Table of contents

In minimizing the electronic energy of the ground state of the hydrogen molecule ion H₂⁺ with respect to the parameters p, α and β in the elaborated Guillemin-Zener wave function ψ = (1 + pRξ) exp(-αRξ) cosh(βRη)

we have located two minima, corresponding to p > 0 and p < 0. We confirm Bhalla and Khubchandani's calculations for p < 0, but find that better results are obtained when p > 0 (the energy being then as low as that corresponding to the most successful variational wave function published up to now). We also report calculations in which the flexibility of the variation process is restricted so that the `local' energy Hψψ is finite at the nuclei.

An exact analytical method is derived for the calculation of the direct Coulomb interaction matrix elements between two hydrogen atoms in their ground states. Explicit interaction potentials for the process H(1s) + H(1s) -> H(nl) + H(primenprimel) are presented. The long-range interaction arising from double transitions is also discussed.

The hydrogen ionization collision H_n-M_B, where H_n is a hydrogen atom in state n and M_B is the atom H, Li or Na and may be left in any final state, is considered. The Born approximation is used, together with an approximation to the sum over all final states of M_B. Also, initially the ionized electron is treated in the plane-wave approximation and later the continuum Coulomb function is used. The results are given in the energy range 20-150 kev and where possible compared with other theoretical and experimental results.

Transitions between the levels ²D_3/2, ²D_5/2 of O⁺ 2p³, produced by electron impact, are of importance in determining the relative intensities of the lines ²D_J-⁴S observed in gaseous nebulae. Saraph, Seaton and Shemming have made calculations for energies above the threshold for excitation of 2p³²P. Below this threshold the ²D_3/2-²D_5/2 cross section contains series of resonances converging on ²P.

The reactance matrices of Saraph et al. are extrapolated to energies below the ²P threshold, and the cross sections are calculated using resonance theory for the case of degenerate closed channels, as developed by Gailitis in 1963 and discussed in the paper `Quantum defect theory VII'.

In previous work, Saraph, Seaton and Shemming have calculated cross sections for electron impact excitation of the O²⁺ ground configuration terms, in the approximation of neglecting collisional coupling to configurations other than 2s²2p². In the present work it is shown that collisional coupling with 2s2p³ produces resonances of the type 2s2p³3s in the near-threshold cross sections.

Calculations are made using semi-empirical methods. Radial functions are calculated using a statistical-model potential, and the binding energy of the 3s electron in the state 2s2p³(⁵S)3s ⁴S is calculated allowing for configuration interaction with 2s2p³(³S)3s ⁴S and 2s²2p³⁴S. A parameter in the potential is then varied so as to obtain agreement with the observed binding energy for this state. Similar calculations are then made for 2s2p³(³D)3s ²D allowing for configuration interaction with 2s2p³(¹D)3s ²D and 2s²2p³²D, and for 2s2p³(³P)3s ²P allowing for interaction with 2s2p³(¹P)3s²P and 2s²2p³²P. It is found that the 3s ²D state lies just above the threshold for excitation of 2s²2p²¹D, and that the 3s ²P state lies just above the threshold for excitation of 2s²2p²¹S.

A generalized reactance matrix is calculated using a variational expression, and the 2s2p³3s functions of the present work and the 2s²2p²kp functions obtained by Saraph, Seaton and Shemming. Resonance structures are calculated using methods of quantum defect theory. It is found that the resonances produce important modifications in the cross sections at near-threshold energies of interest for astrophysical applications.

Differential cross sections and spin polarizations for 3·5-500 eV electrons scattered from mercury have been calculated by the numerical solution of the relativistic Hartree-Fock equations, thus including the effect of exchange but ignoring distortion of the atom and correlation effects. At the upper end of the energy range the inclusion of exchange produces small but significant changes which bring the results into very good agreement with experiment. At lower energies some discrepancies appear, but even at 3·5 eV good qualitative agreement is obtained.

Elastic and inelastic channel measurements in transmission are reported for the resonance scattering of electrons by N₂, CO, O₂ and NO; their interpretation is discussed quantitatively in terms of the compound state model and of the first reflection model. In the case of O₂ and NO, the resonance scattering probably arises from the ground state of the negative ion. For small electron energy losses (excitation of low vibrational quantum numbers) the transmission technique suffers from interference from elastically scattered electrons. A discussion is given of a number of features of electron momentum analysis in the 127° cylindrical selector, including field penetration broadening and background ghosts.

