Table of contents

The author examines the first-order in overlap approximation to the Adams-Gilbert equation derived previously by Kunz (1969). It is shown that this approximation is far more general than previously assumed and is an exact member of the family of local orbitals equation derived by Gilbert (1964). The relationship of this result to the method proposed by Anderson (1968) is discussed, and a class of situation is found where the present formalism may be preferable. Approximations to the present case are discussed and illustrated with a simple calculation for the He₂ molecule.

Perturbation theory is used to calculate the terms of order Z³ and Z² in the expansion of the spin density matrix element for the ns²S states of lithium and its isoelectronic ions. Use is made of the screening approximation and some accurate calculations on lithium to obtain an expression for the spin density for any Z and n.

The generalized phase shift theory previously discussed by the author (1971) has applied to the Stark broadening of the 2P-1S line in hydrogen. Complete allowance is made for both electron and proton dynamics. The results differ somewhat from those obtained by Smith et al. (1969) using another unified theory. The scanty experimental data does not make it possible to choose between the theories.

The cross section profile of the 3s3p ¹P₁ two-electron excitation has been measured in He I. The cross section was assumed to have the form sigma (E)=C(E)+((E-E₀)1/2 Gamma a+(1/2 Gamma )²b)/((E-E₀)²+(1/2 Gamma )²) where the adjustable parameters a, b, 1/2 Gamma and E₀ were determined by a least squares fitting process. The parameter values obtained in the equipment were: a=0.86+or-0.16 cm^-1, b=0.27+or-0.13 cm^-1, 1/2 Gamma =65.9+or-7.0 meV, E₀=69.919+or-0.007 eV. The Fano parameters q and sigma _a were determined from a and b and had the values 1.36+or-0.20 and 0.32+or-0.08 cm^-1 respectively.

Studies have been made of autoionizing transitions in N₂ with excitation by low energy electron impact. Electron ejection is observed from states of the neutral molecule in the continuum region 16-19 eV giving levels of the x ² Sigma _g⁺ state of N₂⁺. Measurements are made of autoionizing states which had previously been detected using photon and high energy electron excitation. In addition new levels are observed which appear to be favoured by low energy electron excitation.

The effects of rotational transitions have been observed in the resonant excitation of N₂ by electrons at an incident energy of about 2 eV. The angular dependences give good agreement with calculations which were based on the assumption that the resonance has a symmetry ² Pi _g.

The '2nd negative' spectrum emitted by the C² Sigma _u⁺ state of N₂⁺ in an electron beam experiment is analysed for different nitrogen isotopes. It is found that in ²⁹N₂ and ³⁰N₂ the vibrational levels v'=3 to v'=7 predissociate about six respectively ten times more slowly than in ²⁸N₂.

The odd-even isotope shift in the lambda =6096 AA and lambda =6074 AA lines of Ne I has been remeasured by conventional high-resolution optical spectroscopy; in contradiction with a recently published value, the shift has been found in good agreement with the mass-shift formula. In addition, the hyperfine structure coupling constants of the 1s₄ and 2p₄ levels of Ne I have been obtained.

Stimulated anti-Stokes emission at 457.6 nm accompanying the transition from the ³D₂ metastable to the ¹S₀ ground state in barium has been observed when the output of a dye laser is tuned close to the intercombination line at 791.1 nm. The emission is interpreted as parametric four-wave coupling. Scattering at other frequencies is also observed and the possibility of using this process to produce tunable ultraviolet light is briefly discussed.

An alternative method is described for calculating the eigenvalues of the primary ion radial variation equation in the theory of the flowing afterglow. This method does not involve the approximations inherent in the usual variational approach, and as a result certain limitations on the theory and thus on the experimental procedure, have been found.

Applying a space translation operation, the Schrodinger equation for an atom in an electromagnetic field is solved with sufficient accuracy to obtain probabilities for multiple absorption of photons from a monochromatic laser beam of arbitrary intensity or frequency. It is shown that the derived expression for the N-photon T-matrix contains the usual single photon matrix elements given by the perturbation theory and that the perturbative result is obtained in the limit of low intensity. Other explicit examples are considered. The conditions of applicability of the method are specified.

The ratio of circular to linear polarization cross sections for multiphoton ionization of hydrogen by intense electromagnetic fields is obtained. A cross over in dominance is seen to occur at large photon number; but this is offset by the cross section then being many order of magnitude smaller than that for the dominant process.

