Table of contents

From the viewpoint of the generator-coordinate method, the authors propose the dilation analytic electronic Hamiltonian which enables one to calculate potential surfaces of molecular electronic resonance states in the adiabatic framework.

For pt.I see ibid., vol.13, no.17, p.L511 (1980). Focusing on a stationarity condition, a practical way is proposed which allows one to calculate potential surfaces of electronic resonance states in a molecule.

The formation of quasi-Landau resonances in the Zeeman effect of absorption spectra across the ionisation threshold is shown to involve a previously unsuspected coupling of diverging and converging eigenmodes of electron propagation across magnetic field lines. The strength of this coupling will control the resonance intensities in analogous processes.

The hyperspherical coordinate method developed by Macek, Fano, Lin and Klar (1968 to 1978) to describe two-electron correlations is used for the first time to treat an atomic photoionisation process. Using adiabatic approximations for both the initial and the final state, the cross section for the process He+y to He⁺1s+e^- is calculated and is found to lie 1% higher than the revised experimental data of Samson (1976) at threshold, 4% lower at 1 Ryd above threshold, and 12% lower at 1.9 Ryd above threshold.

Photon emission from excited NE II and Xe II states produced by single electron capture collisions of Ne²⁺ with Xe was investigated by means of absolute and polarisation-free VUV spectroscopy. The excitation cross sections derived from these measurements are of similar magnitude as the respective cross sections for transfer ionisation which have been obtained to a good approximation from already known cross sections for production of slow electrons. When adding up the cross sections for both types of electron capture reactions, close agreement with the well established total single electron capture cross sections is found over the investigated impact energy range from 15 to 50 keV.

The authors have analysed the effect of polarisation on the bremsstrahlung cross section of low-energy electrons on neutral atoms. They have found a new effect on the intensity of the emitted light in the form of a maximum at a non-zero photon energy for electron energies close to the minima in the elastic cross section.

The authors have calculated the collision strength for the transition 3s²¹S to 3s3p ³P⁰ in Si III using the R-matrix method. Elaborate configuration wavefunctions are used to represent the twelve lowest target states which are included in the expansion of the total wavefunction. Reaction rates are calculated in the temperature range 5000-250000K. Resonance structure considerably increases the rate coefficients compared with other work where these effects are omitted.

Perturbation methods used in the calculation of relativistic energies of atoms have been studied and it is found that the role of certain parameters in the perturbation expressions has been misunderstood by previous authors. The relationships between perturbation expansions corresponding to different approximations obtained by splitting the total Hamiltonian in different ways, are clarified.

The time reversal symmetry of an N-electron Hamiltonian is imposed on the corresponding Hartree-Fock operator. This is ensured by a Slater determinant whose one-electron functions occur in Kramers degenerate pairs. For most point groups, the independent Kramers components are determined by a Hartree-Fock matrix of half the original dimension.

Techniques for calculating improved ( delta (r₁)) values with approximate wavefunctions described in a previous paper (Trivedi, 1980) introduced a free parameter which was then chosen arbitrarily. The author prescribes a way of choosing this parameter. Improved values of ( delta (r₁)) are reported for the helium isoelectronic sequence using Hartree-Fock quality wavefunctions.

Over 400 new identifications of emission lines in the grazing-incidence spectra of the elements from chromium to nickel are reported. The great majority of these lines belong to the 2sⁿ2p^k-2s^n-12p^k+1 transition arrays in the O I to Be I isoelectronic sequences. Some of the spectra belonging to the N I, C I, B I and Be I sequences are identified as intercombination lines. The new data, taken together with other published results in the F I to Li I isoelectronic sequences, allow a complete listing of 2sⁿ2p^k-2s^n-12p^k+1 transitions in the elements from chromium to nickel, with their appropriate term schemes. The term schemes lead to wavelength predictions for various forbidden transitions. The use of these allowed and forbidden transitions has been proposed by other authors for diagnostic purposes in solar-flare and laboratory plasmas. In addition to the n=2-2 transitions the wavelengths of some Na I-like ions of the elements Cr to Ni are presented. The plasma source used to obtain the spectra and to differentiate between the emission from separate ionisation stages was created by focusing the output of a 40 GW neodymium glass laser system onto plane metallic targets.

A relativistic calculation of the energies of the ground state and lowest energy excited states of hydrogen in a strong magnetic field is carried out in a way which takes account of the motion and spin of the proton. It is shown that in the adiabatic approximation the relativistic effects are almost negligible for all reasonable values of B.

A statistical scattering theory approach to the angular distribution and polarisation of inelastically scattered electromagnetic radiation is presented. The authors' theory, which is also applicable to fluorescence, accounts for the influence of the orientation of the target atoms on the radiation pattern of the scattered photons. Their analysis is based on a relativistic generalisation of Placzek's scattering tensor formalism (1934) and on the multipole expansion of the photon-electron interaction. The state of the incoming photons is described by a density matrix and the orientation by statistical tensors. As a result the differential cross section is expressed as a weighted sum of geometrical scattering factors which describe the directions and polarisations of the incoming and scattered radiation. The weight factors are statistical expectation values of dynamical scattering tensors with respect to the oriented initial atomic states. The non-relativistic dipole approximation is considered in detail for weak and strong orientating fields. Illustrative examples of the radiation pattern of K X-ray Raman resonance scattering from oriented systems are given and possible implications of the authors' work with regard to future experiments are pointed out.

An attempt has been undertaken to justify mathematically the r-centroid method in the intensity theory of diatomic molecules. The necessary integrals have been estimated by the steepest descent method in the complex plane. It has been proved that the r-centroid approximation has a quasi-classical nature. It has been shown that the dependence of the electronic transition moment found by the r-centroid method may be interpreted as the dependence of the electronic transition moment in diatomic molecules on the real internuclear separation.

