Table of contents

High-harmonic generation (HHG) is considered on the basis of the interaction of a short intense laser pulse with a thin solid crystal layer. For a selective range of parameters its initial regular structure is preserved during the strong interaction, including the suppression of shock waves in the layer. For this situation, phase matching like in Bragg scattering may be achieved between the fundamental and high-harmonic waves in the presence of substantial free-electron background. This allows us to estimate the spectral intensity of HHG in terms of single-ion signals and to predict very high temporal and spatial coherence in the hard x-ray regime.

In the present study we have investigated three-photon ionization in Ca in which autoionizing states are engaged. The two-photon resonant process (from the Ca ground state 4s^2 1S₀) occurred through or at least in the vicinity of one of the following states: 4s4d ¹D₂, 4p^2 3P₂, 4s6s ¹S₀, 4p^2 1D₂ and 4p^2 1S₀, with the third photon either reaching the continuum directly or one of the autoionizing states. The three-photon resonant transitions to 3dmp, mf: ¹P₁, ³P₁ and ³D₁ autoionizing states for m up to 21 have been observed. Some of the autoionizing resonances which we have found had not been observed before in a high-resolution one-photon absorption experiment (for J = 1) and in multiphoton experiments (for J = 3). We have compared the ionization signal as a function of the laser detuning and the laser intensity with theoretical curves obtained within a simple model (three-level atom + one-mode laser field). This gives information about the order of magnitude of the three-photon ionization probability through autoionizing states.

We investigate in this paper the properties of electron wavepackets created in the continuum by ultrashort pulses, linearly chirped. We consider alkali atoms, where complete quantum calculations can be carried out. The spreading of the wavepacket is radial and mainly due to free propagation, except for very low kinetic energy where Coulomb interaction has to be considered. We show that the wavepacket can be focused into a position located at macroscopic distances far from the ion core. Distances as large as several centimetres are obtained for standard values of laser parameters. Moreover, we derive the conditions where the wavepacket is temporally optimally focused. Finally, we study several characteristics of the wavepacket, such as the temporal divergence (in ps cm^-1) and the temporal profile, when the focusing is not maximum.

There are models for the description of doubly excited states (DES) of H^- and He whose degrees of validity can be tested by comparing their results to those from theory based on the solution of the Schrödinger equation with the full Hamiltonian. Such comparisons are meaningful and definitive when a reasonably wide range of data are available. We present results for the energies and the nature of the wavefunctions of the four lowest ¹P^o DES of H^- and of He for each hydrogenic manifold from N = 6 up to 25. These are used to establish the degree and range of validity of the quantum number n₂ introduced by Herrick and Kellman (Herrick D R and Kellman M E 1980 Phys. Rev. A 21 418) in their triatomic model for qualitative description of the spectra of DES, as well as of two classification schemes, as a function of level of excitation and of type of state. According to the model, the number n₂ is equal to the number of nodes of the density ρ(θ₁₂) of the corresponding DES. We present results of calculations of ρ(θ₁₂) using correlated wavefunctions for the four lowest states in the N = 10 and 25 manifolds. These show for the first time for such highly excited states how the angle opens as excitation increases. Furthermore, they indicate that n₂ provides a valid picture even up to N = 25. The first of the two classification schemes examined here is the (K,T) scheme, introduced by Herrick and Sinanoglu (Herrick D R and Sinanoglu O 1975 Phys. Rev. A 11 97). It is shown quantitatively that it deteriorates as N increases and Z decreases. The second scheme is the (F,T) scheme, introduced by Komninos et al (Komninos Y, Themelis S, Chrysos M and Nicolaides C A 1993 Int. J. Quantum Chem. Suppl. 27 399), where F = N-K-1 and N,K are not good numbers anymore. It is shown that it constitutes a consistently better representation, especially as the relative significance of electron correlation increases, as in the high-lying DES of H^-. For the lowest intrashell and intershell states of each N-manifold, for which the calculation incorporates the effects of electron correlation to very high accuracy, the (F,T) `purity' coefficient is very high, close to one.

Different ab initio methods for computing the non-local energy-dependent width function Γ(E) associated with resonance states of molecular anions are studied. Two new ² approaches to Γ(E) are developed in the contexts of the complex absorbing potential (CAP) and the stabilization methods. Using a model potential and the prototypical ²Π_g shape-type resonance of N₂^-, the two new methods and the established Stieltjes imaging technique are compared. Special emphasis is put on a robust performance for low-quality basis sets as well as on the choice of the discrete state describing the `bound part' of the resonance. In particular, the CAP method turns out to yield satisfactory results even if only atom-centred Gaussian basis sets are employed provided that the absorption is adapted to the energy. The choice of the discrete state has a marked influence on the calculated width function, and from the viewpoint of computing Γ(E) a box-stabilized discrete state is recommended.

