Table of contents

The cross section for ionization of helium by electron impact is calculated using the Born approximation. Accurate wave functions are employed for both the ground and continuum states, the l = 0, 1 and 2 partial waves of the continuum state are represented by polarized-orbitals wave functions, the l = 3, 4 and 5 partial waves are represented by Hartree-Fock wave functions, and the ground state of helium is represented by a six-parameter correlated wave function. The cross section is obtained using both the length and velocity formulations of the Born matrix element. A comparison is made with previous calculations and measurements.

A model for atomic structure calculations is proposed which differs from the Hartree-Fock model. One half of the electronic interaction potential energy is associated with each of the two electrons involved. A best-energy criterion is applied to the one-electron energies instead of to the total energy. The ground states of the He, Ne and Ar atoms are used as numerical examples. It is found that the one-electron energies are widely separated for the outer electrons. The sum of the one-electron energies equals the total energy to first order in perturbation theory and is a good approximation to the experimental total energy. The virial theorem is not immediately satisfied. The spin orbitals form a new ortho-normal set. The electrons are closer to the nucleus on the average than those in the Hartree-Fock model.

The one-electron energies, radial orbitals and radial expectation values for the quasi-independent model are expressed as a scale transformation of those for the Hartree-Fock model.

A modified close-coupling expansion has been developed and applied to calculate elastic electron-hydrogen-atom scattering phase shifts. This expansion into a complete discrete orthonormal basis set is a variant of the more usual close-coupling expansion into eigenstates of the target Hamiltonian. We retain the first few hydrogen-atom eigenstates and augment these terms with pseudo-states chosen, in our particular case, to incorporate fully the ground-state polarizability of the hydrogen atom. The resulting phase shifts are compared, where possible, with those obtained in the most accurate variational calculations available, and they indicate a distinctly improved convergence over those obtained in the close-coupling expansion.

The rotational excitation in Ne-N₂ scattering for energies from threshold to 0·5 ev is studied using a potential interaction obtained from viscosity data and polarizabilities of the pure gases. The cross sections below 0·006 ev are found to be dominated by resonances which are either shape resonances or Feshbach resonances. These two types of resonance are related using the idea of analyticity in angular momentum introduced by Regge.

The crossed-beam method for measuring electron impact ionization cross sections of ions has been developed so that very small cross sections (similar 10^-21 cm²) can now be determined with an accuracy approaching ±10%. The reaction Li⁺ +e->Li³⁺ +3e has been investigated for incident electron energies between threshold (198 ev) and 2·5 kev. The cross section reached a maximum value of 1·04 × 10^-20 cm² and fell to 4·5 × 10^-21 cm² at 2·5 kev. The results are discussed and compared with theoretical and experimental values for the double ionization of helium.

A crossed-beam method has been used to study the reaction Mg²⁺ +e -> Mg³⁺ +2e for electron energies which ranged from threshold (78 ev) to 3 kev. The cross section attained a maximum value of 1·38 × 10^-17 cm² at 300 ev. The results are compared with partial cross sections (for single ionization) of neon and Na⁺, which are the two lower members of the neon sequence. The scaling law for isoelectronic ions, which follows from Thomson's classical theory, is seen to become more accurate with increasing ionic charge for this sequence.

Differential cross sections have been measured for electrons with energies between 3·1 and 19·1 ev which were elastically scattered by helium. The scattering angles ranged from 25° to 145°. The results are compared with the measurements of Ramsauer and Kollath, theoretical predictions, and cross sections recommended by Bransden and McDowell from an analysis of a wide variety of experimental data. The present results are closer to the theoretical predictions and recommended cross sections than the measurements by Ramsauer and Kollath, particularly at the smaller energies and angles.

