Table of contents

Threshold behaviour of the ionization interval function for an electron-hydrogen atom scattering has been examined numerically, using a classical three body computer program. Results confirm earlier calculations and are in accordance with Wannier's theory.

The velocity dependence of the total elastic cross section for 5-90 eV gold neutrals on Ar⁰ has been measured. Information about the interaction potential has been obtained, which shows evidence of a Lennard-Jones type of behaviour. A similarity to the Cs⁰:Ar⁰ case is noted.

Simultaneous excitation and ionization of helium to the n=2 state has been studied between 100 and 200 eV, at angles theta =54 degrees 44' and theta =90 degrees between photon and photo-electron. The cross section ratio ( sigma _2s+ sigma _2p)/ sigma _1s agrees well with the theoretical prediction by Jacobs and Burke; also the theoretical values of sigma _1s/ sigma _2p and asymmetry parameter beta _2p are consistent with experimental data.

A two-particle self-energy expansion is used to study spectral line-broadening in plasmas. The utility of the technique is demonstrated by treating the problem in two different manners. Further possibilities are discussed and the analytic continuation are performed.

A theorem is proved which shows that the Hartree-Fock orbitals for the nsms ¹S states of helium can be assumed orthogonal if, and only if, the zero order total two electron wavefunction in a perturbation expansion in powers of 1/Z, where Z is the nuclear charge, is a certain linear combination of ns²¹S, nsms ¹S and ms²¹S zero order wavefunctions. This provides some insight into the nature of constrained Hartree-Fock wavefunctions. The weights of 1s²¹S and 2s²¹S states in the total zero order wavefunction for obtaining orthogonal orbitals for the particular case of the 1s2s ¹S state are computed numerically.

Predictions are made of the relative energies of electronic states arising from various simple electron configurations of linear molecules. It is shown that while empirical generalizations of Hund's rules may sometimes be useful, they are not always applicable, and more useful criteria for assigning states are given. It is believed that the material herein will provide a useful guide to spectroscopists wishing to interpret the electronic spectra of linear molecules.

Hartree-Fock results for all the LS terms of He 1s2s, C2p3p, and Ca 3d4d are analysed. No marked term dependence is observed. Instead, radial functions are found to depend strongly on whether or not the term is allowed when the electrons are equivalent.

Heisenberg's form of the correspondence principle for non-relativistic matrix elements has been used to evaluate matrix elements for various potentials. These are compared with available quantum mechanical results to check the general validity of the use of classical mechanics and correspondence principles in the derivation of quantum mechanical expressions. Using a one dimensional harmonic oscillator potential matrix elements of the form (n mod q^m mod n+s) and (n mod p^m mod n+s) are worked out. A Morse potential is then considered and the matrix elements for position, momentum, and kinetic energy are evaluated. Using a Coulomb potential a similar procedure is used for functions of various position coordinates, from which dipole and quadrupole moments from transitions between n, l states are calculated. The agreement with quantum mechanics is found to be generally good, and in some cases identical results are obtained.

Various forms of the second Born approximation are applied to electron collisions with helium in the energy range 200 to 500 eV. In each case all intermediate states up to 3¹P are included explicitly, and a closure approximation used for higher states, the energy parameter being chosen to fit the total cross section and dispersion relation values for Re f(0) and Imf(0). Calculations are carried out with and without V⁴ terms, and in a (1,1)-Pade approximation for the 1²S to 1¹S, 2¹S and 2¹P transitions. Results are compared with experiment and with those of other calculations. The present results cast doubt upon the practice of normalizing experiment to the first Born approximation at intermediate energies.

Information about the potential energy of interaction was obtained for the metal ions, Na⁺, Mg⁺, Al⁺, P⁺, Cl⁺, Cu⁺, Ag⁺, Au⁺, Ni⁺, Zr⁺, on the inert gases Ar⁰, Ne⁰. The scattering of an ion beam in the energy range 8-25 keV, by passage through a gas, was used to measure incomplete total cross sections against energy curves from which the parameters K and S in an assumed form for the potential V(r)=K/r^s were determined. Theoretical potentials were compared with those obtained experimentally, and for the range of separation 1.1 AA-1.6 AA a Moliere type screened coulomb potential was found to give good agreement, while the Thomas-Fermi potential of Firsov gave poor agreement. The variation of the potential with Z₁ was noted, and thought to be a product of detailed atomic structure in a way not predicted by any statistically determined potential.

Measurements are reported of the differential cross sections for excitation of inelastic processes in He⁺-He collisions for the range of incident ion energy E from 1 to 3 keV. The use of an improved energy analyser permits the detection of a number of inelastic channels, hitherto unresolved. In particular, the excitation of He in the (1s2p) ^1.3P state is well separated from other channels; the reactions for the formation of He⁺(2p) and He²⁺ are studied for the first time. The results, which are given for scattering angles theta , up to 8 degrees in the laboratory system, confirm that for E>or approximately=4 kev deg. excitation occurs mainly via rotational coupling between the ² Sigma _u and ² Pi _u states and between the ² Sigma _g, ² Pi _g and ² Delta _g states of the He₂⁺ quasi-molecule. As for the measurements of direct ionization the oscillatory structure observed in the energy distribution of the ejected electrons for a given E, is interpreted by a crossing mechanism between the ² Sigma _g state of He⁺₂ and the ² Sigma _g continuum state of the system (He²⁺₂+e).

