Table of contents

The authors have found an infinite number of closed-form solutions to the Schrodinger equation for a well known model atom, by treating its short-range cut-off parameter as an eigenvalue.

The R-matrix and complex coordinate techniques are combined for the first time and applied to the problem of the positive energy spectrum of a non-hydrogenic atom in a laboratory strength magnetic field. Quantum defect theory is extended to calculate the appropriate irregular Coulomb function at complex energy and complex radial distance. Calculations are carried out for lithium to compare with previous experimental measurements and with a corresponding calculation for hydrogen.

Using a two-step laser optogalvanic technique in a Ca DC discharge the authors have measured the energies of the even 3dnd J=0 and J=2 as well as some 3dng J=2 autoionizing states of Ca in the range below 62500 cm^-1, for which calculations have been published. In general the agreement between experimental and theoretical values is very good. Especially important is the detection of the '4p²'¹S₀ and, probably, the 4p5p³D₂ perturbers.

The general form of the distortion approximation for semirelativistic collision energies is given. The problem of the anomalously large spin-flip transitions, identified in the symmetric eikonal model, is resolved. Symmetric distorted wave approximations are thus confirmed in their status as valid relativistic theories.

The influence of a strong, static, homogeneous field on an atom in a dense plasma has been investigated. The electrostatic potential in the atom has been calculated by means of the two-dimensional Thomas-Fermi model, which, in spite of its simplicity, can provide a qualitative understanding of the physical processes. Although the external field does enhance the ionization as expected, its influence becomes less important with higher density.

An extension of the direct variational method to study quantum systems confined by penetrable potentials is proposed. The authors treat explicitly the case of some one- and two-electron atomic systems (H, H^-, He, Li⁺ and Be²⁺) in their ground state within spherical confining barriers. In all cases, a simple representation for the ansatz wavefunction is employed and the corresponding energies are given as a function of size and height of the barrier. Additionally, some quantities of physical interest are evaluated for the case of hydrogen and comparison is made with available exact calculations.

Chaotic scattering of an electron in an unscreened Coulomb field with a superimposed oscillatory electric field is analysed in a classical mechanics framework. Spatial motion is restricted to one dimension, yielding two-dimensional Poincare or asymptotic planes. Emphasis is put on the asymptotic properties of the chaotic scattering process: deflection functions, inelastic cross sections, iterated scattering map. The scattering process in the long range unscreened Coulomb potential is described without any ambiguity using an as large as possible free motion integrable Hamiltonian. The scattering process is nonhyperbolic, because of the infinite number of eigenfrequencies of the Coulomb oscillator: the exponential scaling in the singularity positions of the deflection functions or cross sections is lost, even after moderate enlargements. The scattering is also nongeneric, because of the essential singularity at infinity, as displayed by the iterated scattering map. Cross sections show the large number of inelastic rainbows that are expected. Their positions with respect to the elastic peak are compared to some simple quantum-mechanical expectations.

Two tools to carry out ab initio calculations on complex atoms (perturbation theory and a relativistic formalism) are considered from the point of view of second quantization in the coupled (tensorial) form. A procedure to express general two-particle operators in this scheme is given. In perturbation theory, the creation and annihilation operators are graphically recoupled to their final form. The method is exemplified by a calculation of effective three-particle operators in l²l' configurations. Although based on the 'nonrelativistic' SL scheme, the method can equally well be used in fully relativistic calculations via an SL to jj coupling transformation of the creation and annihilation tensors.

Experimental and theoretical data for energy levels and radiative transitions in Fe VIII and Fe VII are very scarce. The authors' study is a first attempt to present a comprehensive set of data, using an ab initio target representation. The close coupling approximation is used in LS coupling, including the first 9 and 31 terms of Fe⁸⁺ and Fe⁷⁺ respectively. This detailed and systematic approach generates a sound basis for future experimental and more accurate theoretical investigations. The results demonstrate the importance of electron correlation and core excitation effects in these ions.