The B-X and C-X transitions of SiF have been analysed for nu ' values up to 6 and 5 respectively. More precise equilibrium constants are given for the X, B and C electronic states.

The emission spectrum of vanadium monofluoride has been photographed in the region 3440-3660 AA at a reciprocal dispersion of 0.6 AA mm^-1. Although the spectrum is extremely complex, a tentative vibrational analysis is reported in which the bands are assigned to two violet degraded and two red degraded band systems, all of which appear to have a common lower state. It is suggested by comparison with similar molecules that this is the ground state X ⁵ Pi arising from the electronic configuration sigma delta ² pi . The vibrational constants for this state are calculated as omega _e=571.4 cm^-1 and omega _ex_e=3.8 cm^-1.

The long-range interaction energies of H-Ps, Ps-He and Ps-Ps are calculated using the Hylleraas variational method. Implications for low-energy H-Ps and Ps-He scattering theory are discussed.

Differential cross sections for Li(2p) excitation in low-energy (1000 eV) Li-inert-gas collisions have been determined from photon-scattered-atom coincidence measurements; reduced angles tau up to 18 keV deg were studied. The following conclusions are drawn from the data and are illustrated by model calculations with the coupled-state impact parameter method: for Li-Ne, Ar, Kr, and Xe the excitation process is due to non-adiabatic transitions at internuclear distances where the two closed shells of Li⁺ and the inert-gas atom overlap (1.1, 1.6, 1.76 and 2.2 au respectively); for Li-He, Li(2p) excitation is mainly due to direct, non-localised transitions between the molecular states formed from Li(2s) and Li(2p)-He at distances as large as 2 au.

A new technique for the evaluation of the exchange amplitude for the process H⁺+H(1s) to H(nlm)+H⁺ in the Born approximation taking the full interaction into consideration has been presented. This technique is also applied to two other first-order approximations which aim at an improvement over the Born approximation by taking account of the lack of orthogonality of the initial- and final-state wavefunctions. It is found that, over a wide range of incident proton energies, the cross sections for electron capture into different angular momentum states of an excited state having a moderate or high value of the principal quantum number are related to the respective asymptotic cross sections by a simple scaling law. The results in the various approximations discussed have been compared with experimental data.

The continuum distorted-wave approximation of Cheshire (1964) is applied to the case in which a nucleus of charge Z' captures an electron attached to another nucleus of charge Z. Numerical results for the total capture cross sections have been obtained for the particular cases of electron capture from the targets He⁺, Li²⁺, Be³⁺ and C⁵⁺ by protons into the ground state or the excited 2s state. Capture by alpha particles from He⁺, Li²⁺ and Be³⁺ into the ground state or the excited 2s state are also considered. Wherever possible comparisons are made with the Coulomb-Born results.

The process of two-electron transfer in slow ion-atom collisions is considered. The two-electron exchange interaction which determines the probability and the cross section of the process is calculated in closed analytical form by using the asymptotic Landau-Herring method. Cross sections for the reactions He²⁺+He to He+He²⁺ and C⁴⁺+He to C²⁺+He²⁺ are calculated and compared with the experimental data and the results of other theoretical calculations.

A method has been suggested for the numerical integration of electron-hydrogen ionisation amplitudes in the Born approximation, where the two outgoing electrons are described as the product of two Coulomb waves. Different sets of the effective charges of the scattered and ejected electrons have been considered. The expression for the amplitude has been reduced to a one-dimensional integral in real space and the results are compared with the other theoretical and experimental findings.

Experimentally determined electron drift velocities are fitted directly with a three-parameter modified effective range theory (MERT) representation of the S-wave phaseshift together with fixed values of the much smaller P- and D-wave phaseshifts calculated from the MERT formulae representing the phaseshifts derived from other sources. The result is an improved value of the e-Ne scattering length of (0.214+or-0.005) a₀, and phaseshifts from zero to above 2 eV. Comparisons are made with other phaseshifts and momentum-transfer, total and differential cross sections.

Electron-collision induced orientation in Na has been measured for the 3²P to 3²S transition, the excited Na(3²P) being prepared by laser optical pumping. Incident electron energies have been 3, 10 and 20 eV at electron scattering angles theta _col from 0 to 22.5 degrees . The experiment agrees well with close-coupling theory especially for 3 eV, while distorted-wave calculations need some improvement at low energies. The sign of the orientation is found to be positive indicating an attractive force. Interesting conclusions can be drawn for the phase parameter phi connecting scattering amplitudes to different magnetic substates.

Total cross sections for electron scattering by H₂ are obtained for impact energies ranging from 25 to 750 eV. The method used is a linearisation of the Ramsauer-type experiment, which enables good angular and energy resolution; the accuracy obtained in the total cross sections is better than 4%. The authors compare their results with existing experimental data of other groups in this energy range. By means of analysis of theories and experiments on total cross sections for elastic scattering, excitation and ionisation the authors evaluate a set of semi-empirical total cross sections from 20 up to 2000 eV impact energy, which are accurate to about 5% over most of this energy interval. In the overlapping range the authors find excellent agreement of the data obtained thus with our experimental results.

The total differential cross section for scattering into all final states of a strongly polar molecule initially in state j, m by a low-energy electron (<or approximately=10 eV) has been calculated using the Glauber (1959) approximation and the point dipole potential. Such cross sections may vary by a factor of three as the azimuthal scattering angle is changed for small polar scattering angles ( psi <10 degrees ), and by up to 50% at larger angles. Detailed results are presented for the j=1, m=0 and j=3, m=1 initial states of KI at 6.74 eV. For small polar scattering angles the Born approximation is satisfactory, while the behaviour at large angles can be understood using classical perturbation theory with quantal interference.