Table of contents

The principal methods of calculating relativistic corrections are analysed from the point of view of the relativistic perturbation theory. The conditions under which the Breit-Pauli method is consistent with the relativistic perturbation method of Layzer and Bachall (1962) are formulated. Difficulties arising in the application of perturbation expansions in terms of 1/Z to relativistic Hartree-Fock equations, are demonstrated. Some typical numerical data are examined in the light of these discussions.

Relativistic Hartree-Fock calculations of the electron density at the nucleus in Eu yield improved agreement with empirical screening ratios. It is shown that this is due to the relativistic enhancement of the change in density being strongly dependent upon whether s or p electrons or d or f electrons are excited.

Low energy photoionization in the vicinity of the singly excited autoionization states of neon is considered using a multiconfiguration close coupling method for the wavefunctions. The positions and widths of the first ten 1s²2s2p⁶ nu _np resonances, the shape of the lowest resonance, and the shape of the nonresonant partial cross sections up to an electron energy of 2.8 Ryd are calculated and compared with experiment where possible.

For pt. II see abstr. A595 of 1972. The collective properties of the 4d¹⁰ shell in Xe are studied, making use of a previously developed method for analysing the linked diagram expansion for the polarizability. The infinite series of bubble and ladder diagrams (RPA with exchange) are considered for the (4d;nf)¹P channel and sum the on the energy shell part exactly. The off the energy shell part is given by a reaction matrix integral equation. An approximate, closed solution of Fredholm type is found to have two poles for energies between the continuum threshold and 2 Ryd above, in which region the exact reaction matrix equation cannot be solved by iteration. This result is interpreted in terms of a broad collective resonance in the (4d;nf)¹P channel, very clearly seen in the photoabsorption cross section. The theory is extended to include some effects of intershell interaction, representing core relaxation and improved agreement is found with experiments for low energies above the 4d⁹ threshold.

Accurate oscillator strengths (f-values) for the 1s²2s²¹S-1s²2s2p ¹P⁰, 1s²2s2p ¹P⁰-1s²2p²¹D, 1s²2s2p ¹P⁰-1s²2p²¹S lines of the Beryllium sequences are calculated using wavefunctions (the 'charge wavefunctions' Psi _c) containing all of the specifically non-closed shell type correlation effects given by Sinanoglu's (1970) non-closed shell many electron theory (NCMET). Comparison with the numerous Beam-Foil experimental results using both the dipole length and dipole velocity formulae, yields very good agreement except for the Be I 1s²2s2p ¹P⁰-1s²2p²¹S line. For this line, the dipole length and velocity calculations yield f_R=0.396, f_V=0.100 while two experiments give f=0.122 and f=0.119.

The quadratic Stark effect on hfs levels of the Li⁷ ground state is investigated. The spin-optimized self-consistent-field (SOSCF) method is used. Parting with previous calculations, where the electric field was treated as a perturbation, the SOSCF equations with the electric field included in the hamiltonian are solved. The calculated shift for the (F=2, M=0) to or from (F=1, M=0) transition is -0.0627 Hz KV^-2 cm^-2, in agreement with the experimental -0.061+or-0.002. Most of the effect results from the decrease in the net electron spin density at the Li nucleus; contributions of other terms in the hfs operator are negligible. The polarizability of the Li ground state is also calculated and found to be in good agreement with previous results. Predictions are made for the shift in the (F=2, M=-2) to or from (F=2, M=-1) transition, which has been measured for several alkali-metal atoms but not for lithium.

Using energy eigenfunctions obtained by semi-empirical analysis of the Lu-Fano plot (1949) of energy level positions and employing the Coulomb approximation of Bates and Damgaard (see abstr. A70754 of 1970) the absolute line strengths for transitions between the neon two-channel Rydberg series 2p⁵(²P₃2,1/2/)nsJ=1 and 2p⁵(²P₃2,1/2/)n'pJ=0 for n, n'=3,4 are calculated. Each Rydberg series is analysed separately to obtain a set of five parameters which completely define the energy eigenfunctions for all values of n and n'. Interactions between the nsJ=1 and the ndJ=1 Rydberg series have been ignored. The one-channel neon p and s series are also discussed and line strengths for transition between them presented. The line strengths for 3s to 3p and 4s to 4p transitions are in excellent agreement with the experimental and theoretical work of others. The results for 3s to 4p and 4s to 3p transitions are not in agreement with previous work and differ substantially with intermediate coupling theory.

