Table of contents

Shank's generalisation (1955) of Aitken's delta ² transformation is presented as a ratio of persymmetric determinants, and an algorithm for calculating these is given. The superiority of the generalised transformation over repeated delta ² transformations for summing perturbation series is shown.

A model for ion-atom collisions at intermediate energies is proposed in which the conventional close-coupled approach and the eikonal theory of Glauber are unified. The results are presented for direct H(1s) to H(2s) excitation by proton impact in a two-channel formalism. The conditions under which the model becomes applicable to electron-atom scattering are also examined.

Atomic excitation via rotational coupling between two quasimolecular orbitals formed in a slow ion-atom encounter is treated in a non-perturbative approach utilising the uniform Airy approximation. A closed-form expression for the differential excitation probability is presented and applied to a specific example.

Total cross sections for He²⁺ production from the combined processes of ionisation and charge transfer in H⁺-He⁺ collisions have been measured in the centre-of-mass energy range 40-386 keV. Results were obtained using the authors' previous experimental approach (see ibid., vol.10, p.1897 (1977)) but improvements to the apparatus and measuring procedure have provided data of greatly increased statistical accuracy in an extended energy range. At the higher impact energies the cross sections obtained show a significant departure from theoretical cross sections for ionisation based on the Born approximation.

A generalisation of the finite-element method is used to construct a series of highly efficient finite-basis-set methods for the solution of a one-dimensional Schrodinger equation in the continuum part of the eigenvalue spectrum. These methods are far more accurate than the standard R-matrix method and effectively eliminate the need for the correction procedures commonly applied to this earlier method. The poor convergence of the R-matrix method is found to be the result of an analogue of the Gibb's phenomenon of Fourier series expansions arising due to the inability of the basis functions to resolve the boundary conditions. It is shown how this problem can be removed by adding a few local basis functions which then allow the boundary conditions to be resolved at any energy.

The time-dependent first-order Bethe-Goldstone theory is defined by using the Hartree-Fock approximation in the Bethe-Goldstone equation with the external field fully coupled in. Starting from this equation and using the Gell-Mann and Low projection technique various amplitude equations are obtained. Finally an equation is obtained in differential form for the excited-state pair amplitude. This can be used to calculate transition moments between the ground and excited states of atomic or molecular systems which incorporate short-range correlation effects.

A model-potential Hamiltonian is proposed which reproduces spin-orbit splittings, intercombination effects and relativistic orbital reorganisations in the valence shell of heavy atoms. The model Hamiltonian is tested on atomic states with two valence electrons; full CI results are compared with experimental data and with relativistic all-electrons MC-SCF calculations. The 'relativistic model-potential approach' has been used for an investigation of ground and excited states of negative ions of the monovalent metal atoms.

A radiofrequency inductively coupled plasma discharge in argon has been employed as an excitation source for the study of the spectrum of atomic sulphur produced on introduction of low concentrations of sulphur dioxide into the discharge. Several previously unassigned lines in the observed spectrum have been attributed to transitions occurring in the SI atom from stable states above the ⁴S₃2/⁰ first ionisation limit.

The electron-photon delayed-coincidence technique has been used to measure the lifetimes of excited states in neutral and singly ionised natural zinc. These states, with their lifetimes, are Zn I: 5¹S (41.1+or-0.4) ns, 4¹D (21.1+or-0.4) ns, 6¹S (103+or-3) ns, 5¹D (89+or-4) ns; Zn II: 4p²P (3.2+or-0.2) ns.

A method is developed for calculating the multiphoton ionisation probabilities of atoms based on the use of the Green's function of the optical electron, obtained with the help of the model-potential method. The compound matrix elements of perturbation theory are presented in the form of rapidly convergent hypergeometric-type series, which are easily computed. The multiphoton ionisation probabilities of alkali metals, rare gases and mercury atoms are calculated in a wide range of frequencies. The results indicate sufficient accuracy and convenience of the method developed.

The behaviour of a rigid diatomic polar molecule in a strong uniform electric field is considered. Recurrence relations have been obtained which allow one to find asymptotic expansion coefficients for the energy and wavefunction in power series of sigma =(2/lambda )^1/2, lambda =2I mu E/h(cross)²>>1. Here I is the moment of inertia of the molecule, mu is its electric dipole moment and E is the electric field strength. These relations can be used for calculations on a computer. For some states the detailed calculations are carried out up to order sigma ¹⁶. Matrix elements of the dipole transitions are also obtained up to the same order. The results of the asymptotic calculations are compared with precise numerical data.