Configuration interaction wavefunctions have been calculated and used to evaluate oscillator strengths and transition probabilities for dipole and allowed transitions from the ground state levels to those of the 3s3p⁶ and 3s²3p⁴3d states of Cu XIII, in both LS and LSJ coupling schemes. Lifetimes of the excited state levels are determined. A study of cancellation effects in the oscillator strengths, arising from configuration mixing, provides an explanation of why experimental data are sparse.

A series of multireference configuration interaction (CI) calculations using an extended Gaussian basis set have been performed on the X¹ Sigma ⁺ ground state of the PN molecule in order to accurately determine the potential energy surface in the vicinity of the minimum. With the help of this curve a wide assortment of spectroscopic observables have been computed. The overall agreement with experiment is good. Marked correlation energy effects are found for the electric dipole/quadrupole moments and nitrogen nuclear coupling. Pure rotational excitations calculated by means of the numerical solutions of the radial Schrodinger equation are found to be in quite good agreement with experiment. Average values of the electric dipole moment over the first vibrational levels have been derived and the trend exhibited by the experimental data is well reflected by the theoretical results. Vibrorotational transitions, pure vibrational and vibrorotational lifetimes have also been determined which, to date, have not been determined experimentally.

Using Doppler-free laser spectroscopy with thermionic detection the 4f¹⁴6s9d and 4f¹⁴6s10d ¹D₂ and ³D₂ levels as well as the 4f¹³5d6s6p (7/2, 3/2) J=2 level at 48135.6 cm^-1 and the 4f¹⁴6p²¹S₀ level in neutral ytterbium have been investigated via two-photon transitions from the 4f¹⁴6s²¹S₀ ground state. The spectra have been analysed with regard to the hyperfine splitting in the excited states and the isotope shift in the corresponding transition. The isotope shifts in the transitions involving the ³D₂ states exhibit strong influences of second-order hyperfine interaction for the isotopes ¹⁷¹Yb and ¹⁷³Yb. The experimental results of the hyperfine splitting constants have been interpreted in terms of intermediate coupling schemes. In addition a mixing of the 4f¹⁴6s9d and-to a minor degree-of the 4f¹⁴6s10d configurations with the 4f¹⁴6p² configuration could be verified for the ¹D₂ states.

The hydrogen atom in a circularly polarized microwave electric field is treated as a periodically time-dependent quantum system. Quasienergy states of Rydberg manifolds are determined by applying second-order perturbation theory, while the n=2 manifold is treated with inclusion of relativistic effects. The photoabsorption spectrum for transitions from the n=2 manifold to Rydberg manifolds is calculated.

The authors present high-order harmonic generation results obtained with different laser systems, a 1 ps 1053 nm Nd-glass laser, a 2 ps 616 nm synchronously pumped dye laser, a 36 ps 1064 nm mode-locked Nd-YAG laser and the second harmonics (308 nm and 532 nm) of the latter two systems. They investigate the influence of the laser pulse width, the excitation wavelength (from the near infrared to the ultraviolet) and the atomic medium on the number of photons produced and on the maximum energy attained. Harmonic generation also depends strongly on the focusing conditions. By using simple arguments and results of numerical calculations in xenon, they show that the conversion efficiency in general follows a simple b³ power law, b denoting the laser confocal parameter, up to a transition regime where the coherence length of the process becomes equal to the medium length. By applying the b³ scaling as a normalization factor, they can then compare experimental results obtained in different focusing geometries. Their experimental data show that the optimization of the photon energy produced is favoured by using long incident wavelengths and light atomic systems with a high ionization energy.

The IR absorption spectrum of rotationally jet cooled ¹³CF₃I molecules, with vibrational energy near the dissociation threshold D=19000 cm^-1, has been measured by using a photodissociation IR spectroscopy method in the range of the nu ₁ and nu ₄ mode frequencies. A comparison of this spectrum is made with that of ¹²CF₃I. To explain the strong difference observed in the nu ₄ mode spectra, a crucial influence of fourth-order Fermi resonance interaction is suggested. The anharmonic shifts appear to be strongly nonlinear with respect to energy.