Classical cross sections for collisions between electrons and highly excited atoms of ionization energy U are calculated for incident electron energies E in the range. U/4<or=E<or=4U and energy transfers down to 0.02U. The orbit integration or Monte Carlo method is used, and most statistical errors for the important energy transfers are of order 3% or less. The cross sections are needed for an understanding of recombination lines emitted from cool interstellar regions. Final classical states of the individual collisions have been recorded on magnetic tape for future use.

The diagonalization method is used to study proton-hydrogen scattering. A second order approximation is introduced and the results are compared with close-coupling ones. The improvement brought with respect to first order calculation seems to be very important. Calculations including twenty states are performed. The cross sections evaluated by various theoretical methods for 1s-2s transition are compared. The cross sections obtained for d and f states are very different from those found with the Born approximation. Polarizations of 3d-2p and 2p-1s lines are also calculated.

Flowing afterglow techniques are employed for the study of the thermal energy reactions of He⁺ with Zn, Cd, and Se, and of Ne⁺ with Mg. The He⁺ reactions have a practical importance as excitation mechanisms in the He-Zn; He-Cd and He-Se laser systems. The degree to which excited states of the metal ion closest to the rare gas ionization energy are preferentially populated in the formation process is investigated. Relative reaction rates are deduced from measurements of the emission line intensities with the aid of calculated transition probabilities. The largest reaction rates are found to be those for levels of the product ion lying some 0.1-0.4 eV below exact resonance. Such behaviour is shown to be consistent with the predictions of a semi-empirical 'curve-crossing' model of the ion-atom interaction.

A local effective potential, H_ex has been used to account for electron exchange, together with a model hamiltonian for the helium atom in Kohn's variational approximation to the electron helium scattering length, a. H_ex was chosen to give agreement with the Born-exchange and static-exchange approximations. Correlation was introduced in the 84 term that trial function by using interelectronic coordinates. The method provides an upper bound to the 'model' scattering length and the value of 1.16a₀ was obtained in good agreement with more elaborate calculations and with experiment.

Recently Peterkop and Rabik (see abstr. A2987 of 1972) have calculated the positron hydrogen scattering length using an inexact target wavefunction in Kohn's variational method. They showed that the usual minimum principle is violated. Kohn's variational approximation to the scattering length is derived when the trial function includes an approximation to the target wavefunction. In addition calculations are reported of the positron helium scattering length in which several different approximations to the helium ground state wavefunction have been used. The results of Peterkop and Rabik are confirmed and reference is made to the 'method of models' which recovers the minimum principle of Kohn's variational method. A suggestion for extending this method to electron helium collisions is included.

The crossed beam method for observing the ionisation of ions by electrons has been refined by the inclusion of a 127 degrees electrostatic electron energy selector. This enhances the resolution of the measurements, by an order of magnitude, to about 0.15 eV. With this apparatus, autoionization thresholds have been resolved in the ionization function for, Ba⁺+e to Ba²⁺+2e, at energies of 15.8, 16.8, 19.2 and 21.9 eV. Observations have also been made of the near-threshold ionization of K⁺.

The authors present the results of an ab initio calculation of the particles Cu₂(¹ Sigma _g⁺, ³ Sigma _u⁺, ¹ Sigma _u⁺) and Cu₂⁺(² Sigma _g⁺) and make a comparison of these results with experiment. By adding to a minimal basis the components 4p sigma , 4p pi , 4d sigma , 4d pi , 4d delta , a satisfactory agreement with experiment for the main physical constants: equilibrium distance, dissociation and ionization energies has been obtained.

The applicability of an r-centroid approximation to polyatomic molecules is discussed. The transformation between sets of normal coordinates for the same distorted molecule, but related to different reference configurations is investigated and shown to be a function of the distortion. The significance of this fact for the interpretation of Franck-Condon factors in polyatomic molecules is examined in relation to other approximations currently made.

Exact quantum mechanical vibrational transition probabilities are obtained for a collinear atom-diatomic molecule collision using the reactance matrix K. Both the Morse and harmonic binding potentials are considered and it is shown that the transition probabilities for the Morse oscillator may differ considerably from the equivalent harmonic oscillator results. The exact transition probabilities are compared with those of several approximate theories, and it is shown that the revised first order distorted wave approximation of Mies is valid, provided that the scaled reduced mass (m) of the incident atom is not large.

