Table of contents

The electron impact excitation of Ca⁺ from the ground state to four terms of the autoionising configurations 3p⁵3d4s and 3p⁵4s² is calculated using the R-matrix method. Close to threshold electron capture ionisation is found to be important. Good agreement is obtained with the ionisation measurements of Peart and Dolder (1975) over a wide energy range.

A new integral equation for the Jost solution is derived. This integral equation requires the potential to be defined as a Laplace transform (i.e. V(r)= integral ₀^infinity U( alpha )e^{- alpha r}d alpha ). In contrast to the usual integral equation, the new equation does not suffer from divergence problems as k becomes complex. A simple numerical algorithm is proposed to solve this integral equation approximately. Restricting the study to s-wave scattering and to potentials defined as a sum of exponentials (i.e. V(r)= Sigma _nU_ne^{-n alpha 0r}) the proposed numerical algorithm becomes exact. For such potentials the author found an exact expression for the Jost function defined on the entire complex plane. The trajectories of the zeros of the Jost function (i.e. the poles of the S matrix) are investigated for a model potential with variable potential strength. A product representation of the Jost function.

The use of hyperspherical harmonics for describing the L=0 ground state of molecular systems is presented. Calculations on e₂⁺e^-, on He and on the hypothetical systems with particle masses ranging from m_e to 256 m_e show that the dispersion of the distance between the two heavy particles becomes less as the mass increases so indicating the origins of molecular structure. The usefulness, limitations and possible extension of the method of hyperspherical harmonics is discussed.

The Thomas-Fermi equations for heavy positive ions in the limit of extremely strong magnetic fields H is solved analytically by perturbation theory about the neutral atom solution. This is useful for an ion, with atomic number Z and N(<or=Z) electrons, with small ionisation number, i.e. when q (=1-N/Z) is small.

Radiative lifetimes of fifteen levels of Ca I have been measured using pulsed laser excitation and a single-photon counting technique. An influence of perturbing states on the lifetimes was observed in the 4sns ¹S₀ sequence at n=14 and in the 4snd ¹D₂ series around n=9.

The two-photon spectrum of a system with two transitions coupled by inelastic collisions is examined. This is of interest both as a method of determining inelastic collision rates at low pressures and as a model of more complicated redistribution effects. The mixing is considered to be a Markov random process and the one- and two-photon spectra are compared for various mixing rates. It is shown that line overlapping has an important influence on the spectra and that the interpretation in terms of simple population transfer is not always possible. The limits of the impact approximation for the collisions are also discussed.

The authors incorporate in the theory of collisional redistribution of resonance radiation the effect of a finite bandwidth of the intense incident radiation. The phase of the radiation is treated as a process with independent increments, which contains the phase-diffusion model as a special case. These phase fluctuations give rise to effective decay operators affecting the evolution of the density matrix and the regression of the correlation function. For a two-level atom suffering binary collisions the combined effect of collisions and phase fluctuations on the fluorescence spectrum is evaluated in several limiting cases of practical interest.

Two different ways of factorising the intra- and interchannel matrix elements are proposed and introduced in the resolution of Lippmann-Schwinger equations in photoemission. After developing the general formalism which allows the authors to determine directly the dipole matrix element and its phase in each channel. They have applied it to photoemission of xenon over quite a large energy range involving the coupling of as many as three ionised subshells (5p, 5s and 4d). The results relative to photoemission cross sections and corresponding angular distribution parameters are in good agreement with experiment. Dealing with xenon is a good test of the method which appears to be quite appropriate and suitable to treating photoemission of complex systems requiring the coupling of many channels, for instance the case of open-shell systems for which very little work has been achieved up to now.

The authors report experimental data on 'above-threshold' multiphoton ionisation of Xe via a three-photon resonance. The ratio of the five-photon ionisation probability to that for (5+1)-photon ionisation is interpreted in terms of the measured angular distributions for both processes and the 'energy conserving' continuum-continuum matrix elements. A calculation of these matrix elements on the basis of a model potential leads to a ratio of the (5+1)-photon signal over the five-photon signal in good agreement with the experimental value of about 3*10^-3 at an intensity of 10¹¹ W cm^-2.

