Table of contents

The partial photoionization cross sections and the angular distribution asymmetry parameter for photoelectrons ejected from helium in the transitions to the n=2 states of the He⁺ ion are calculated for incident photon energies from just above the threshold to 160.6 eV. Good agreement is obtained with experiment.

Double differential cross sections d² sigma /dKdq, for the ionization of hydrogen by electron impact have been computed in the Glauber approximation. The Glauber cross section for large momentum transfer differs from the simpler coulomb-Born results.

Changes in the fluorescence yield of the copper L shell due to multiple M shell ionization are considered. The results are found to be very different to previously published results on the argon L shell. In particular the copper L shell fluorescence yield is essentially constant (varies less than 10%) for as many as six M shell vacancies. Reasons for the different characteristics of argon and copper are discussed.

Experimental and theoretical determinations of the cross section for proton production in e-H₂⁺ collisions are surveyed. The reliability of the various experimental data are discussed as well as the extent to which theory and experiment are in agreement.

Fine structure effects and the rotation of the internuclear axis have to be taken into account in an atom-atom collision treatment, especially at high temperatures. An application is made to pressure broadening effects.

When the variational procedure of the SCF-LCAO-MO approximation for a closed shell ground state is modified so as to include as constraint the expectation value of an operator of the form M= Sigma M_i+ Sigma Sigma M_ij, the result is a set of modified SCF-LCAO-MO equations. A perturbation approach for solving these constrained orbital equations is developed. The perturbation treatment is carried out to third order in the perturbation parameter. The determination of the orbitals involves solving a set of coupled, linear equations, within each order of the perturbation approximation. No iterative procedure is involved. Perturbation formulae are derived for the constrained orbital energies and for the total, constrained energy.

For pt. I see ibid. vol. 5, 721, 1972. The perturbation procedure for solving constrained SCF-LCAO-MO equations is applied to a calculation on the ground state of the N₂ molecule. As a starting point for the calculation the LCAO-MO wavefunction of Scherr is taken. This wavefunction is then constrained to satisfy the molecular virial theorem. The perturbation treatment is carried out through third order in the perturbation parameter. Convergence of the perturbation series is checked and found to be very satisfactory. The effect of constraining on the values of various molecular properties is examined. On the basis of this examination it is believed that the constrained wavefunction represents a better approximation to the true charge distribution in the region near the nuclei than does the unconstrained function, but a less good approximation in the region farther out. The sacrifice in energy on constrained is less than 0.01% and is negligible compared with the correlation energy.

It is shown under rather general conditions that variational wavefunctions satisfy an adiabatic theorem.

An independent particle model of an atom regards the core of filled shells as spherically symmetric, thus neglecting the positive holes induced in the core by the valence electrons. Taking the core- valence interaction as a perturbation, the author obtains formulae for corrections to optical oscillator strengths and single-triplet splittings of atoms with two valence electrons. Neglecting valence-valence correlations, he presents approximate calculations for the core polarization corrections to the lowest (ns)² to (ns)(np) oscillator strengths and the singlet-triplet splittings of the lowest (ns)(np) configurations of Be, Mg, Ca, Sr and Ba. The core polarization corrections are found to improve significantly agreement between theory and experiment for the larger atoms, namely Ca, Sr and Ba.

A semiempirical calculation of single bond energies and dipole moments of diatomic molecules is presented using an empirical form for the two electron repulsion integral. Assuming, in addition, a form for the resonance integral, the bond stretching force constants are also evaluated.

Accurate numerical Hartree-Fock (HF) self-consistent-field (SCF) wavefunctions are calculated for Pb⁴⁺((Xe)4f¹⁴5d¹⁰). The results represent the only wavefunctions available for this ion. Values of several Hartree-Fock parameters have also been obtained using these wavefunctions.

The complete orbit-orbit interaction, including the intra- and inter-shell contributions, has been evaluated for the ground state of all singly ionized positive ions, neutral atoms, and negative ions from He to Kr, using analytical Hartree-Fock functions.

In the Hartree-Fock-Roothaan (HFR) formulation for molecules of the form XH_N, molecular orbitals (MO) may be written as a one centre expansion (OCE) or as a poly centre expansion (PCE). The isoelectronic molecules CH₄ and HF represent opposite extremes for the application of the OCE representation. For CH₄ and HF, a series of PCE and OCE wavefunctions already exist. Consequently, it is possible to carry out a comparative analysis and merit assessment between the two forms of MO representation. The authors determined electron density rho (r) contour maps, profile diagrams, radial density distributions and (rⁿ). For each molecule, a term by term comparison was made within harmonic expansion of rho (r). Multipole moments and the coherent X-ray scattering factor were also evaluated. As the basis sets were extended the changes in the properties were examined.