Excitation cross sections are calculated for Si XII by the coulomb-Born method, using numerical Hartree-Fock radial functions. The transitions considered are 2s-np, ns-n'd, 2p-nd and 3s-np. Reasonable agreement with the general results of Bely and Petrini is obtained, but an appreciable difference occurs for 2s-7p. The effect of including higher multipoles in the coulomb-Born method is illustrated. For comparison, the plane wave Born approximation is also used to obtain cross sections for the 2s-np transitions, as well as for 2s-ns and 2s-nd, and is found to approach the correct result to within a factor of three for incident energies greater than three times the threshold value.

The least squares variational method has been shown to be a conceptually and computationally simple means of calculating accurate energies and wavefunctions for the unbound 2s²¹S and 2p²¹S states of He. It has also been used, with basis set functions which are asymptotically correct to a high order, to calculate energies and wavefunctions of the ground stage of H^- and of the ground state and several excited bound states of He.

The effects of the dipole moment of HD⁺ ion on the differential and total cross section for the collision induced dissociation of HD⁺ ion by electron impact have been analysed quantitatively. For this purpose the Born-Oppenheimer approximation has been used and the electron-dipole interaction term has been included in the hamiltonian for exchange scattering amplitude. Some very interesting features in the differential and total cross sections for dissociation have been predicted which are due to the heteronuclearity and the dipole moment of the molecular ion.

The possibility of explanation of the observed asymmetry in the forward-backward scattering of He⁺ fragment produced from the collision induced dissociation by electron impact of (HeH)⁺ ion, in terms of the distortion polarization of the orbitals has been examined. The results that this factor cannot account for the observed effect.

Collision-induced rotational energy transfer in electronically excited sodium molecule has been investigated. It has been confirmed that the recently discovered asymmetry in the cross section ( sigma ( Delta j=+1) not= sigma ( Delta J=-1)) exist for most of the vibration-rotational levels in the Na₂(B ¹ Pi _u) state. Levels with rotational quantum numbers from J'=12 to J'=99 in the optically populated B ¹ Pi _u state have been included. As collision partners all rare gases were used as well as H₂, HD, D₂, N₂ and CH₄. It has been found that the asymmetry in the cross section depends strongly on the nature of the collision partner and that it varies monotonically with the quantum number J' of the Na₂ molecule. Evidence for a temperature dependence of the asymmetry is also given, and some preliminary results on collisional depolarization are deduced. Finally, a semi-classical model is proposed describing the transition process by means of trajectories.

Apparatus for the investigation of ionizing collisions of heavy particles by electron spectroscopy is described. Collisions of He⁺ and He on Ne, Ar, Kr, and Xe are studied in the kinetic energy range from 100 eV-5000eV by measurement of energy spectra and angular distributions of the ejected electrons. As in collisions at higher energies, the spectra are composed of discrete peaks arising from autoionizations of the separated particles, and a continuous part. This latter part is much more pronounced for collisions with He⁺. A mechanism for the production of the continuous part is proposed, which explains this fact. The angular distributions of electrons of discrete energies (peaks) are found to be nonisotropic in some cases, and dependent on the collision energy. In one case the distribution is asymmetrical with respect to theta = pi /2 (angle measured from beam direction).

Cross sections for electron capture by H(2s) in collisions with argon, nitrogen and oxygen have been measured in the energy range 1.4-8 keV. At 1.4 keV the capture cross section is as large as 2*10^-15 cm² for argon and roughly an order of magnitude smaller for oxygen and nitrogen. In all three cases the cross section for capture by metastables decreases rapidly as a function of energy and approaches the cross section for electron capture by ground state hydrogen at the high energy end of the range. Using earlier measurements on electron loss from metastable hydrogen a lower bound to the total destruction cross section is established.

The Fox-Duffendack-Barker (A ² Pi _u-X ² Pi _g) and the ultraviolet doublet (B ² Sigma _g⁺-X ² Pi _g) band systems of CO⁺₂ have been excited in the hollow cathode of a igh voltage discharge through a mixture of CO₂ and O₂. Relative intensity measurements have been measured and interpreted in terms of experimental band strengths for the Fox-Duffendack-Barker system. The experimental band strengths agree for the most part with those predicted by previous Franck-Condon factor calculations by the authors.

Self broadened widths of eight rotational lines of CH₂F₂ have been measured on a double modulation microwave spectrograph. The experimental line width parameters ( Delta _nu /p) have been compared with the theoretically calculated results obtained by using Murphy and Boggs' theory of pressure broadening taking only the dipole-dipole interaction.