Table of contents

The multichannel quantum defect theory is derived by using the level-matrix parametrization of the collision matrix. It is proved that the specific aspects of the multichannel quantum defect theory originate in the jump across threshold of the logarithmic derivative. The connections to the reduced collision matrix and to the threshold cusp theory are established.

We present non-perturbative ab initio calculations of resonant two-photon ionization in which the ground state of a complex atom is resonantly coupled by a laser field to two Rydberg states, each of which belongs to a different Rydberg series. As an example, we have studied the resonant two-photon ionization of neon via the 5s and 4d Rydberg states using the R-matrix-Floquet theory. We find that for weak fields, where the Rydberg states are not overlapping, interference effects are already present which lead to a suppression of ionization for a particular laser frequency. For strong fields, the field induced coupling between the two Rydberg states can strongly modify the weak-field behaviour. We give a qualitative explanation of these phenomena by considering the dressed states of a simple three-level model atom coupled to two continua. Finally we show, by varying the intensity, how the Floquet eigenstates corresponding to the ground state and the two Rydberg states of neon are adiabatically connected to the field-free states.

Angle-resolved high-resolution photoelectron spectra of CO C 1s satellite lines were taken at a photon energy of 330 eV. The observed angular distributions assist in identifying the correlation effects which lead to the formation of different satellite lines, confirming recent theoretical and experimental results on this topic. Four conjugate shake-up satellite lines with beta =0 were observed, leading to a strongly aligned core-excited state in the molecular ion. These states decay anisotropically via participator Auger transitions, which carry along the angular momentum of the ionized core to double-hole final states. We present the first clear identification of the initial states of these recently observed K-shell satellite Auger transitions with pronounced decay anisotropy.

The near-threshold Rydberg diamagnetic (even parity, magnetic quantum number m=-2) spectrum of Na in a uniform magnetic field of 4.2 T is obtained using two distinct methods. The first method developed by Halley et al. (1992) combines R-matrix and quantum defect theory whilst the other method involves the use of a model potential. Our results agree well with those from experiment. The discrete diamagnetic (odd parity, magnetic quantum number m=0) spectrum of Na in a magnetic field of B=6.1 T is also calculated. We discuss the effect of quantum defect values on the spectra and the effect of variation of magnetic field strength on the position, the height, and the spacings of dominant lines. The results show that the methods mentioned above are effective in calculating the spectra of atoms in laboratory-strength fields, and that in basis-set calculations, the contribution from field-free continuum states is very important in the vicinity of the field-free ionization limit.

Branching ratios and partial decay widths for the fluorescent decay of Kr III 4p³np states have been calculated. Besides the non-correlative transitions of the type Kr III 4p³np to Kr III 4p³n`s/d also the purely correlative transitions of the type Kr III 4p³np to Kr III 4s4p⁵ have been considered. The partial widths of the correlative transitions turned out to be non-negligible in many cases.

By using a photon-ion merging-beam apparatus, the relative photoion-yield spectra for Sr²⁺ and Sr³⁺ from Sr⁺ ions in the ground state were measured around the 3d-ionization region. In the Sr³⁺-yield spectrum, some discrete lines are observed and a broad structure which reflects the giant resonance corresponding to the 3d- epsilon f transition is found. The observed spectra were analysed with the results of a multiconfiguration Dirac-Fock calculation code. The computation reveals that the observed discrete lines are composed of many lines which have a character due to the strong 5s-4d mixing effect. This is understood from the fact that after the 3d-hole creation, the final 4d-wavefunction collapses and its orbital energy sits beneath that of the 5s orbital.

Ejected electrons from the singlet and triplet states of doubly excited O⁴⁺ (1s²3l3l') and O⁴⁺ (1s²3l4l') ions, produced by 60 and 120 keV O⁶⁺ (1s²) ¹S+X collisions (X identical to He, Ne, Ar), have been measured with high resolution zero-degree electron spectroscopy. Only the singlet states were observed when He gas was the target. In contrast, mainly triplet states were observed when Ne gas was used. Both singlet and triplet states contributed to the electron spectra, produced by O⁶⁺ (1s²) ¹S+Ar collisions. Two theoretical methods, perturbation theory or Z-expansion (MZ code) and multiconfigurational Hartree-Fock (Cowan code) were used for identification of ejected-electron spectra. The contribution of correlation effects is discussed by comparison with other theoretical energies.

