Table of contents

The Ca I-like spectrum of doubly ionized titanium, Ti III, has been investigated by using the dual laser plasma technique. The 3d photoabsorption spectrum of Ti III has been recorded in the 17-27 eV region. It was found that single-electron transitions from the 3p⁶3d² ground configuration to 3p⁶3d¹np, mf excited configurations dominate the spectrum. A total of 49 lines, in the region from 460 to 730 Å, have been observed and identified. The transitions were identified with the aid of multiconfiguration Hartree-Fock calculations.

Excitation rate coefficients, for transitions from the ground level to excited levels of Gd XXXVII, have been calculated over the temperature range 500-2500 eV using the R-matrix method. It is observed that the contribution of resonances enhances the rates by up to an order of magnitude over the available (non-resonant) results of Hagelstein (Hagelstein P L 1986 Phys. Rev. A 34 874).

Recent experiments have demonstrated that light pulses can be made to propagate `superluminally' or, at the opposite extreme, to come to a complete stop. Some of the basic physics underlying these studies and their antecedents are reviewed.

Electron energy-loss spectra for the Xe atom were measured for a given set of scattering angles (1.5°-20.0°), in an energy-loss range from 40 to 180 eV using an incident electron energy of 1045 eV and an energy resolution of 1.0 eV. The absolute generalized oscillator strength (GOS) and cross section have been determined for the intense shape resonance (4d→εf) and for the discrete resonance 4d(¹S₀)→6p(²D_5/2) in the Xe atom. The GOS curve as a function of the square of the momentum transfer for the shape resonance presents a well-defined minimum. In order to obtain the optical oscillator strength for our data normalization, the electron energy-loss spectrum (1.5°) was converted to a photoabsorption spectrum. A broad band has also been observed in the energy-loss spectra, centred at 80.0 eV. According to previous analysis, it has been assigned to double excitations (4d^-15p^-1).

The B-spline density functional method for the electronic continuum is employed to calculate the cross section and the asymmetry parameter profiles of valence and core photoionization in M@C₆₀ (M = Be, Mg and Ca). For the valence photoionization significant differences are identified through the series and oscillations similar to those observed in the HOMO/HOMO-1 ratio in C₆₀ have been calculated for Ca@C₆₀. Core M 1s and Ca 2p ionizations are studied with the help of the `dipole prepared' continuum orbitals, which allows the identification of the leading mechanisms which give rise to the characteristic sharp and intense shape resonances, typical of these compounds.

We solve the time-dependent Schrödinger equation (TDSE) that describes the resonant excitation of the hydrogen 1s state to Rydberg states and wavepackets using the electric dipole approximation (EDA) in the length form as well as the full electric interaction of the multipolar Hamiltonian. The time-dependent wavefunctions are expanded in a hydrogenic basis and the TDSE is transformed into a system of coupled integro-differential equations. The truncation of this expansion is done systematically and judiciously within a scheme which we call the multimanifold intrashell approximation, according to which the intershell matrix elements are ignored. The ensuing drastic reduction in the size of the overall calculation allows an economic and meaningful solution of the problem when the multipolar interaction to all orders is taken into account. Three categories of calculations were carried out, all involving many hydrogenic n-manifolds, without and with intrashell couplings. A series of computations dealt with resonant excitation of manifolds up to n_res = 85. The first two categories of calculations involved the EDA and multimanifold expansions without and with intrashell matrix elements. The third category involved the full multipolar interaction and multimanifold expansions with intrashell matrix elements. The reported time-dependent survival probabilities revealed that, even for the weak field used (8.75×10⁷ W cm^-2), as the level of the resonant excitation rises beyond n⩾10, the EDA fails to describe the correct dynamics of such processes. The results herein provide quantitative information and demonstrate beyond doubt the limitations and inaccuracies of the EDA when the field-atom coupling involves extended wavefunctions, such as the high-lying Rydberg states.

