Table of contents

Convenient, accurate and completely analytical expressions of the rovibrational eigenenergies for the Lennard-Jones (10, 6) potential are obtained from the hypervirial expressions of Mateo et al (1990) by exploiting the fact that the minimum of the LJ (10, 6) effective potential can be put in analytical form. The eigenvalues obtained from such expressions are compared with the WKB eigenvalues for the estimation of accuracy.

Total electron scattering cross sections for C₂H₄, C₂H₆, C₃H₆ (propene and cyclopropane) and C₃H₈ have been measured in the energy range between 4 and 500 eV. Measured results show a remarkable isomer effect and dependence on the geometrical dimension of the molecule.

Based on the projection operator formalism of scattering theory, a time-dependent wavepacket description of dissociative electron attachment is developed. The spacetime integro-differential equation of motion has been explicitly (numerically) solved for two models representing dissociative attachment via shape resonances. Friction in the dissociative motion is identified as a generic feature of the dynamics of such systems.

The authors present theoretical studies of high-order harmonic generation in a rare-gas medium. The experimental results obtained at Saclay with a 1064 nm Nd-YAG laser in the 10¹³ W cm^-2 intensity range are summarized. The harmonic emission strengths, first decrease rather steeply for the first orders, then form a long plateau up to the 21st harmonic in xenon, or up to the 33rd harmonic in argon, before decreasing again rather abruptly. The theoretical description of these experiments consists first in the calculation of the photoemission spectra emitted by a single atom. The spectra are obtained by numerically integrating a time dependent Schrodinger equation for the laser-excited rare-gas atom. Second, one must account for collective effects in the medium, described by Maxwell's equations. A theoretical framework for describing the generation and propagation of harmonics in strong laser fields is developed. An numerical solution of the propagation equations for the harmonic fields in xenon at 1064 nm provides results which agree well with experimental data.

By means of a variational procedure the authors find a lower bound to the Thomas-Fermi kinetic energy of a fermionic system in the ground state, in terms of the moments (r^-2), (r^-1) of the fermionic density rho (r), and the number of particles, N, given by a formula which improves previous results. This expression allows them to bound the exact kinetic energy of a fermionic system by using the works of Lieb and Thirring. This variational technique can also be applied in order to bound density-dependent quantities of atoms as the exchange energy in Dirac's form and the average electron radial ( rho ) and momentum ( gamma ) densities, numerical and asymptotically because in these cases it is not possible to find exact analytical solutions.

An approach combining the saddle-point technique with the R-matrix method is applied to calculate the autoionization energies and widths of Li-like ions for (1s(2s2p)³P)²P and (1s(2s2p)¹P)²P states with Z=3 -10 and for (1s2p2p)²D states with Z=3, 4. The character of the autoionization state for Li-like ions is discussed. The authors' value for the width of the (1s(2s2p)³P)²P state in Be II is 4.48 meV, which agrees with the experimental result of 4.58+or-0.13 meV. Their value for the width of the (1s2p2p)²D state in Be II is 26.63 meV, that of Davis and Chung is 27.56 meV and the experimental one is 30.3+or-1.1 meV.

A previous Breit-Pauli R-matrix calculation for photoionization of the excited initial state (6s6p) ¹P₁^o of atomic barium (Bartschat and McLaughlin, 1990) has been extended over a wide range of energies and various final ionic states. The complicated resonance structure was fully resolved and has been analysed in terms of quantum defect theory. While the agreement of this fully ab initio calculation with other recent theoretical and experimental work is quite satisfactory, the use of a semi-empirical core potential may be necessary to further improve the agreement between experimental and theoretical resonance positions.

The authors utilize Liouville-space and projection operator methods, introducing additional atomic projection operators, and derive master equations for an atom coupled to a radiation reservoir and to an additional external field via multi-photon interactions; the explicit forms of the equations are studied in detail for two-photon processes. The coupling coefficients of the equations are expressed in terms of effective operators for two-photon transitions. The expressions for the probability of transfer of coherence via two-photon transitions and for the dephasing due to elastic interactions with the reservoir are obtained quantum mechanically for the first time.

The authors present calculations using a variational method for the time-dependent Schrodinger equation for the study of multiphoton ionization of H atoms in intense laser fields. The trial wavefunction is chosen to be an anisotropic Gaussian wavepacket and the case of linear polarization of the laser field is considered. They report on ionization rates as a function of laser intensity (in the range 10¹⁵-10¹⁶ W cm²) and frequency (corresponding to ionization by three or more photons) and momentum-dependent electron spectra. Comparison is made with results obtained when the trial wavefunction is an isotropic Gaussian wavepacket and with large-scale numerical calculations. The present method gives reliable results for nonresonant ionization in the limit of high field intensity as well as in the low-frequency limit. The electron momentum distributions are singly peaked and provide a qualitative picture of the ionization process at high field strengths.

A crossed-beam technique developed previously in this laboratory has been used to determine cross sections for the formation of Balmer alpha radiation in collision of He⁺ and He²⁺ with H₂ in the energy ranges 2.5-25 keV amu^-1 and 17-67 keV amu^-1 respectively. Comparison is made with other relevant data.