Positions and widths of the Auger states 2s2p⁶ns, np, nd (n=3-7) of Na⁺ are calculated in the Hartree-Fock approximation with additional inclusion of the inner-core and core-polarization correlations. A detailed analysis of various correlation corrections for excitation energies and partial widths is given. The results obtained agree well with the experimental data and the main conclusion about the key influence of the inner-core correlation on the partial widths is supported by analysing the relative intensities of Auger lines observed.

The 3p photoabsorption spectra of K II and Ca III have been recorded in the 25-55 eV region using the dual laser plasma technique. With the help of calculations performed with the Cowan code and Rydberg series expansions, many 3p to ns, d transitions have been identified in these ions. Strong LS-term-dependent behaviour arising from 3d wavefunction contraction is seen to influence intensities and quantum defects in the 3p to nd series.

The three-electron systems H+He and He⁺+He are treated in the semiclassical approximation. The nuclei are described classically moving on straight-line trajectories and the electrons quantum mechanically by solving time-dependent coupled channel equations. As physical basis states we use products of H, He⁺ and He states with proper translation factors and completely antisymmetrized wavefunctions. In order to calculate the matrix elements of the electron-electron interaction analytically as far as possible, we expand the wavefunctions into Cartesian Gaussian basis functions. In the energy range E_lab=2-300 keV for H+He and E_lab=10-600 keV for He⁺+He we present cross sections for excitation, charge transfer and ionization and compare them with various experimental data and other theoretical calculations.

A classical description of state selective excitation processes in atom-charged particle collisions is provided for arbitrary values of the collision energy. Closed-form expressions for the cross sections of nl to n', nl to l' and nl to n'l' transitions are obtained in the high energy limit. The scaling properties of sigma (nl to n'l') cross sections are briefly discussed.

We have calculated total and single differential cross sections for electron-impact ionization of Ar⁹⁺ in its ground (1s²2s²2p⁵)²p⁰ state by using a method that combines the distorted-wave Born approximation and the R-matrix theory. The incident and the scattered electrons are described by distorted waves, while the wavefunctions of the initial ground state of the Ar⁹⁺ ion and its final continuum state (Ar¹⁰⁺+e^-) are calculated by using the R-matrix approach. This allows us to take into account the excitation-autoionization process. Five states of the final Ar¹⁰⁺ ion, namely 1s²2s²2p⁴³P, ¹D, ¹S and 1s²2s2p⁵³P⁰, ¹P⁰, have been included in our calculation. Up to the 24-pole components of the interaction with the ionizing electron were included, exciting ten distinct Ar⁹⁺ continuum symmetries. The single differential cross sections exhibit considerable structure due to autoionizing resonances. Total cross sections for production of Ar¹⁰⁺ in each of the five states are presented for impact energies from the threshold energy at 17.6 to 100 au. Our theoretical values for the total cross section are in fair agreement with the experimental results.

A distorted wave calculation for electron impact 4²S-4²P excitation in potassium has been performed. Results for differential cross sections, alignment, orientation and spin asymmetry parameters are obtained. The differential cross sections have been compared with the available recent theoretical results and experimental data while spin resolved and spin averaged orientation parameters and asymmetry results are compared with the only available coupled channel optical calculations.

Second-order distorted-wave Born results are reported for electron-copper scattering for incident electrons with energy between 10 and 100 eV. The importance of the second-order effects of polarization and absorption is examined. Both differential and integrated cross sections are presented and compared with existing experimental and theoretical results. Good agreement between experiment and theory is found for the integrated cross sections if the theoretical results are adjusted to the known optical oscillator strength. For the differential cross sections, on the other hand, there is almost an order of magnitude difference between theory and experiment for large scattering angles.

Cross sections for electron-impact double ionization of W^q+ ions in charge states q=1-6 as well as triple ionization in charge states q=1-4 have been measured using the crossed-beams technique. A new semiempirical formula for multiple ionization of three or more target electrons is in very good agreement with the measurements. Together with previously obtained experimental data for single ionization of tungsten ions, the measured cross sections are used to study the influence of multiple ionization on the W^q+ charge state evolution if tungsten atoms are exposed to an electron flux at 700 eV energy. It is shown that the charge state evolution is significantly influenced by multiple-ionization processes.