We describe the perturbation induced in a plasma by a charged particle in circular motion, analysing in detail the evolution of the induced charge, the electrostatic potential and the energy loss of the particle. We describe the initial transitory behaviour and the different ways in which convergence to final stationary solutions may be obtained depending on the basic parameters of the problem. The results for the stopping power show a resonant behaviour which may give place to large stopping enhancement values as compared with the case of particles in straight-line motion with the same linear velocity. The results also explain a resonant effect recently obtained for particles in circular motion in magnetized plasmas.

Using an electron beam ion trap (EBIT) and a crystal spectrometer in the Johann geometry, the 1s Lamb shift of hydrogen-like Ti²¹⁺ has been measured; the result is L(1s) = 2.29(14) eV, in agreement with the theoretical value. The measurement was made by calibrating the Lyman-α wavelengths using the characteristic Kα wavelengths of neutral vanadium. The Kα spectrum was produced by inserting a wire probe near the electron beam of the EBIT. While the present measurement is preliminary, achieving only modest precision, it suggests that much higher precision could be achieved in the future.

A quasiclassical approximation to quantum mechanical scattering in the Møller formalism is developed. While keeping the numerical advantage of a standard classical trajectory Monte Carlo calculation, our approach is no longer restricted to using stationary initial distributions. This allows one to improve the results by using better suited initial phase space distributions than the microcanonical one and to gain insight into the collision mechanism by studying the influence of different initial distributions on the cross section. A comprehensive account of results for single, double and triple differential cross sections for atomic hydrogen will be given, in comparison with experiment and other theories.

The potential energy has been calculated for the 49 lowest molecular states Ω^{( + /-)} of the molecule RbCs within the 5-23 a₀ range of internuclear distances R. Spin-orbit interactions are taken into account through a semi-empirical spin-orbit pseudo-potential added to the electrostatic Hamiltonian. Molecular spectroscopic constants have been derived for bound states in the vicinity of their (inner) well. To the best of our knowledge, the vast majority of the results presented here are the first for this molecule. Extensive tables presenting energy values versus R are available at the following address: http://lasim.univ-lyon1.fr/allouche/rbcs-so.htm.

State-of-the-art ab initio methodologies have been used to perform calculations on the torsion along the vinyl-phenyl groups in styrene. The methods employed range from the Hartree-Fock and Möller-Plesset perturbation theories and coupled-cluster theory up to density functional (DF) ones. The effect of the basis set has also been considered by using several extrapolation formulae to the complete basis set limit. The torsional profile is analysed in terms of the π-conjugation and steric repulsions. The calculations indicate the existence of a global twisted minimum with a slightly lower energy than the planar structure. However, the exchange-correlation functionals used in the DF calculations are unable to predict this twisted minimum.

Oxygen ion impurity radiation is a potential source of inaccuracy in ion temperature determination with the aid of the commonly used C VI transition n = 8→n' = 7, produced by charge-exchange recombination (CXR) of C⁶⁺ ions, since the corresponding transition in O VI cannot be resolved under typical plasma conditions in the tokamak. In order to demonstrate the possible importance of oxygen ion impurity radiation, we have selected a convenient spectroscopic `window' (about 8 Å wide) containing the major Zeeman components of two prominent lines in the visible (multiplet 1), one emitted by C²⁺ and one by O⁺. Observations have been performed in this wavelength range, both tangentially and perpendicularly to the magnetic flux surfaces, in the second case with the aid of a special graphite test limiter. Measurements include the case of special plasma discharges in which oxygen gas was introduced from the test limiter. The temperatures of both species are evaluated from the Doppler broadening of the respective Zeeman components, and compared with the results from a model for collisional heating by impact with hot protons (deuterons) in the plasma edge. The spectra and derived results show that impurity identification in tokamak edge plasmas should not be carried out with the aid of spectral lines from highly excited levels populated by CXR, but using lines corresponding to much more species-specific transitions from lower ionization stages. The identification and quantitative analysis should be performed with the aid of carefully measured and calculated Zeeman-(Paschen-Back-) broadened line profiles, since these have features practically unique to the species under investigation. Some allowance may, however, be required for deviation, from a statistical distribution, of population among fine-structure sublevels.