Recent experiments have found both an unexpected enhancement and structure of the binary peak in the spectrum of electrons ejected in partially stripped ion-atom collisions. Utilizing the theoretical approach which has been used to elucidate the origin of this behaviour, a survey of their manifestation is presented over a broad range of nuclear and ionic charges (C, F, Fe, I and U ions) and impact energies (0.1 to 100 MeV u^-1). For forward binary electron emission it is shown that the greatest enhancement occurs for the lowest projectile ion charge states (highly screened nuclei). The magnitude of the enhancement maximizes near an energy that is characteristic of each nuclear species and results in a cross section several times larger than that for impact by the fully stripped ion. Those ions, collision energies and ejection angles for which unusual binary peak structures are likely to be observable are illustrated. The authors point out what consequences these effects have for modelling energy deposition in the collision of ions with dense targets.

Potential energy curves and radial couplings have been calculated for electron capture from H by the ground and metastable excited states of Ne²⁺. The electron transfer can be accompanied by excitation of a core electron of Ne²⁺. Cross sections and rate coefficients have been estimated at collision energies of a few eV. The fastest rate coefficient for electron capture, 6*10^-11 cm³ s^-1, is that from the ¹D entrance channel. This rate is much too low to explain values inferred from observations of planetary nebulae.

Configuration interaction wavefunctions have been constructed for 26 target states of O III arising from the configurations (1s²)2s²2p², 2s2p³, 2p⁴, 2s²2p3s, 2s²2p3p and 2s²2p3d. The calculated threshold energies are in agreement within 5% (except for two states) with the experimental values. A good agreement (better than 10%) between the length and velocity formulations of the oscillator strengths is also found for most of the transitions though differences are quite striking for some of them. The oscillator strengths are tabulated and compared with the earlier results for the 59 optically allowed LS transitions. Calculations have also been done for collision strengths in the LS coupling scheme. These have been computed using the standard R-matrix program for L<or=12 and the no-exchange R-matrix program for L)12. Calculations have, however, been done at energies above the thresholds only.

A Breit-Pauli R-matrix calculation for the electron impact collision strengths of Fe²⁺ is reported involving transitions among the lowest 17 levels corresponding to the 3d⁶⁵D, ³H, ³P, ³F and ³G terms. Resonance structures are elucidated for the first time. The calculated collision strengths at impact energies above the resonance region show some disagreements with those from an earlier five-term R-matrix calculation of Garstang et al. (1978) for example the ⁵D-³H and ³H-³P collision strengths are a factor of three larger than in the earlier calculation. The present calculation also investigates the variation of collision strengths with energy; in particular, resonances are found to enhance the thermally averaged effective collision strengths by up to 40% for transitions among the fine-structure levels of the ⁵D ground state. Effective collision strengths for all transitions among the 17 levels are tabulated for electron temperatures 10000 K and 20000 K.

Differential cross sections are calculated for electron-H₂ collisions for scattering energies up to 20 eV. Elastic scattering and excitation from the ground, X ¹ Sigma _g⁺, to the lowest six excited electronic states, b³ Sigma _u⁺, a³ Sigma _g⁺, c³ Pi _u, B¹ Sigma _u⁺, E, F ¹ Sigma _g⁺ and C ¹ Pi _u, is explicitly considered for all total symmetries up to and including ² Phi _g for a single fixed H₂ geometry. The target states are represented using a full configuration interaction treatment within a basis of Slater-type orbitals optimized to give accurate vertical excitation energies. Results are presented for both resonant and non-resonant differential cross sections. Comparison is made with the available experimental and theoretical data. Excellent agreement is obtained for elastic differential cross sections; agreement for the inelastic differential cross sections is only moderate. Possible improvements to these calculations are discussed.

Absolute total cross sections for scattering of electrons by water molecules measured in the 4-20 eV incident energy range using a linear electron transmission device are presented. The results are compared with previous data.

The energy dependencies of the elastic scattering cross section and of the electron impact excitation of the three fundamental vibrational modes of CO₂ have been investigated in the energy region below 1 eV. The elastic scattering cross section shows a rapid increase with decreasing impact energy, and all three vibrational excitation functions show sharp threshold peaks. The onsets and the widths of these peaks are much sharper and narrower than previously reported. Comparison with theoretical models shows that the simple Born approximation does not adequately describe the excitation of the two infrared-active modes. The virtual state model in its present form also fails to reproduce excitation functions.

The n=2 excited state capture cross sections in e⁺-H₂ scattering have been calculated using the first Born approximation. The integrated and differential capture cross sections are predicted in the energy range 30-1000 eV. The total Ps formation cross sections ( sigma _T^Ps= sigma _rg^Ps+ Sigma _2s^Ps+ sigma _2p^Ps) are found to be in good agreement with the measured values in the energy range 50-150 eV.

The molecular R-matrix method has been used to perform ab initio positron-N₂ scattering calculations in the fixed-nuclei approximation. Various treatments of polarization and correlation effects have been studied, including the introduction of up to 22 polarized pseudostates. A model in which the N₂ comprised an SCF ground state and 10 excited pseudostates was adopted for 12 internuclear geometries ranging from 1.6 to 2.9 a₀. Vibrationally elastic and inelastic cross sections are obtained using the adiabatic nuclei approximation and a non-adiabatic model. Non-adiabatic effects are significant for the v=0 to 1 cross section (and dominate the small v=0 to 2 result). Some early calculations at the equilibrium geometry (R=2.068 a₀) have been corrected.