Semiclassical approximations are derived for the angular dependence of the scattering cross section σ(θ) for two cases, involving the forward and backward directions, where the classical scattering is infinite. The results are approximations uniform in angle and valid from the ordinary semiclassical region where σ(θ) is O(ℏ⁰) right round to θ = 0 or π for a glory σ(θ) is then O(ℏ^-1) and the forward diffraction peak σ(θ) is O(ℏ^-2) or larger, depending on the form of the long-range tail of the scattering potential. The formulae are all expressed in terms of the action functions along the paths of the classical problems.

An application of the Boltzmann transport equation to the analysis of electron swarm experiments is presented and the attendant computational procedures are described. The analysis is then applied specifically to determining the relation between E/p and the mean energy for electron swarms in oxygen. Finally, measurements of the oxygen dissociative attachment reaction obtained in electron swarm and electron beam experiments are compared and the contribution of the prevailing electron energy distribution on the data is assessed.

High-resolution streak photography has been used to show that, in laser-produced breakdown of helium in the initial pressure range 1 to 4 atm, the scattering of incident light at the breakdown front is due to reflection at the refractive index change in the quasi-spherical plasma boundary. The strongly non-linear variation of scattered intensity with initial gas pressure and the spatial distribution of the scattered laser light are explicable in terms of this mechanism. Interpretation of diagnostic data obtained from the scattered light in the study of radiation-driven breakdown waves is made more reliable if the scattering mechanism is known.

A systematic study of the L emission spectrum of gadolinium reveals the existence of the quadrupole lines λλ 1502·01 and 1616·22 X.U. corresponding to the transitions L_IN_IV,V and L_IIN_III, respectively, and the octupole line L_IIM_V (λ 1834·77 X.U.). The presence of the dipole line L_IIO_I(γ₈) and that of the quadrupole line corresponding to the transition L_IO_IV,V, reported for this element by Sakellaridis, have been confirmed. Also the discrepancy between the wavelength values reported for the dipole line L_IIIO_I(β₇) by Coster and Sakellaridis has been removed.

The rotational analysis of three bands of the C-X system of ³²S₂ has been completed. The structure of the bands is similar to that of some of the bands of the main system B ³Σ_u^--X ³Σ_g^- in which, in addition to the six main branches, the branches ^NP₁₃, ^PR₁₃, ^RP₃₁ and ^TR₃₁ also appear with appreciable strength. Constants (cm^-1) for state C are as follows:

Te = 55 581·66	ωe = 829·15 ± 0·32	xeωe = 3·34 ± 0·10
Bo = 0·321 15 ± 0·000 10	107Do = 2·2 ± 0·2,	λo = -11·61 ± 0·21
γo = +0·033 ± 0·001	re = 1·810 Angstrom

It appears that C is a Rydberg state, with the likely configuration... σ_g²π_u⁴π_g(π_u4p).

Using a 40 cm and a 20 cm curved mica crystal spectrograph of the transmission type, the α region of the L emission spectrum of thulium has been investigated. Three new diagram lines at 1583·4, 1600·9 and 1886·8 X.U. have been reported for the first time. The first line has been assigned to the forbidden transition L_IM_I, whereas the remaining two correspond to the quadrupole transitions L_IIM_III(β₁₇) and L_IIIM_II(t) respectively. The measurements on the previously known diagram lines in the region under study have been compared with those of the earlier workers.

Results obtained for the drift velocities of positive oxygen ions in oxygen for E/N less, similar 450 × 10^-17 v cm² are described. The data confirm recent observations by Dutton and Howells.

An estimate of the quadratic Stark constants of some of the transitions in the Cu I spectrum has been made using the time-independent perturbation theory, LS coupling equations and Bates and Damgaard's matrix elements.

Collision strengths are calculated for transitions between the levels ⁴S_3/2, ²D_3/2, ²D_5/2, ²P_1/2 and ²P_3/2 in the ions O⁺, F²⁺, Ne³⁺ and Na⁴⁺, with configurations 1s²2s²2p³. Below the ²P threshold the collision strengths are averaged over resonances in series converging onto ²P.