A two dimensional semiclassical approximation is used to examine the sigma polarization spectrum of a hydrogen like atom in a strong magnetic field. Resonances above the zero field ionization limit are found and their energy separations are computed over the region from the ionization limit to 40 h(cross) omega _c above, where omega _c is the cyclotron frequency, for magnetic fields of 10, 17, 25, 32, 40 and 47 kG. At the ionization limit the separation between resonances is found to be 1.500 h(cross) omega _c, independent of magnetic field strength, which is in agreement with a separation of 1.5 h(cross) omega _c observed experimentally by Garton and Tomkins (1969) in the sigma polarization spectrum of barium in a magnetic field of 24 kG. The energy separations are found to decrease above the ionization limit toward the value h(cross) omega _c, which is characteristic of the levels of a free electron in a homogeneous magnetic field.

Second-order hyperfine interactions are considered for a one-electron atom, treating the nucleus as a point magnetic dipole of infinite mass and charge Z. The dominant contribution to the hyperfine splittings in the 1s and 2s states is found to arise from the ultra- relativistic continuum. In the high momentum limit the Schrodinger calculation gives a linear divergence while the Dirac and QED calculations give a logarithmic divergence. This explains why the non-relativistic variational result of gregson et al. (1970) is too large by a factor of 10². The Dirac result is ⁸/₉ of the QED result, (⁹/₄)( alpha / pi )( mu m/M)ln( rho _max), because of a missing retardation term. The Schrodinger and Dirac residuals are in good agreement.

A new general method is described for obtaining SCF orbitals for electronic systems without restrictions of the symmetry of the open shells. With a Green's function method an optimal SCF operator is constructed for each state of a given configuration. The unperturbed one-particle Green's function is optimal with this operator and permits a quasiparticle interpretation. The SCF equations are derived in matrix formulation convenient for numerical applications within a limited basis set. It is shown that the SCF orbitals thus obtained satisfy the necessary conditions for the energy to be stationary. An application of the SCF method is given for the three lowest S states of the helium atom.

Solutions of coupled equations for electron-atom collision theory, having known asymptotic forms, can be calculated using asymptotic expansions at some large values of r, say r=r_p and r_p+1. At some smaller values of r, say r=r₁ and r₂, it is required to match the asymptotic solutions to solutions which are bounded at the origin. When some channels are closed, inwards integrations from (r_p,r_p+1) to (r₁,r₂) can give solutions which have poor linear independence at (r₁,r₂). It is shown that good linear independence can be obtained using a Fox-Goodwin technique for the solution of two-point boundary value problems.

The Eikonal distorted wave theory is applied to the inelastic scattering of electrons and protons by atoms at intermediate energies. Absorption effects are explicitly taken into account in the optical potentials describing elastic scattering in the initial and final channels. Detailed numerical calculations are performed for the excitation of the n=2 states of atomic hydrogen.

In the classical binary encounter approximation the period during which the field of the projectile nucleus acts on the electron, while that of the target nucleus does not, is infinite. A modification is introduced making this period finite. It leads to satisfactory results for capture in high energy H⁺-H(1s) collisions and it also leads to satisfactory results for ionization (particularly if allowance is made for the change in the potential energy of the electron in the field of the target nucleus caused by the transient interaction with the projectile nucleus). The classical binary encounter approximation fails in first order, to account for capture. Its success in the case of ionization is partly due to cancellation of errors from two unrelated sources.

The photoionization cross section of magnesium was calculated from 0 to approximately 4 eV (0.15 au) above the first ionization threshold in both the dipole-length and dipole-velocity formulations. The method of configuration interaction was used with explicit inclusion of autoionizing and continuum configurations. As expected, the cross section is dominated by autoionization from the 3pns and 3pnd series. The widths of the 3pns lines are on the order of a few tenths of an eV or less, which is about one-half their separation. The widths of the 3pnd lines are on the order of one hundred times less than those of the 3pns series. The positions of the autoionizing levels as determined from the phase shift, agree extremely well with close-coupling calculations and quite well with experimental results. The overall shape of the cross section as determined in the dipole-velocity formulation compares favourably with experiment. The energies of the 3sns(¹S), n=3 to 9, series were found from the eigenvalues of the 47 configuration ground state used and agree with other theoretical work and experiment. Also, the energies and multiplet strengths of the 3snp(¹P), n=3 to 6, series were calculated.

The ionization of a gas molecule has been experimentally studied by measurement of both the electron-molecule ionization cross section in an electron beam, Q_i, and the electron ionization coefficient of an electron swarm, alpha /N. The results are presented for both hydrogen and deuterium and a comparison of the theoretical values of alpha /N, calculated from the present values of Q_i using various electron energy distribution functions, F( epsilon ), with the present experimental values of alpha /N in hydrogen, indicates which form of F( epsilon ) is most probable in this gas.

The impact parameter method is used to investigate the excitation of the (2p⁵3s)¹P of Ne in He⁺Ne collision. It is assumed that excitation occurs mainly by a transition from the B² Sigma state to the excited C² Sigma state in the vicinity of the pseudo crossing of their respective potential energy curves. The potential parameters of Sidis and Lefebvre-Brion (1971) are adopted. The calculations which have been made at impact energies 0.7 keV and 1.58 keV are in very good agreement for tau <3 keV deg with the experimental results of Baudon et al. (1970). Limitations of the methods used are discussed.