The authors develop the WKB theory of multiphoton above-threshold ionisation, when the atomic electrons can absorb more photons than required for ionisation. The probability ratios for additional absorption of photons are analytically calculated in the frame of perturbation theory. Also the angular distributions of photoelectron yield are derived. The limits of perturbation theory for the value of radiation intensity strength are obtained. The analytic results agree well with the well known numerical calculations. But these theoretical results are in contrast with the latest experimental data.

Cross sections and the rate of photodissociation of the MgH molecule by the X² Sigma ⁺ to B'² Sigma ⁺ transition have been calculated for the conditions of the solar atmosphere. Photodissociation from all the vibrational levels v=0-7 of the ground X state have been considered and the rotational level has been taken as J=18, the most probable value at the solar temperature (5780K). The total cross sections have been obtained by summing over the partial cross sections for each ro-vibrational level of the ground state with an appropriate weighting factor. The calculations have been made over the whole range of wavelengths accessible to the X to B' transition. The photodissociation rate has been calculated from the total cross sections. The authors have obtained new features in the photodissociation cross sections of MgH which have not been found for simpler diatomic molecules or ions.

Probabilities for K vacancy exchange are calculated for near-symmetric collision systems by solving numerically two-state coupled equations. The calculations are based on analytic model matrix elements deduced from orthogonalised hydrogenic 1s orbitals. The matrix elements scale primarily with the screened nuclear charges of the collision partners. Energies for the molecular orbitals 1 sigma and 2 sigma are derived in good agreement with Hartree-Fock calculations. Probabilities for single passage of the transition region agree well with the Meyerhof-Demkov model of the K-vacancy sharing. Interference structures in the double passage probabilities are reproduced for the F⁸⁺+Ne system studied previously.

Theoretical results are given for the angular distribution of low-energy electrons scattered in collisions with He⁺ in which the 1s state is excited to the 2s state. The distribution was calculated using T matrices obtained from R-matrix calculations with three states 1s, 2s, 2p and also with six states 1s, 2s, 2p, 3s, 3p, 3d. In both approximations for low electron energies the differential cross section is largest for backward scattering with a maximum at approximately 90 degrees . This disagrees with early calculations of the differential cross section obtained using the distorted-wave approximation.

Electron collision strengths for the fine-structure transitions within the 1s²2s²2p²³P ground state of Ne V have been calculated using the R-matrix program. Configuration interaction wavefunctions have been employed in the calculations and computations have been made in a large energy region below 40 Ryd. All partial waves with L<or=9 have been included and the reactance matrices obtained in the LS coupling scheme from the R-matrix program have been transformed to pair coupling using the program JAJOM. The collision strengths obtained show a complex pattern of resonances in the entire threshold energy region and are given graphically for electron energies below 0.8 Ryd. The entire collision strength spectrum has been averaged over a Maxwellian distribution of electron velocities and the results so obtained for the effective collision strengths are tabulated for electron temperatures below 1*10⁶K.

The ejected-electron spectrum of thallium vapour has been observed at 75 degrees with respect to an incident electron beam of 15-500 eV kinetic energy. A total of 92 ejected-electron lines corresponding to autoionisation processes in Tl I are reported. Hartree-Fock calculations together with data from photoabsorption measurements have been used to assign the observed lines where possible.

To describe inelastic resonant electron-molecule collisions, two models have been established. These models have been shown to be exactly solvable (i.e. one can evaluate all physical characteristics of the processes by solving the three-term recurrence relation without any extra mathematical assumptions). The models treat all accessible channels (including the associative detachment and dissociative attachment) on the same basis and impose no restrictions on the intermediate state. As an example, the virtual intermediate state has been considered in connection with e^-+HCl collisions. The cross-sections of vibrational excitation and dissociative attachment processes have been computed and qualitative agreement with the available experimental data has been obtained.

An electron impact spectrometer has been used to observe proton (deuteron) production in H₂ (D₂) via autoionising states. This technique has enabled detection of autoionising states built on the lambda 2l core known as Q₂ states. The lowest Q₂ state ¹ Sigma _g⁺ has been detected in H₂ and appears to intersect the ² Sigma _u⁺ state of H₂⁺ near 31 eV. A second state, which would be the ¹ Pi _u state, was also detected. The potential curve of this state was obtained in the Franck-Condon region and information on the behaviour of its width over a large range of internuclear distances was obtained.