state R -matrix theory. Our cross sections for the 2s² 2p³⁴ S^o -2s² 2p³² D^oand 2s² 2p³⁴ S^o -2s2p⁴⁴ P transitions show good agreement with the merged-beams energy-loss experiment and the 11-state R -matrix theory.

Nuclear recoil corrections to the energies of helium S levels of order m² /M⁵are presented. They are shown to contribute only a small amount to the ionization energies of the 2 ¹ S and 2 ³ S states, but to contribute significantly on the scale of accuracy of modern ⁴ He-³ He isotope shift experiments.

Cross sections for electron-impact single ionization of ground state Kr¹⁰⁺and Kr¹¹⁺ions have been calculated in the distorted-wave approximation including both direct ionization and excitation-autoionization processes. The direct ionization cross sections are calculated for the ejection of 3s, 3p and 3d subshell electrons and the excitation-autoionization cross sections are calculated for the inner-shell excitations of the type 3pnl(n= 4,5,6;l= 0,1,2,3) and 3sn ´l ´ (n ´ = 4,5;l ´ = 0,1,2,3). In addition, the inner-shell excitation of the type 2p 3d, 4l(l= 0,1,2,3) is included for Kr¹¹⁺ . The radiative decay effect has been found to be negligible by carrying out explicit calculations of the radiative rates and autoionizing rates. The present results show that the direct process dominates the total ionization cross section for the two ions and that the contributions of excitation-autoionization are about 15% and 13% of the total cross sections for Kr¹⁰⁺and Kr¹¹⁺ions, respectively. The present results are in good agreement with the experimental measurement of Oualim et al .

Dissociative single and double photoionization of N₂as a function of the exciting-photon energy has been investigated using monochromatized synchrotron radiation in the exciting-photon energy range between 37 and 69 eV by dispersed VUV fluorescence spectroscopy (80 nm _fl 200 nm). Relative partial emission cross sections for N I and N II fluorescence have been recorded as a function of the exciting-photon energy. There is strong evidence that the precursors of dissociative single ionization with one of the fragments being excited are the N₂⁺2_g^-12_g⁺state with its closely lying correlation states only. An approximately linear excess energy dependence of the cross sections for the molecular double photoionization into the N₂²⁺D ¹_u⁺state has been observed in the excitation spectrum of D ¹_u⁺X¹_g⁺fluorescence in N₂²⁺close to its threshold. Evidence for dissociative double photoionization with excitation has been found.

General equations are presented for determining the field-dependent variation of the wavefunctions, matrix elements and intensities of dipole transitions between Stark levels of a hydrogen atom in a field range where the fine-structure effects may be neglected. The Sturm-series resolution for the reduced Coulomb-Green function is used to derive analytical expressions for the first-order corrections in terms of parabolic quantum numbers of initial and final states. Simple forms of these expressions as functions of the upper-state quantum numbers are presented explicitly for the Lyman and Balmer series. The selective action of the dc electric field on the intensity of Stark components of hydrogen lines is revealed in numerical calculations for both and types of emitted radiation. This selectivity may cause, in particular, enhancement of the high-frequency and damping of the low-frequency Stark -lines of the Lyman series.

The seminal experiment of Franck and Hertz, which helped lay the foundations of quantum and atomic physics, is investigated through solution of the Boltzmann equation, using both eigenfunction expansion methods and spatial finite-difference techniques. We consider electrons in both a model gas and in mercury, the gas originally used by Franck and Hertz, and focus upon the effects of both inelastic and elastic collisions. It is pointed out that the periodic spatial structures encountered in the Franck-Hertz experiment have a physical origin similar to the oscillatory phenomena observed by Fletcher and others previously in low-pressure, low-current discharges, and by Winkler et al , and other contemporary authors in simulations of low-temperature plasmas.

Radiative lifetimes of nine levels in Eu II (4f⁷ 6p, 4f⁶ 5d6s and 4f⁶ 5d² ) and Eu III (4f⁶ 5d) have been measured using time-resolved laser-induced fluorescence spectroscopy on a laser-produced europium plasma. Oscillator strengths for a number of Eu II lines have been derived by combining the lifetimes with branching ratios measured in the emission spectrum of a hollow-cathode lamp.

The angular distribution of photoelectrons from fixed-in-space molecular hydrogen has been measured in the 44-76 eV photon energy range for an ionic state, with a state energy of 38 eV measured from the H₂ground state, dissociating to H⁺ +H(n= 2). The photoelectrons are ejected nearly isotropically at 44 eV when their energy is relatively low, while ejection perpendicular to the molecular axis becomes more and more favoured as the photon energy increases. This behaviour is possibly explained in terms of direct photoionization to the 2p_uand 2s_gstates of H₂⁺ ; the former being favoured at 44 eV, and the latter at photon energies far from threshold.

The quantum analogy of the usual spinodal decomposition is explored for the recently achieved binary alkali Bose-Einstein condensates mixture. We conclude that an analogy is possible within the formulation of coupled nonlinear Schrödinger equations, and find that the quantum spinodal decomposition consists of two stages. The non-equilibrium stage I is dominated by the fastest growth mode, associated with a characteristic length. Expressions for both time and length scales in stage I are obtained. Stage II is a relaxation process of approaching equilibrium, dominated by the slowest mode. We propose that for this state the slow evolution towards the phase segregation is due to the Josephson effect between different domains of the same condensate, and its time scale is estimated.

The electronic structure of the helium atom in the magnetic field regime B= 0-100 au is investigated, using a full configuration-interaction approach which is based on a nonlinearly optimized anisotropic Gaussian basis set of one-particle functions. The corresponding generalized eigenvalue problem is solved for the magnetic quantum number M= -1 and for both even and odd z -parity as well as singlet and triplet spin symmetry. Accurate total electronic energies of the ground state and the first four excitations in each subspace as well as their one-electron ionization energies are presented as a function of the magnetic field. Additionally we present energies for electromagnetic transitions within the M= -1 subspace and between the M= -1 subspace and the M= 0 subspace treated in a previous work. A complete table of wavelengths and field strengths for the detected stationary points is given.

We have carried out a joint study, experimental and theoretical, of the binary depolarized collision-induced light scattering spectrum by gaseous helium at room temperature. The intensities from helium pairs, calibrated on an absolute scale, have been measured in the much extended, previously unexplored, 5-680 cm^-1spectral domain. A critical analysis of the spectrum has been made by using ab initioanisotropy models available in the literature. Quantum-mechanical computations have enabled us to determine the spectral response of the pair polarizability terms which compose the most up-to-date anisotropy data (Moszynski et al1996 J. Chem. Phys.1046997). The conclusion has been drawn that internuclear distances shorter than the helium atomic diameter are probed via the very far wing of our spectrum.

The convergent close-coupling method is applied to electron-impact ionization of the ground state of atomic hydrogen at incident energies of 15.6, 17.6, 20, 25 and 30 eV. Absolute fully differential cross sections are presented for the case of equal energy sharing of the excess energy. Comparison with experiment shows some unexpected discrepancies with the overall agreement being best at the lowest, and most difficult for experiment and theory, energy considered.