In analysing the elastic small angle scattering of ions at atoms in the high energy region it is advantageous to separate the repulsive and the attractive terms of the interaction potential. Both terms dominate the scattering in different ranges of the scattering angle. The repulsive potential leads to undulations in the cross section which are found in the range of approximately=10^-4 to approximately=10^-3 rad for systems of ⁷Li⁺ ions and rare gas atoms at energies about 30 keV. The undulations are caused by the diffraction of the matter waves at the atoms. With this knowledge a simple characteristic correlation between the positions of the undulation extrema and the parameters of the repulsive potential can be given. The undulation effect can be used for determining the repulsive potential term. The influence of the attractive forces between ions and atoms on the small angle scattering is studied for two different attenuated polarization potentials. The calculations show that this potential term has its main influence in the region below the undulation extrema. If the depth of the potential minimum is sufficiently large, the first minimum of the fast oscillations becomes measurable.

An experiment is described in which large numbers ( approximately 10¹⁶) of calcium atoms are placed in the 4s4p ³P metastable level by optical pumping with a tunable dye laser and then studied spectroscopically. Equations governing the degree of excitation by the laser are derived. Predictions of the theory are shown to be in good agreement with experimental results. In particular, at low optical depths produced by 10¹⁵ ground state atoms cm^-2 the dye laser raises approximately 50% of the calcium atoms into the metastable state. At higher optical depths associated with 10¹⁷ ground state atoms cm^-2 the number of excited states is limited only by the laser energy and line width. For the dye laser used the largest number of metastables produced was approximately 10¹⁶. The absorption spectra of the 4s4p ²P level is seen out to 4s4p ³P to 4s22d ³D. The relaxation rate between the excited state fine structure is studied directly with an optically delayed dye laser continuum. Other applications of this technique of producing large numbers of excited states are briefly discussed.

Weak lines have been found close to positions indicated by theory for the 2s ¹S₀-2p ¹P₁ transition of N VI at 2896.4 AA and for O VII at 2450.0 AA; the 2s ³S₁-2p ³P_2,1,0 lines were identified at substantially the same wavelengths as published by others. The experimental results and theoretical work are applied to an evaluation of the ground term of C V and absolute terms of N VI and O VII.

Results are reported of measurements of excitation rate coefficients for the following transitions in Ne VIII: 2S-2P, 2S-3S, 2S-3P and 2P-3D. The first three were measured by a method similar to that used by Boland et al (1970) but for a plasma of higher density (n_e approximately 10¹⁶ cm^-3). The last was measured by a new method that has allowed a significant improvement in the quoted accuracy of the result: +or-35% as compared with 'a factor 2' quoted for example by Kunze and Johnston (1971). All the experimental results lie within the total uncertainty when compared with the theoretical values due to Bely and Petrini (1970).

The motion of gaseous ions in arbitrarily strong electrostatic fields has been studied by Monte-Carlo simulation techniques, assuming various forms of the ion-neutral interaction law. Approximate expressions for the mobility and the mean square velocity suggested by Wannier (1953) were in most cases found to predict the correct values within 20%. The lateral diffusion coefficient to mobility ratio D_{perpendicular to} / mu was in all cases studied found to be remarkably accurately connected to the mean square velocity normal to the electric field through a generalized Nernst-Townsend relation. The longitudinal diffusion coefficient D/sub /// does not, on the other hand, seem to be simply related in any way to the mean square random velocity in the field direction, except near thermal energies. For hard sphere interaction and non-vanishing fields the lateral diffusion coefficient is always larger than the longitudinal one.

The line width of carbonyl sulphide (OCS) methyl cyanide (CH₃CN) and formaldehyde (HCHO) molecules have been measured at room temperature by using a double modulation microwave spectrometer. Twenty cases of self-broadening and foreign gas broadening have been studied. The experimental results have been compared with the calculated results using impact theory of Anderson (1955) and collision broadening theory of Murphy and Boggs (1967-8). The experimental results are in good agreement with the theoretical values of line width parameter for linear molecules. In case of symmetric molecules the theoretical results are higher than the experimentally observed results. The quadrupole moments of OCS, CO₂ and N₂ are obtained from these measurements. The observed results agree better with Murphy and Boggs theory than with Anderson's theory.

The visible bands of SbF molecule have been photographed in a high frequency discharge at a dispersion of 7.5 AA/mm in the first order of a plane grating spectrograph. A new band system in the region lambda lambda 4730-5770 AA belonging to this molecule has been analysed and the vibrational constants are determined. The electronic transition which can be assigned to this new system is discussed.