The two-photon optogalvanic spectrum of the C-X system of HgBr has been recorded using an Nd: YAG laser-pumped dye laser. Many new bands not observed earlier have been detected. Assignments of the bands to appropriate vibrational transitions have been confirmed using the bromine isotopic shift and an extended Deslandre table has been prepared for this band system of HgBr. Molecular constants for the two participating electronic states are determined. Potential energy curves are also reported.

The relative production rates of Rb⁺ and Rb⁺₂ ions through the multiphoton ionization (MPI) of Rb₂ and the effective order of non-linearity k for these ions were measured in the wavelength range 620-670 nm. The measured results indicated that these ions were produced by two- or three-photon ionization of Rb₂. The Franck-Condon factors calculated for the transition from the ground state (X ¹ Sigma ⁺_g) to the first intermediate state (B ¹ Pi _u) were in good agreement with the production rates obtained for Rb⁺ and Rb⁺₂ ions. From these reasons the authors concluded that in the process of MPI of Rb₂ the transition to the Bu ¹ Pi _u state plays a crucial role in the production of both ions. The competitive relations between the production processes of Rb⁺₂ and Rb⁺ ions were derived. In the wavelength range at around 669 nm the ratio of the number of Rb⁺ ions to that of Rb⁺₂ ions produced through three-photon ionization of Rb₂ was about 4/1.

Vibrationally excited states of spherically symmetric molecules have larger collisional diameters compared with the ground state. Molecular gases are mixtures of different excited states in different vibrational modes. Therefore the concept of a single potential of interaction between two molecules fails to describe both transport and thermodynamic properties simultaneously. A model of a gas with slightly different interactions between vibrational states is proposed. It agrees with experimental data well within the corresponding errors. As an example CF₄ is considered and the model proposed here describes fairly well 87 experimental points. The alternative model of a single potential leads to a RMS which is factor of three larger and on average exceeds by two times the accepted experimental errors.

Experimental cross sections for non-radiative single and double electron capture from Ne target into decelerated H-like Ge ions at collision energies of (4-12) MeV u^-1 are presented. The results are compared with theoretical calculations and an empirical scaling rule. Information concerning the impact parameter dependence of electron capture is extracted using classical trajectory Monte Carlo calculations.

The authors have investigated multiple electron capture into autoionizing projectile states during 108 keV Ar⁹⁺ and 80 keV ¹³C⁵⁺ collisions on Ne by measuring autoionization electrons in coincidence with charge state selected target ions. They have determined partial electron energy spectra, corresponding to a well defined number of initially captured electrons. The set-up of the ion and electron spectrometer is described. Trajectory calculations for the determination of detection efficiencies are presented. The partial spectra are discussed in terms of the 'extended classical barrier' model.

Variational R-matrix calculations have been performed for electron scattering by the HF molecule. Calculations over a grid of internuclear distances are used to compute the vibronic R-matrix, using a new adiabatic phase matrix method described here. This body-frame vibronic R-matrix is converted to the rovibronic R-matrix by a modified frame transformation at the R-matrix boundary. The external rovibronic close-coupling equations are solved by analytic methods. This methodology makes it feasible to carry out full first-principles calculations including molecular rotation and vibration, although only vibrationally elastic results are reported in the present paper. The threshold behaviour of the body-frame results can be described in terms of dipole eigenfunctions. Validity in the laboratory frame show that influence of rotation on vibrationally elastic e-HF collisions. The computed cross sections at small energies, close to the rotational thresholds, show rather sharp peaks that are dominated by j to j+or-1 excitations.

Electron impact excitation cross sections of the 2s and 2p states of hydrogen-like ions with nuclear charge Z>or=26 have been calculated in a fully relativistic distorted wave approximation. The importance of including the Moller interaction for the more highly charged ions is demonstrated. Excellent agreement, of the order of a few per cent, is obtained with the older calculations of Walker (1975) and results by Fontes (1992).

