Table of contents

New electron density distributions of the atoms Ne, Ar, Kr, Xe were calculated by extending the statistical model of Tomishima-Yonei (i.e. a Thomas-Fermi model with a λ = 0·2 kinetic energy and the usual exchange correction) in taking into account electron correlation statistically due to Gombas and Cowan. Slight improvements of the corresponding susceptibilities, similar to those in the work of Tong and Sham, were found.

Harmonic oscillators perturbed by Gaussian functions are useful for double minimum and circular minimum potential functions. The matrix elements of exp(-bξ²) are evaluated in closed form for the one-, two- and three-dimensional oscillators. Recursion relations among matrix elements are also obtained, which are more useful in computer programmes for finding energy levels.

The consequences of adopting a precise definition of the extended Hartree-Fock scheme proposed in an earlier paper are examined. It is shown that the extended Hartree-Fock scheme can correct for the zero-order mixing of configurations for certain, but not all, states of small atoms. An earlier calculation of the second-order extended Hartree-Fock energy of the ground states of beryllium-like ions is shown to be in error and the correct value is calculated by an alternative but more accurate and yet simpler method. The extended Hartree-Fock scheme is shown to give an augmented significance to the perturbation treatment of Hartree-Fock equations. It is also shown that in this scheme the purely variationally determined mixing coefficients for configurations depend, in general, on the nuclear charge Z.

Radial transition integrals and gf values for excited-state transitions of the Be isoelectronic sequence involving 3l orbitals have been calculated within the context of the Z expansion method and perturbation theory in the LS coupling scheme with the `frozen core' Hartree-Fock approximation. Comparison of transition integrals from the present calculation with those from numerical Hartree-Fock results shows that agreement is satisfactory. gf values are calculated using experimental wavelengths. The results should be more reliable for higher members of the isoelectronic sequence.

A method for calculating atomic structures, suitable for the electronic computer, is outlined; the method allows for configuration interaction in a very general way. It is based on the expansion of wave functions in terms of Slater states. All relativistic interactions are disregarded and an SL coupling scheme is used. The number of terms SL considered is that resulting from all configurations included; the configurations are the only input apart from the nuclear charge Z. The energy matrix is expressed in terms of radial integrals with purely algebraic coefficients. A scheme is described for computing these coefficients. The integrals are evaluated using radial wave functions calculated in a scaled Thomas-Fermi potential. Numerical examples for Na I and Mg I isoelectronic sequences are given. Layzer pointed out the importance of configuration interaction within a complex; his predictions for stages of high ionization are confirmed. It is shown that for stages of medium or low ionization interaction with configurations belonging to other complexes can become important.

A general formula describing the direct interaction between a hydrogen atom and a positive ion with one electron is derived. Born, two-state and four-state impact-parameter treatments are carried out for the processes H(1s) + He⁺(1s) -> H(2s or 2p) + He⁺(1s) with incident hydrogen energies E in the range 4 <or= E <or= 625 kev. The four-state calculation takes full account of distortion, back-coupling, rotational coupling and the virtual transition sequence 1s r arr over l arr 2p r arr over l arr 2s. The long-range 2s-2p dipole coupling produces a marked effect on the 1s-2s excitation cross section, which in the Born and two-state treatments is determined solely by short-range interactions. The rotational coupling and distortion (both long-range in this case) exhibit a much greater influence on the 2p cross section than was in evidence for the excitation of hydrogen by neutral hydrogen or helium.

Comparison with a four-state treatment of the excitation of hydrogen by proton impact demonstrates that, at moderate and high velocities, the orbital electron so effectively screens the helium nucleus that the helium ion behaves almost exactly as a singly charged structureless particle. The proton-hydrogen results are also compared with the second Born-wave calculations of Moiseiwitsch and his associates.

The percentage polarization of the emitted Lyman α radiation for both proton and helium-ion impact is also determined.

Cross sections for the formation of secondary H₂⁺ and H⁺ ions when 1·4-46 kev H₂⁺ ions pass through thin targets of hydrogen have been determined using a mass spectrometer which was designed to ensure that all secondary ions were recorded with a high and uniform collection efficiency. The influence of vibrational excitation of the H₂⁺ primary ions on the observed yields of the slow H₂⁺ and H⁺ ions has also been investigated. The results have been used to take account of dissociative processes in the derivation of the symmetrical charge-transfer cross section σ₁ for the process

H₂⁺ (v = 0) + H₂(v= 0) -> H₂(Σv) + H₂⁺(Σv)

using the previous experimental data of McClure. Upper and lower bounds for σ₁ have been estimated for energies within the present range and these values lie considerably below the theoretical cross sections due to Bates and Reid.

Upper and lower bounds to the Born approximation cross sections have been calculated for the excitation of ground-state He⁺ ions in collisions with free carbon atoms. Transitions to all orbital angular momentum states in the levels n = 2 to n = 7 have been considered at incident He⁺ laboratory energies between 0·504 and 6·472 MeV. A single Slater determinant has been used to represent the carbon wave function, thus allowing a closed-form sum over all final states of the carbon atom.