We show how to adapt the ideas of local energy and momentum conservation in order to derive modifications to the Gross-Pitaevskii equation which can be used phenomenologically to describe irreversible effects in a Bose-Einstein condensate. Our approach involves the derivation of a simplified quantum kinetic theory, in which all processes are treated locally. It is shown that this kinetic theory can then be transformed into a number of phase-space representations, of which the Wigner function description, although approximate, is shown to be the most advantageous. In this description, the quantum kinetic master equation takes the form of a Gross-Pitaevskii equation with noise and damping added according to a well defined prescription - an equation we call the stochastic Gross-Pitaevskii equation. From this, a very simplified description we call the phenomenological growth equation can be derived. We use this equation to study (i) the nucleation and growth of vortex lattices, and (ii) nonlinear losses in a hydrogen condensate, which it is shown can lead to a curious instability phenomenon.

The R-matrix method is used to treat electron collisions with the molecular radical CF₂. These calculations concentrate on obtaining low-energy (less than 10 eV) elastic and excitation cross sections of the six lowest-lying electronically excited states of the CF₂ molecule. These states have symmetry ³B₁, ¹B₁, ³A₂, ¹A₂, ³B₂ and ¹B₂ and vertical excitation energies in the range 2.44-10 eV. Two shape resonances of ²A₁ and ²B₁ symmetries are found at 5.61 and 0.95 eV respectively. Calculations which stretch one C-F bond show that the ²B₁ resonance becomes bound at a bond length beyond 3.2 a₀. No other bound CF₂^- states are found.

The dynamics of Bose-Einstein condensates in a double-well magnetic trap is studied using the Gross-Pitaevskii equation (GPE) and a two-mode approximation. The self-trapping instability occurs when a sufficiently high potential barrier is formed in the centre of the trap. Close to the instability threshold, the GPE is reduced to a simple amplitude equation. In the case where weakly dissipative effects are taken into account, the condensate exhibits aperiodic oscillations which can be described by the Lorenz thermal convection model.

It has been drawn to our attention (Dere and Mason 2002) that the high temperature (≳ 15 eV) dipole effective collision strengths of Anderson et al (2000) do not approach the assumed asymptotic form. On investigation, we have found that the underlying collision strengths approach the assumed asymptotic form at high energies, but that the problem lies in their Maxwell averaging. A least squares fit was made to the high energy collision strengths, utilizing the infinite energy limit point. However, R-matrix with pseudo-states collision strengths exhibit shallow oscillatory behaviour at all energies, due to high-lying pseudo thresholds. Consequently, the least squares fit gave increasingly inaccurate results for the collision strengths at energies beyond the highest calculated energy and this in turn had an increasing effect on the high temperature Maxwell-averaged effective collision strengths. Using the original collision strengths of Anderson et al (2000), we have recomputed the dipole effective collision strengths, this time using a simple linear interpolation of reduced collision strengths between the highest finite energy and the infinite energy limit value. Results for the non-dipole transitions were originally computed by extrapolating the collision strengths as a constant and so were not subject to the inaccuracy inherent in the least-squares fitting. However, we can also improve the accuracy of the high temperature non-dipole effective collision strengths by making use of the infinite energy limit Born collision strength, which was not available to Anderson et al (2000). Again, we use a simple linear interpolation of the original Anderson et al (2000) collision strengths between the highest finite energy and the infinite energy limit Born value. The revised effective collision strengths are given in table 1 (see pdf file) of this corrigendum and they replace the values in table 2 of Anderson et al (2000). The conclusions of the modelling carried out by Anderson et al (2000) are unaffected as this was primarily at temperatures below 15 eV, where the change in the effective collision strengths is ≲ 10%. The coronal fractional abundance of H at 15 eV is < 10^-5. The revised adf04 data file for hydrogen is available from http://www-cfadc.phy.ornl.gov/data\_and\_codes/.

References

[1] Anderson H, Ballance C P, Badnell N R and Summers H P 2000 J. Phys. B: At. Mol. Opt. Phys.33 1255-62

[2] Dere K P and Mason H E 2002 Private Communication