Electron impact calculations are presented for H₃⁺ and H₃O⁺ at their equilibrium geometry using coupled states expansions. The R-matrix method is employed as it is very efficient for characterizing the many resonances found in electron-ion collisions. Positions, widths and symmetries are obtained for the lowest ten Feshbach resonances for each ion. These resonances are important for explaining features observed in dissociative recombination experiments at energies of 5-10 eV. In addition a broad shape resonance at about 4.5 eV is identified for H₃O⁺. Electronic excitation cross sections are obtained in reasonable agreement with recent storage ring experiments.

The method of complex-coordinate rotation is applied to calculate D-wave resonances in e⁺-H scattering. The wavefunctions of the resonance states are constructed using Hylleraas coordinates. The resonance energies and widths below the positronium n = 4 threshold are reported. Comparisons are made with other available calculations.

Fully correlated calculations of the Zeeman g_J-factors for lithium-like ions in the 2 ²S and 3 ²S states are presented, including relativistic and radiative corrections of orders α², α²m/M, and α³. The isotope shifts in g_J are determined accurately.

Experimental cross sections are presented for single and multiple electron stripping from Xe¹⁸⁺ projectiles in collisions with N₂ at energies 2.0-9.3 MeV u^-1. The data are compared to 2-30 MeV u^-1n-body classical trajectory Monte Carlo calculations that explicitly include electrons on both centres. Two-centre electron-electron (e-e) and electron-screened nuclear interactions contribute to the ionization reactions. The computations are in reasonable accord for the total stripping cross section but underestimate the higher stages of multiple electron loss. An energy deposition model gives improved agreement with experiment. The energy dependence of the total stripping cross section is close to E^-0.5. Calculations are also presented for target ionization by Xe⁺, Xe⁸⁺ and Xe¹⁸⁺ at 10 and 20 MeV u^-1. Projectile and target ionization cross sections are found to be comparable. Cross sections for projectile stripping by ionized targets are also calculated and found to be relatively insensitive to the ionization stage of the target. This latter observation is attributed to the compensating contributions between the two-centre e-e and electron-screened nuclear interactions.

Generalized cross sections for two-, three-, and four-photon ionization of H₂ by linearly polarized laser light have been calculated. Three different situations are considered: the laser polarization being parallel or perpendicular to the internuclear axis and the case of an isotropical distribution of H₂ molecules. The main features of the spectra are discussed. In order to assess the reliability of the results, two completely different ab initio methods have been developed and used for the parallel orientation; good agreement is found between them. The impact of the present results on the question of alignment of molecules in laser fields is discussed.

Simultaneous observations of the vacuum ultraviolet (VUV) and visible-near-IR emission from radio frequency discharges in gaseous Kr with small (<0.1%) Xe admixture concentrations were conducted in the pressure range 80-400 hPa. The spectra were used for investigation of energy transfer from the lowest excited states of both atomic krypton and krypton molecules to the ground state xenon atoms. The VUV emission spectra allowed us to obtain a value of 3.9×10⁷×P_Xe hPa^-1 s^-1 for the energy transfer rate from the 1_u state of Kr₂* molecules and a rate of 1.7×10⁶×P_Xe hPa^-1 s^-1 for the energy transfer rate from the system of the four lowest Kr excited states to Xe ground state atoms. A value of 1.6×10⁶×P_Xe hPa^-1 s^-1 was independently obtained for this atom-to-atom energy transfer channel based on our observations of IR emission.

The Kα and Kβ satellite and hypersatellite x-ray lines for highly ionized sulphur projectiles passing through carbon foils of thickness between 15-210 µg cm^-2 with energies of 99 and 122 MeV have been recorded using a Si(Li) detector. A new theoretical model based on the results of single-configuration Dirac-Fock calculations (and using equilibrium charge state distribution and fluorescence yields) has been proposed in order to evaluate the average population of different shells and to estimate the probability of appearance of the most important configurations in the sulphur ions passing through the carbon foils. The reliability of the model has been proved by a very good reproduction of the measured energy shifts for all Kα and Kβ satellite and hypersatellite peaks. The role of non-equilibrium charge fractions in various shells of sulphur ions has also been investigated in detail.

A general scheme is given for evaluating various matrix elements related to relativistic and QED corrections for the Schrödinger Hamiltonian within a variational approach. The nonrelativistic wavefunction is expanded using an exponential basis set of the Slater type for states of arbitrary angular momentum, where the rotational symmetry is expanded in terms of bipolar harmonics. Special emphasis is placed on numerical implementation of the algorithms described.

We present an analytical calculation that predicts the collapse of vibrational wavepackets in molecules due to the coupling of the rotational and vibrational degrees of freedom. At longer times a new class of revivals is predicted in the vibrational degree of freedom, due to the finite size and discrete nature of the rotational reservoir. The interplay of these competing behaviours is studied in the context of current experiments, and conditions for observing the revivals are described. Furthermore, the conditions for which the molecular vibration and rotation can be regarded as a system and its reservoir-like environment are described, in which case the ro-vibrational coupling can be considered effectively as a mechanism for decoherence of the vibrational motion. Comparison of the dephasing time predicted by this model with that observed in recent experiments is made.