Millimetre microwave interferometers have been used to measure electron densities over the range 1·5 × 10¹⁴ to 8 × 10¹¹ cm^-3 in decaying hydrogen and deuterium plasmas without a confining magnetic field, at gas pressures ranging from 5 to 650 mtorr. Variation of the discharge energy input from 8 to 33 mJ cm^-3 produced a radical change in the afterglow decay of both gases. At the lower energy the decay was controlled by collisional radiative recombination and ambipolar diffusion. However, at the maximum discharge energy of 33 mJ cm^-3 calculations showed that full ionization was possible below 200 mtorr, indicating that the independence of the decay on density and pressure in both gases below this pressure was due to direct charged-particle expansion to the discharge walls. No previous results in deuterium afterglows appear to have been reported.

Radiative transitions from autoionizing levels of Be III were observed in the far ultra-violet spectrum produced by a vacuum spark. Classification of these transitions and determination of autoionizing level energies are given. Dependence of the intensity of these transitions on discharge parameters and the importance of the dielectronic recombination process are discussed.

The band spectrum emitted by a mixture of germanium tetrachloride vapour and argon as excited in a high-frequency discharge revealed characteristic new bands, degraded towards the red in the visible region λλ 6360-4370 Angstrom. These bands are attributed to the diatomic GeCl molecule and analysed as belonging to two sub-systems arising from a common excited state. The following vibrational formulae represent the bands: sub-system I ν = 21 844·6 + 251·2(vprime + ½) - 404·0(v−or+ + ½) - 0·62(vprime + ½)² + 1·06(v−or+ + ½)²sub-system II ν = 20 881·3 + 251·2(vprime + ½) - 407·2(v−or+ + ½) - 0·62(vprime + ½)² + 1·20(v−or+ + ½)². From the near equality of the vibrational constants the lower states of the two sub-systems may be identified as the ²II_1/2 and ²II_3/2 components of the ground state of the GeCl molecule. A study of the isotope effect of germanium and chlorine has been made for some of the bands with high vibrational quanta.

Expressions are derived which contain experimentally measurable parameters and allow the study by the phase and modulation technique of the process of resonance energy transfer in viscous media. Computations are made of the donor fluorescence phase angle and degree of modulation for the system phenanthrene-acridine in cyclohexanol, and the results are compared with those corresponding to a statistical mixing of the molecules during the lifetime of the excited donor.

Measurements of the shift-to-width ratio of the Ar II 4806 Angstrom line are reported in this paper. The profile-splitting interferometer developed by Burgess and Cooper (1965 a) was used for these measurements on the line radiated by a Z pinch filled with argon. Observations cover the temperature range 25 000-45 000 °k.

In continuation of our earlier work we have calculated the values of the screening constant σ₂ for N_IIN_III, N_IVN_V and N_VIN_VII doublets. We find that σ₂ is not constant for different values of Z and it varies unsystematically with Z, although the variation is small.

An approximation method is formulated for calculating resonance frequency shifts caused by the radio-frequency field in double-resonance experiments. The method can be used in regions where the perturbation approach is no longer valid. In such regions the shift induced by the presence of another level tends to become linear in H₁ rather than in H₁², where H₁ is the radio-frequency field strength.

The large discrepancy reported by Schmieder et al. in 1968 between their value for the electric quadrupole coupling constant of the 5 ²P_3/2 state of ³⁹K and an earlier value measured by Ritter and Series in 1957 is investigated.

By means of an approximation method formulated for this purpose by Pegg in 1969, it is shown that the discrepancy can be attributed to the shift induced by the strong oscillating field used of necessity in the Ritter and Series experiment. The positions of the resonances can be expressed in terms of effective hyperfine coupling constants, where the electric quadrupole term is strongly dependent on the radio-frequency field strength, while the magnetic dipole term is independent of the field strength.

It is shown that the rotating-field approximation is not appropriate for the calculation of shifts in double-resonance experiments in zero magnetic field.

A one-centre expression is derived for the long-range dispersion contribution to the hyperfine pressure shift of a paramagnetic atom in an inert buffer gas, and the use of oscillator strength sums in the evaluation of the leading term is discussed. Accurate calculations are carried out for atomic hydrogen in each of the inert gases.

An asymptotic expression for the cross section for excitation by fast protons of hydrogen atoms to any state ns has been obtained. Good agreement with the exact results has been found for impact energies greater than or equal to 25 kev.

A model for electron scattering by an atom is proposed in which, outside the atom, correlation between the incident electron and the atomic electrons is neglected. A description using Green functions is indicated. Results of a calculation for electron scattering by hydrogen atoms based on this model are given.

The possibility of the existence of a magnetic dipole transition with change in orbital angular momentum l of ±2 and its effect on the classification of the forbidden transitions in x-ray spectra has been pointed out.