Cross sections for electron impact ionization from the 1s and 2s shells of He-like, Li-like and Be-like U ions have been calculated by the relativistic distorted wave method at incident electron energies up to five times the ionization energy. Differences between the results obtained using the Moller and Coulomb interactions are attributed to differences in the contribution from interference between direct and exchange ionization. Excellent agreement is obtained between the Moller result and an EBIT experimental result for He-like U at an incident electron energy of 198 keV.

We consider spin-dependent effects in low-energy electron molecule scattering. Until now no explicit spin dependent effects have been included in ab initio calculations. We discuss the fine-structure effect, well known from atomic physics, for diatomic molecules as a model which can describe deviations from pure exchange scattering. Numerical results for the a³ Pi excitation of CO will give an indication of the magnitude of the effects. Resolving the fine-structure of the target leads to the different coupling schemes for diatomic molecules. We consider in this paper Hund`s cases (a) and (b) as the two most important ones. In particular, differential cross sections and spin polarization for unpolarized projectiles and targets are discussed. For molecules obeying Hund`s case (a) coupling scheme orientation and alignment parameters are introduced.

Collision strengths for low-energy electron-impact excitation of Mg II are computed in a ten-state close-coupling approximation using the R-matrix method. Fine-structure transitions among the 17 associated levels are considered explicitly through algebraic transformation of the scattering matrices. Detailed comparisons are made with the merged-beam experiment of Smith and co-workers (1993) and the crossed-beam experiment of Zapesochnyl and co-workers (1984); the present results are found to be in very good agreement with the former for the 3s-3p resonance transition. A comparison with earlier theoretical calculations is also made. Maxwellian-averaged rate coefficients are calculated for transitions between the target levels considered, and a selection of these results is presented for practical applications.

We consider laser-stimulated resonance scattering of electrons in a bichromatic laser field in the framework of a one-dimensional potential model. The two fields have the frequencies omega and 2 omega and are out of phase by phi . Changing phi permits us to coherently control the shape and height of the resonance peaks: in particular, a pure Breit-Wigner distribution can be obtained.

A hyperspherical close-coupling method is used to calculate the elastic, positronium formation and excitation cross sections for positron collisions with atomic hydrogen at energies below the H(n=4) threshold for L=0 and 1 partial waves. A new two-dimensional coordinate transformation is used such that the Schrodinger equation at large hyper-radii can be solved accurately. The coupled hyper-radial equations are integrated to a large hyper-radius at which the solution is matched to the dipole states in the outer region. From the extracted K-matrix, the elastic, positronium formation and atomic hydrogen excitation cross sections are computed. Resonance positions, total widths, and partial cross sections are also examined and compared with those from other calculations.

A variational treatment for obtaining the binding energies, wavefunctions and internal distances of the positronium molecule (Ps₂) is presented. For this purpose, very modern Hylleraas-type trial wavefunctions, as well as different envelope functions ( upsilon ^m6e^{- gamma upsilon} where m₆=0, 1, 2, 3 and upsilon is the distance between the two positrons), are employed. The resulting binding energies show excellent convergence when the number of components of the wavefunction considered is increased. Our results at m₆=2 show that only 22 components of our wavefunction are sufficient for obtaining the binding energy omega P(s₂)=-0.03 Ryd (=-0.41 eV) which is identical to the binding energy calculated by Ho via 400 components of his trial wavefunctions. The best convergence, however, has been achieved via 22 components of our wavefunctions at m₆=1. In this case, omega P(s₂)=-0.042 Ryd (=-0.573 eV). Comparison with the very recent value of omega P(s₂)(=-0.435 eV) determined by Kinghorn and Poshusta (1993) and Kozlowski and Adamowicz (1993), using 300 components of their trial wavefunctions, supports the opinion that the exact binding energy of Ps₂ is less than -0.41 eV. Our average values for the internal distances of Ps₂ agree quite well with those determined by previous authors and emphasize the argument that the size of the molecule is decreased when the binding energy is lowered.

A new algorithm is introduced for the calculation of the polarizational bremsstrahlung cross section. This method is particularly efficient for carrying out the slowly converging partial-wave series, which characterize the cross section of the process. The frequency and the angular distributions of photons emitted in a collision of a 0.2-10 keV electron with Eu are calculated for the photon frequencies above the 4d-threshold: omega =100-200 eV. The polarizational bremsstrahlung is taken into account.