A phase-shift analysis of electron-helium elastic scattering in the energy range 3·1 to 19·1 ev has been made. s- and p-wave phase shifts consistent with the dispersion relation and with experimental information on the total elastic scattering cross section, the diffusion cross section and recent measurements of the differential cross section, to within 5% are obtained. The Gibson-Dolder measurements of the differential scattering cross section are shown to be theoretically preferable to the earlier measurements of Ramsauer and Kollath. The d-wave phase shift cannot be determined to better than 25% by available experimental information. The phase shifts obtained are consistent with, but do not distinguish between, recent non-adiabatic theoretical calculations, but exclude the simple polarized orbital model. They satisfy Spruch bounds based on the experimental polarizability and yield a scattering length of 1·1a₀ in agreement with other determinations.

The simplified second Born approximation is applied to the 1s -> 3s, 1s -> 3p, 2s -> 3s excitations of atomic hydrogen by both electron and proton impact. The excitations from the ground state give total cross sections which behave similarly, with respect to the respective first Born cross sections, to those previously calculated for the 1s -> 2s, 1s -> 2p excitations; they indicate that the first Born total cross sections for optically allowed excitations are reliable over a larger energy range than those for optically forbidden excitations.

Alternative methods of calculating bound-free matrix elements for atomic hydrogen are presented. Expressions previously given for ionization from 2s and 2p states are shown to be incorrect, and new expressions are derived.

Multi-configuration Hartree-Fock calculations are reported to study the term splitting in the 1s²2s²2p² configuration from Z = 7·0 to Z = 15·0. The wave functions include the Hartree-Fock configuration 1s²2s²2p², the `quasi-degenerate' configuration 1s²2p⁴, the single replacement configurations 1s²2s3d2p² and 1s²2s²2p4f, the double replacement configurations from the 2p shell 1s²2s²3l3l′ (l, l′ = 0, 1, 2) and, finally, the intershell configuration 1s²2s3s2p3p. The separations of the ³P, ¹D and ¹S levels predicted from these functions are in very good agreement with experiment not only for the ratio (³P-¹D)/(¹D-¹S) but also for the individual transitions.

These functions have also been studied from Z = 6·0 to Z = 30·0 to compute the contribution to the correlation energy which arises from each configuration. For the ³P and ¹D states the 1s²2s3d2p² configurations make a larger contribution to the correlation energy than does the 1s²2p⁴ configuration at low Z. At higher Z the reverse is true. For the ¹S state all the configurations except the 1s²2p⁴ configuration make a small contribution to the correlation energy throughout the isoelectronic series.

The frequency spectrum of the depolarized light scattered from a dilute solution of large, rigid molecules can give information about their principal axis of inertia and therefore their symmetries. It is shown that, for spherical molecules, one finds a single Lorentzian line.

In the case of axial symmetry, the spectrum is the sum of two Lorentzian lines. Linewidths and relative intensities of lines are calculated as a function of the optical polarizability tensor and rotational diffusion coefficients of the molecule.

Polarized absorption spectra of a very thin fluorene crystal (0·1 μm -0·2 μm) have been studied. From the polarized absorption spectra it has been found that the ratio of the intensity of absorption along the b axis to that along the a axis of the crystal is nearly equal to 1·63 for the first system and 1·40 for the second system of transition. As these results roughly agree with the oriented gas model value for the short-axis transition, one may be inclined to suggest that the transition is along the short axis of the molecule. But, from further consideration of the molecular orientation and particularly of the absorption coefficient data, the authors suggest that the transition is mostly along the long axis of the molecule, with a weak short-axis contribution.

Photoelectric intensity measurements made in emission on 36 bands of the O₂ Herzberg I system excited in an argon-oxygen afterglow have been interpreted with the aid of realistic Franck-Condon factors and r centroids to determine band strengths and the variation of the electron transition moment with internuclear separation. A discussion is made of the excitation of this band system in the afterglow and in the airglow.

The accuracy of the simplified second Born approximation calculations of Holt and Moiseiwitsch on the 1s -> 2s and 1s -> 2p excitations of atomic hydrogen by proton impact is assessed by comparing with the zero- and first-order approximations of Cheshire and Sullivan.

The theory recently derived by Salin for the ionization by ion impact of atomic hydrogen is generalized to the ionization of complex atoms.