Table of contents

The method recently developed for treating Bloch-Siegert shift of the main resonance in a magnetic resonance experiment is successfully applied to the higher order resonances due to multiquantum transitions. A general analytical expression for the (2n+1)th resonances is given. Results for the main and third order resonance in the low or vanishingly low range of static magnetic fields are also reported.

The elaborated Guillemin-Zener function: psi =(1+pR zeta )exp(- alpha R zeta +or- beta R eta ) is investigated as a non-standard basis function for approximating the ground state wavefunction of the hydrogen molecule using numerical integration. A significant improvement on total energy is reached compared to the traditional Slater type orbital, except if noninteger values are allowed for n quantum number in the latter.

A preliminary report is presented of a study in which relativistic effects on total collision strengths are considered within a formulation which is based upon the Breit-Pauli approximation.

The positron-helium wavefunctions obtained previously (Humberston 1973) are used to calculate the annihilation rate parameter Z_efff at several positron momenta. A mistake in the previously quoted value of Z_eff at zero energy for the helium model H5 is corrected, and the new result agrees well with a recent measurement. The angular distribution of the annihilation gamma rays is also calculated, but the agreement with experiment is not as good for the model H5 as it is for the cruder model DB. An explanation of this phenomenon is suggested.

Neutral particle angular distributions have been determined in charge exchange collisions of atomic (H⁺, He⁺, Ne⁺, Ar⁺), diatomic (H₂⁺, N₂⁺, O₂⁺, NO⁺) and triatomic (H₂O⁺, H₃⁺, D₃⁺, HD₂⁺) ions on water molecules, in the energy range 5-50 keV. A minimum is observed at zero angle for collisions involving the triatomic ions H₃⁺, D₃⁺ and HD₂⁺; this result is compared to predictions derived from Fan's classical theory.

The metastable fraction of a He beam produced by electric-field detachment from He^- ions has been measured by the beam- attenuation technique in the energy range from 20 to 700 keV. It is shown that H₂ as an attenuation gas gives the correct metastable fraction. The data further suggest the existence of a long-lived ( approximately 10 mu s) bound doublet state of He^-.

A simple but powerful extension of fluorescence scattering methods for the measurement of decay rates is described together with results of an experiment on a helium plasma. The technique should allow measurements of A-values and excitation rates for vacuum UV transitions from observations of visible fluorescence, and reduces the need for short pulse lasers for decay rate measurements.

Oxygen (plus six) and (plus eight) at 30 MeV incident energy have been used to induce Auger electron spectra of Ne. The high instrumental resolution (0.02% FWHM) spectra show specifically that the charge state of the incident oxygen ion considerably affects the distribution of the K-Auger electron yield among the charge states of multiply ionized neon.

Applying general molecular orientation averaging with respect to orientations of the incident and slow scattering neutron, it is shown that Krieger-Nelkin approximate orientation averaging can be successfully applied to the most general form of molecular anisotropic vibrations.

A recurrence relation is presented which connects the general (n' not=n) hydrogenic radial matrix element of r^beta , where beta is a complex number to matrix elements involving exponents beta +2, beta -1, and beta -2 but the same sets of quantum numbers. This identity is found solely from the boundary conditions on the wavefunctions and the radial differential equation and should be of use in simplifying r^k forms given elsewhere. For n'=n, the recurrence relation reveals a proportionality between the - beta -2, beta -1 matrix elements that includes the Pasternack-Sternheimer identity as a special case. Further results may be obtained by beta -differentiation, and new identities for matrix elements of r^k log (r) are given. The n'=n matrix elements of r^k are studied for k>or=-1; closed-product expressions are found for k-values near the sum and difference of the angular momenta, so that simple prescriptions can be given for the iterative calculation of n-dependent explicit forms. It is suggested that complex-variable theory be applied to a study of these results.

Optical oscillator strengths, generalized oscillator strengths, first Born total cross sections and the polarization of impact radiation are calculated for the excitation of the resonance (¹S-¹P) lines of atomic magnesium and calcium. Large multi-configuration wavefunctions are used to represent the initial and final states, and excellent agreement is obtained with recent experimental results.