The probability amplitude V_lambda for the emission of an electron in a certain partial wave lambda with projection m onto the internuclear axis can be defined within the Born-Oppenheimer approximation. Formulae which relate these quantities to the experimentally measurable electron angular distribution in the laboratory frame are derived. Further it is shown that the quantities V_lambda can be derived from experimental angular distributions in a rather straightforward way once the complex interaction potential V*-¹/₂i Gamma between the colliding atoms is known. An 'internal' angular distribution is defined and its simple connection to the laboratory distribution is given.

A critical study of local optical models for elastic electron-atom scattering is presented. The partial-wave amplitudes arising from the exact second-order optical potential are calculated, for the case of scattering by hydrogen and helium at energies of less than or equal to 400 eV, and compared with the corresponding results of several local approximations. The correction to be expected from a third-order optical model is estimated.

For pt.I see ibid., vol.10, p.2639 (1977). Elastic scattering of electrons by atoms is considered in the approximation of using polarised atom states, which gives a system of coupled differential equations. Solutions for large r(r>r_N) are obtained using the method of the previous paper in this series. Solutions in the finite range 0<or=r<or=r_N are obtained on reducing the differential equations to linear algebraic equations and then using partitioned matrices to reduce the many-channel problem to an effective one-channel problem. The effects of target distortion are represented by a matrix operator nu (t,s) which is a discrete-ordinate approximation to an integral operator. Numerical results for e-H scattering show that nu is markedly non-local and has a variation with energy which is significant but not pronounced.

The method suggested by Crothers and McCarroll (see Proc. Phys. Soc., vol.86, p.753 (1965)) for the study of electron-impact excitation of neutral atoms has been used to calculate the differential and total excitation cross section in hydrogen and helium. Transitions from the ground state to ns, np and nd (n>or=3) in hydrogen and to m ¹P states (m=2 and 3) in helium have been considered. Highly accurate wavefunctions of Hartree-Fock type as well as approximate but simple wavefunctions due to Messmer have been employed respectively for the ground and excited states of helium. The results of the present calculations are compared with the other available theoretical and experimental results.

The differential cross sections for excitation of the ground state of helium to the 2³S, 2¹S 2³P and 2¹P states is calculated using the R-matrix method of Berrington et al. (see ibid., vol.8, p.1459 (1975)). Results are presented at electron scattering angles of 30, 60, 90 and 120 degrees from the excitation threshold up to about 22.4 eV. The calculations are compared with the absolute differential cross section measurements of Pichou et al. (see ibid., vol.9, p.933 (1976)).

The concentric-electron-beam device is operated in the steady-state mode as described previously by Hasted and Awad (see ibid., vol.5, p.1719 (1972)). Electron impact ionisation cross sections in the impact energy range 40-500 eV are reported for C⁺, C²⁺, O⁺ and O²⁺, the data conform to the empirical scaling formulae. Measurements on five previously measured cross sections have been repeated, and agreement is found. The hollow-electron-beam space-charge ion trap has been operated in a pulsed mode, and the rate at which the trap fills up with ions has been measured and analysed.

The relative abundance of protons formed by electron impact on H₂ has been measured as a function of the primary electron energy, the proton kinetic energy and the angle between the electron and proton beams. Apart from the known thresholds for direct dissociative ionisation three (averaged) threshold energies 23.5+or-0.7, 26.1+or-0.5 and 27.7+or-0.6 eV have been found for groups of protons with kinetic energies ranging from 0.75 to 3, 0.75 to 3.9 and 3 to 4.85 eV, respectively. The experimental data are interpreted in terms of H₂** autoionising states recently calculated by O'Malley (1969), Bottcher (1976) and Hazi (1975).

Dissociation of H₂ and D₂ by electron impact, leading to the emission of Balmer alpha and beta radiation, has been studied for electron energies up to 100 eV. Normalised excitation functions, their isotope ratio, and polarisation are reported. Care was taken to eliminate magnetic and electric fields, and to allow for molecular radiation near the Balmer lines. Compared with previous reported work the shape of the cross sections found is substantially the same, while showing an additional threshold near 43 eV, but the isotope ratios are markedly different at low energies while agreeing at higher energies. Complete polarisation measurements are reported for the first time.

The central structure of the Stark-broadened Balmer line H_beta has been analysed in the plasma produced behind the reflected shock in a combustion-driven shock tube of internal diameter 10 cm. The incident shock is propagated at a Mach number typically of M=8 in a mixture of 0.5% H₂(D₂), 80% Ne, 20% He (Ar) at an initial pressure of 10 Torr creating in the reflected-shock region temperatures close to 10⁴K and electron number densities 10¹⁶<N_e<10¹⁷. Measuring times are 150 mu s. The variation of centre dip with reduced mass which has now been measured in two widely differing plasma sources strongly suggests that the discrepancy between theory and experiment for the central structure of H_beta is due to ion dynamical effects.