The cross section and rate constant of the chemi-ionization reaction CH+O to HCO⁺+e are calculated from a theoretical model. The treatment assumes that the collision partners follow classical adiabatic trajectories up to the region where the potential surfaces cross, and that either the Landau-Zener model or a unit probability gives the transition probability for curve-crossing along the single dimension defined by the trajectory. Potential surfaces were obtained from experimental data and INDO calculations. Cross sections and rates were computed for a variety of parameters, in order to test their sensitivity to the model. The process can proceed from CH+O in their ground states; of the available potential surfaces of neutral HCO, the most important is that of the ² Sigma ^- state, followed by the two surfaces associated with the ² Delta state. The cross section for the ² Sigma ^- surface may be as high as 8 AA² for collisions of very low velocity. The rate coefficient curve deemed most probable gives values of ca. 3.5*10^-11 cm³ s^-1 at 1000 K, and about 7*10^-12 cm³ s^-1 at 25 K.

Translational energy spectra of H^- ions arising from single- and double-collision double charge transfer of 4 keV protons on N₂, O₂ and NO have been measured. The energy values of some double ionized states of these molecules were determined. The spin conservation rule is shown to hold strictly for these processes. Approximate selection rules bearing on the symmetry of the involved states are proposed and used for the discussion of the results.

The widths of the J=1 to 2 transition of OCS broadened by collisions with OCS and with CHF₃ and the J=0 to 1 transition CHF₃ broadened by collisions with CHF₃ and with OCS have been measured by a digital fitting of the recorded line shape to the theoretical line shape function. Present theory of rotation energy transfer accurately predicts the width of the self-broadened CHF₃ line and the two foreign gas broadening cases, but there is a small but apparently real discrepancy in the case of the OCS self-broadening.

Thin gold film techniques and infinite plane-parallel electrode geometry have been used for precise measurements of ionization growth in molecular nitrogen over a range of values of E/p (60-2000 V cm^-1 Torr^-1) and p (0.5-60 Torr at 0 degrees C). With gold film as anode the transition from equilibrium to non-equilibrium ionization has been investigated and where possible new values for the primary and secondary ionization coefficients have been obtained. With gold film as cathode the total ionization is enhanced considerably at low values of E/p<or approximately=100 where decreases in threshold breakdown voltage as large as 1800 V have been noted. A variation of the secondary coefficient with electrode separation and a marked sensitivity to impurity in the gas sample have been observed. It is shown that this is consistent with secondary electron emission at the gold film by metastable (A³ Sigma _u⁺) particles which diffuse to the boundary surface after production by electron impact excitation in the gas.

For pt. I see ibid., vol. 6, no.1, 214 of 1973. Detailed spatial and temporal studies of ionization growth in nitrogen at moderate values of E/p ( approximately 100 V cm^-1 Torr^-1) have revealed that the dominant secondary electron emission arises from bombardment of the cathode surface by metastable N₂(A³ Sigma _u⁺) molecules following diffusion through the parent gas. It is shown that the peaks in omega / alpha against E/p curves observed in this gas are due to this effect and not to photo-electric effects, as inferred from previous measurements. Thin evaporated gold films show a particularly strong sensitivity to the influence of the metastable particles and have possible applications as metastable particle detectors.

All five levels of the ground configuration 4p⁴ and all the ten 5s, along with eighteen 4d, eight 5d, seven 6s and two 7s levels, built on the 4p³ core have been determined. The analysis is based on 99 classified lines. The ionization potential 4p⁴³P₂-4p³⁴S_3/2 is found to be 719950+or-2000 cm^-1.

The differential cross section for total scattering in ⁴He on ⁴He and ³He on ³He collisions has been measured between 0.25 keV and 3 keV. The effect of the nuclear symmetry in these collisions is studied. The amplitudes and the phases of the oscillations in the cross sections corresponding to ⁴He atoms (bosons) or to ³He atoms (fermions) are compared.

Calculations of the temperature sensitive line-to-continuum intensity ratio of the He II 4686 and 3203 lines are presented for the temperature range below 80 000 K where a density dependence sets in. When electron density is such that partial LTE holds, the method provides very accurate temperature measurements. The effect of small hydrogen admixtures is also outlined.

Electron detachment cross sections for He^-(1s2s2p ⁴P) ions in He, H₂, and Ar target gases are obtained from the classical impulse approximation method of Bates and Walker (see abstr. A8710 and A13833 of 1967) and compared with recent experimental measurements.