The convergence of the Born series for potential scattering is examined. It is demonstrated that calculations of differential cross sections using the second Born approximation can be inferior to those using the first Born approximation. Calculations using third and fourth Born approximations are also presented, and whilst it is true that the higher Born approximations are generally superior to the first Born approximation, it is clear that no definite convergence pattern exists. Following an idea of Moiseiwitsch (1961), however, it is shown that it is possible to obtain accurate differential cross sections using the second Born approximation, provided that the contributions of the lowest few partial waves are suitably corrected.

The cross section for the collision processes H(1s)+H⁺(He²⁺) to H(3d)+H⁺(He²⁺) are evaluated using the distortion approximation of H⁺ energies between 10 keV to 2000 keV (or He²⁺ energies between 50 keV to 2000 keV). A comparison has been made with the corresponding results obtained using the first Born approximation and the Glauber approximation.

A new plane wave approximation for calculating exchange scattering amplitudes is described and applied to the calculation of some singlet-triplet cross sections in helium. Comparison is made with experimental measurements of both total and differential cross sections. It is shown that a considerable improvement over previous techniques is obtained but that there remain significant differences between the theory presented and experimental measurement.

Starting from a five state (1S-2S-2P) close coupling approximation, a variational calculation has been performed for the low energy e-He collision. Cross sections for elastic scattering from the He ground state and the first excited state and for the transition between these states have been derived. Comparison with experiment shows good agreement between calculated and experimental results.

The equivalent operator formalism is used to perform calculations of transition probabilities ³P₁ to ¹S₀ in group II elements. Usually these transitions proceed from the spin-orbit mixing between ³P₁ state and ¹P₁ state, but in a relativistic treatment two phenomena occur simultaneously: deviation from LS coupling and relativistically allowed spontaneous decay of ³P₁. These two effects are shown to be comparable. The agreement between theoretical and experimental lifetimes of the lowest ³P₁ level is quite satisfying taking into account the simplicity of the method.

In the high velocity limit there ought to exist a connection between the correct classical and quantum mechanical treatments of the forward capture of a light particle. By means of a semi-classical treatment it is shown that there is a proper connection between the classical treatment of Thomas (1927) and the second Born approximation.

By using functional differential techniques it is shown how to obtain an expression for the hole-particle vertex function which has been partially summed. This expression is approximated in low order and inserted into the Bethe-Salpeter equation. An amplitude equation previously derived by another method (Csanak et al 1973) is obtained which has been suggested as a good 'second-order' theory for inelastic electron-atom scattering. The perturbational analysis of the approximate response functions is discussed.

Electric and magnetic susceptibilities are calculated in relativistic theory for hydrogen-like atoms. The results are the combination of the hypergeometrical function ₃F₂ with the unit argument. The case of small alpha Z is investigated. The method of Green's function is used in the calculations.

Measurements are reported of angular distributions for electrons elastically scattered from argon in the energy range from 15 eV to 200 eV. A modulated crossed beam technique was employed and an angular resolution of about 3 degrees realized in the range 20 degrees -140 degrees . The results agree well with those of previous workers at the high energies but it is observed that the dynamic range of the present results is far greater at the intermediate and lower energies. Angular distributions have been calculated using a semiphenomenological optical model and find good agreement with the experimental data down to 30 eV. The recent relativistic calculations of Walker (1971) are in good agreement with the data over the whole energy range. The measured relative dependence with energy of the differential cross section at 30 degrees is compared with theory and a previous experiment.

A phase-amplitude method has been used in deriving differential and total elastic scattering cross sections for electron collisions in atomic and diatomic molecular nitrogen and oxygen. The energy range considered has been from 1 keV to below 50 eV. Available theoretical and experimental cross sections for both atoms and molecules have been compared with the present calculations.

Discusses two-photon ionization of diatomic molecules taking as an example the hydrogen molecular ion. The Green's function in spheroidal coordinates is obtained for the quantum detect method. The total cross section and angular distribution coefficients of the ejected electrons are computed for two-photon ionization of H₂⁺ in the ground state at the equilibrium internuclear distance. A frequency range up to first resonance is covered. The cases of linear and circular polarization of the absorbed photons are investigated.

In the freely-expanding and recombining plasma produced by target irradiation with a high-powered laser the excited states below the thermal may develop an inverted population distribution. This situation is experimentally confirmed from intensity measurements of the Lyman line series of C⁵⁺ ions from a polyethylene target. The density of the inverted populations is however too small to observe stimulated emission.