Two similar theories of dissociative attachment have recently been criticized for giving an incomplete treatment of a crossing of the potential curves of a negative ion and a neutral molecule. (At such a crossing, an electronic resonance moves past an excitation threshold.) In particular, some authors have suggested that non- adiabatic effects are crucial at such a crossing. A crossing is analysed in a model sufficiently simple for the energy curves to be calculated. It is shown that non-adiabatic effects are not important in the model, and that the curve crossing has no connection with the Landau-Zener problem. The conclusion is that no modification of the original theories is needed to meet the criticisms.

Wavefunctions are calculated for helium-like atomic systems, taking fully into account the 'correlation' term of the hamiltonian. They are in a form which is easily separable into a sum of products of one-electron functions.

Analytic methods are used to evaluate certain integrals which occur in the determination of cross sections for electron impact ionization. A considerable increase in both speed and accuracy is obtained over the more usual numerical methods.

In calculating the elastic scattering of slow electrons by heavy atoms like mercury, there are the complicating effects of relativity, electron exchange, virtual transitions and correlations, and the first two have already been considered in detail by other workers. In this paper the effect of virtual transitions alone is considered, to see whether the use of either a polarization potential or the channel coupling method provides a satisfactory treatment. It appears that these methods overestimate the effects at low energies and that more sophisticated methods, which are available but which require very lengthy calculations, are necessary to improve the existing calculations for mercury.

A theoretical assessment of the beam foil measurements of Berry et al (see abstr. A39568 of 1971) is made. It is concluded that the line at 293.8 AA is not due to the (23sp^-)¹P-2¹S transition. Alternative identifications of some of the experimentally observed lines are proposed.

The role played by large scattering angle, high momentum-transfer collisions in the Boltzmann collision integral is discussed. In particular, the Lorentz plasma and the single component plasma are considered. It is found that the Fokker-Planck equation, which excludes collisions involving large scattering angles, is adequate for furnishing transport coefficients, but does not provide a completely accurate representation of the anisotropic part of the distribution function.

Argon at approximately atmospheric pressure is 'seeded' with small amounts of potassium vapour and heated to about 1300 K in a specially designed furnace. The DC conductivity of the thermally produced plasma is measured by means of two electrodes whose separation is variable and one of which is equipped with a guard ring. By measuring the DC conductivity of the plasma over a wide range of potassium pressures, the cross sections for momentum transfer of argon and potassium have been measured much more accurately than hitherto.

For Pt. I see abstr. A3144 of 1972. Cross sections for the dissociative excitation of H₂⁺ by electrons have been measured for interaction energies between 25.4 and 715 eV. A source was used which produced H₂⁺ ions under clearly defined conditions. Over the whole energy range, the measurements agree very closely with values obtained by averaging the theoretical cross sections of Peek in 1967 and Peek and Green in 1969 over a vibrational population given by Franck-Condon factors between hydrogen and H₂⁺.

Measurements of temperature in laser pulse induced gas breakdown are described. Data are presented for breakdown in air and helium at atmospheric pressure and above by ruby laser pulses up to 200 MW. Temperatures in the range 35 eV to 55 eV were obtained. It is shown that for these conditions temperatures deduced from absolute values of soft X-ray flux transmitted through a metal filter are subject to much less error than those deduced using the two foil ratio technique.

The semiclassical description of an RF resonance measurement on a doublet excited state is formulated. The solution of the density matrix equation of motion is obtained as a continued fraction. The single quantum and multiple quantum transitions are seen as resonances in the measured quantities. An analytic solution is obtained for the case of degenerate doublet (the Hanle phenomena) and the RF modification of the g-value is obtained. It is shown that the continued fraction solution gives simple computations of strong field saturation effects.

For Pt. I see ibid., vol.5, no.4, 878. The author presents calculations of the positions and shapes of the multiple quantum resonances, caused by a large intensity RF field, using a continued fraction solution presented in an earlier paper. The shift of the line is given for up to 11 quantum transitions and the width up to 7 quantum transitions. It is shown in which parameter ranges the results differ from earlier work by Shirley and Cohen-Tannoudji and Haroche.

The authors have measured the lifetimes of the first two vibronic levels of the B¹ Sigma ⁺ state of carbon monoxide using the inelastic electron-photon coincidence technique. Their respective values are 21.8+or-0.3 and 15.5+or-0.7 ns. They attribute this dependence on the vibrational quantum number to a very strong dependence of the B-X transition moment on the internuclear distance and have determined this transition moment in the r centroid approximation.