New absolute cross section measurement for the reaction H^-+e to H⁺+3e^- is reported for interaction energies from threshold to 2 keV by using the animated crossed beam method. The present results confirm the disagreement between the previous results of this laboratory and the results of Peart et al. (1970, 1971).

In order to explore the range of applicability of the classical trajectory Monte Carlo technique concerning the phenomena associated with light-particle impact of atoms and molecules, the authors present calculations of the singly and doubly differential cross sections for 100 eV electron and positron impact of He and H₂. Through comparison with experimental measurements it is noted in what regimes of ejection energy and angle the classical model describes reasonably the process of ionization by electrons. They find that reasonable agreement is obtained regarding the integrated (singly differential and total) cross sections, while the features of the doubly differential cross section which evidently come about due to quantum mechanical aspects of the collision are not reproduced. In these instances the classical cross sections reflect an averaging over electron angles and energies of the observed doubly differential cross sections.

Previous relativistic DWBA calculations based on the Pauli form of the Schrodinger equation have been extended to excitation of the (np⁵(n+1)s)^1.3P^o₁ states and the metastable (np⁵(n+1)s)³P^o_0.2 states of neon, argon, krypton and xenon. Results for several collision energies are presented and compared with experiment. In agreement with experimental evidence, strong deviations from the statistical branching ratio of 5:1 in the cross sections for excitation of the states with J=2 and j=0 were found for the xenon target. When comparing relativistic and non-relativistic DWBA calculations, it becomes evident that these effects are mainly due to the energy dependence of the T-operator because of different fine-structure excitation energies rather than to explicitly spin-dependent terms in the projectile-target interaction.

Electron-impact excitation of the Hg*(6³P₁) state has been studied by means of electron-photon coincidences involving polarized electrons. Differential Stokes parameters (photon polarization components) have been determined for scattering angles ranging from 10 to 90' at E=8 eV and from 10 to 60' at E=15 eV. The state multipole formalism has been used to extract the charge-cloud distribution of the Hg*(6³P₁) state from the measured Stokes parameters at E=8 eV. At this energy shape and size of the charge-cloud distribution depend strongly on the direction of the electron polarization vector. The experimental data at E=8 eV are compared with R-matrix calculations where good agreement is obtained.

A minimum has been observed in the generalized oscillator strength (GOS) for the A(²A^''₂) from X(¹A₁) transition of ammonia at K²=0.9 au. The GOS were determined from the inelastic differential cross sections measured with a previously described electron energy-loss spectrometer. The incident electron energy was 1 keV and the energy resolution 0.6 eV.

Based on the Feshbach projection-operator formalism a method for calculating angle-integrated and resonant cross sections for vibrational excitation and dissociative attachment of diatomic molecules by low-energy electrons is developed. The method allows for a treatment of the non-local character of the scattering potentials. The basic formulae reduce to a set of linear equations. As a first example the HCl molecule is considered using model potentials. The calculated cross sections are found to be in good agreement with the results of an exact solution of the model problem.

New calculations of the differential and integrated cross sections are reported for positronium formation in positron-hydrogen collisions using the multiple-scattering expansion method. Discussion and comparison of the present results with other theoretical calculations are made.

Maxwell's equations provide the basis for explaining many electromagnetic phenomena, both in vacuum and in matter. While some of these effects may be described within the electric dipole approximation D= in ₀E+P and H= mu ^-1₀ B, there are others which require the inclusion of higher multipole terms in the fields D and H. Various practices for doing this have been adopted in the past, such as the use of traceless quadrupole and higher moments, and the neglect of certain moments. Some of these practices are shown to lead to Maxwell equations which are not translationally invariant, in that they depend on the choice of origin to which the multiple moments are referred, even though they may also yield expressions for observables which do not possess this defect. It is also shown how to obtain general multipolar forms for D and H which ensure origin-independent Maxwell equations.