Table of contents

The theory of electron capture into the ground state from ground-state hydrogen atoms by high-energy incident protons is generalised to allow for relativistic effects arising from the high velocity of relative motion of the particles involved in the collision and from the use of Dirac wavefunctions for the atomic electron. The Oppenheimer-Brinkman-Kramers approximation is employed to obtain scattering amplitudes for capture without and with change of electron spin. Simple but accurate analytical expressions for the OBK capture cross sections are derived by expanding in powers of the fine-structure constant. At extremely high energies the capture cross sections are found to decay slowly as E_kin^-1, where E_kin is the kinetic energy of the incident proton, in accordance with the result previously obtained by Mittleman (1964).

Using single and cube perturbation theory, all the independent hyperpolarisabilities, quadrupole and field-gradient quadrupole polarisabilities of H₂⁺ are determined for internuclear separations from 0.2 to 10.0 Bohr. The results are considered to have converged to at least five significant figures. This is the first such molecular calculation of its kind and the first time the static higher polarisabilities of H₂⁺ have been determined.

Predissociation of the A"₂ state in NH₃ is investigated from ab initio UHF calculations of the relevant cross section of the potential energy surface. Emphasis is placed on dissociation products and the role of the Rydberg 3s orbital. The force constants, Rydberg ionisation limit, dissociation barrier and dissociation products are systematically calculated and comparison with experiment is made. A critical examination of a previous hypothesis concerning the predissociation is made and some new aspects are obtained.

An extensive variational-perturbation study of the second-order correlation energies of Mg and Ar is made to analyse the nature of various correlation effects. The variational-perturbation symmetry-adapted pair functions are taken in the form of partial-wave expansions. The results for the partial-wave energy increments, pair energies and total correlation energies are compared with related results. Special attention is paid to the M-intrashell and KM- and LM-intershell correlation effects. For the first time ab initio total correlation energies are obtained for atoms containing M-shell electrons. The results: E₂^Mg=-0.4279 and E₂^Ar=-0.7060 au agree very well with the estimates of the total correlation energies.

A theory for calculating energies and wavelengths using the Z-expansion technique is presented; it is suitable for degenerate autoionisation states of many-electron ions. The Hartree-Fock energy, correlation energy and relativistic corrections have been taken into account. To calculate the relativistic part the first non-zero term of the expansion in powers of Z alpha was considered, which, in fact, is described by the Breit Hamiltonian. Four-electron systems are considered as an example. Results of calculations of the wavelengths as well as the theory and numerical results for autoionisation rates and radiative transition probabilities will be given in future papers.

The influence of the following two calculational details on the internal conversion coefficients of gamma-rays and photoionisation cross sections in the framework of the Dirac-Slater atomic potential is discussed: (i) a different choice of the constant of proportionality C=1 or C=2/3 in the exchange term of the Dirac-Slater potential; (ii) the problem of considering the hole in the atomic shell where the conversion or the photoionisation process occurred. A comparison of various types of calculation give credence to the scheme in which the bound electron wavefunctions are calculated in the field of a neutral atom while those for the free electrons are calculated in the field of an ion with a hole in the shell where the conversion process occurred.

The author examines some simple models for multiphoton ionisation which can be constructed when the bound-free transition rates are much smaller than the bound-bound transition rates and considers how to proceed when this condition is relaxed. The author identifies a regime where the transition rate is time independent. If the laser has a sufficiently broad linewidth one can use a rate equation approach; this assertion is justified and applied to two-, three- and N-photon ionisation. If the laser is narrow-band, a density matrix method has to be used and the effects of different laser lineshapes are discussed. In three-photon ionisation the role of optical pumping effects is emphasised. Explicit expressions for the multiphoton ionisation probabilities are presented and finally some extensions of the method are briefly discussed.

The threshold behaviour of the multiphoton ionisation cross section is examined analytically for the ground-state hydrogen atom. The cross sections become independent of the electron momentum. Generalisation of the results is indicated.

Presents a study of the effect of an electric field on the electronic structure of diatomic molecular systems, using the variational method. Some new features which appear in the molecular Stark effect are shown with the help of simple examples. A near-degenerate perturbation scheme is proposed to complement, or replace, the conventional perturbation treatment for internuclear distances where the usual polarisability tensor is not a useful quantity.

The continuum-distorted wave method is used to calculate cross sections for electron capture by fast protons from the lithium atom and its related positive ions. With the exception of Li²⁺(1²S), each target electronic state is described by a Hartree-Fock wavefunction. For the lithium atom, capture can occur from either the K or L shell and the resulting ion can exist either in its ground state 1¹S or in one of the excited states 2¹S or 2³S; cross sections are tabulated for each of these states for capture into the hydrogen levels (nl). Results for the individual capture states (nl) are also reported for the Li⁺ target. Total capture cross sections are calculated for each target by means of the Oppenheimer n^-3 rule. For Li and Li⁺, total cross sections are also evaluated at E<200 keV. A procedure for determining the effective screening of the target nucleus by the uncaptured electrons is discussed and the sensitivity of the cross sections with respect to such screening is examined.

Results are obtained for intermediate coupling scaled collision strengths Z² Omega _IC for inner-shell excitation from the 1s²2s²S_1/2 ground level to all fine-structure levels of the 1s2s², 1s2s2p and 1s2p² configurations in highly charged Li-like ions. The approach used is a Coulomb-Born-exchange method that can be regarded as a perturbation theory approach in which the zeroth-order functions are composed of hydrogenic orbitals. It is shown that even with inclusion of intermediate coupling, configuration mixing and parentage mixing effects, the results can be expressed in a simple form. Illustrative numerical results for Z² Omega _IC are given for Li-like argon, iron and molybdenum ions.

There are a number of theoretical predictions that the characteristic X-radiation following electron impact ionisation is partially polarised and has a non-isotropic angular distribution. The angular distributions of L and K radiation of selenium following electron impact ionisation at bombarding energies of 600 and 300 keV, and that of the M, L_l, L_alpha , L_beta , L_gamma radiations of bismuth at bombarding energies of 100 and 300 keV have been measured. Within experimental error these radiations were found to be isotropic.

Distorted-wave cross sections are reported for the excitation of the B³ Pi _g, C³ Pi _u and E³ Sigma _g⁺ states of N₂ by low-energy electron impact. We use a discrete-basis-set method to obtain the electron-molecule continuum wavefunctions. Differential and integrated cross sections are presented from near threshold up to 50 eV electron impact energy. Comparison is made with available experimental data and with other calculations.