Table of contents

For pt.I see ibid., vol.7, no.12, 1506 (1974). The leading term in an asymptotic expansion of the resonant ionization probability in the interaction of slow hydrogen-like atoms with solid state surfaces is obtained in closed form. A procedure for calculation of the subsequent terms is also outlined.

The dependence of the equilibrium annihilation rate of positrons in an Ar-CO mixture on electric field and on molecular concentration has been investigated by solving the diffusion equation.

The tables of free-free integrals for attractive Coulomb fields, given by Burgess (see abstr. A55239 of 1970) have been corrected and extended. The source of inaccuracy is discussed, and a sum rule is derived which is of interest in connection with partial collision strengths, oscillator strengths and Gaunt factors.

Configuration interaction wavefunctions have been used to evaluate absorption oscillator strengths, using both the length and velocity forms, for transitions between the 1s²2s2p and 1s²2p² states: ³P⁰ to ³P^e; ¹P⁰ to ¹D^e; ¹P⁰ to ¹S^e. It is found that the length values stabilize fairly quickly while the corresponding velocity values are more sensitive. Both L-shell and K-L inter-shell correlations are considered. The latter make small changes to length values, but alter velocity values by up to 10%. All-external configurations are important for neutral beryllium and to some extent for B II also. The 1s²2p²¹S state of neutral beryllium appears to be about 0.01 a.u. above the Be⁺ 2s threshold. The calculations of Burke (1972) for the 1s²2s²¹S to 1s²2s2p¹P⁰ transition are extended, and compared with the accurate calculations of Sims and Whitten (1973). Agreement to within 2% is achieved.

The existence of collective oscillations in the electron shells of atoms is discussed. By solving numerically the equations for the effective interaction in the random phase approximation with exchange, it is shown that, at least for atoms of the noble gases, there are no collective levels in the excitation spectrum. Nevertheless, the many-electron correlations play an important role, so that there is a significant difference between the effective and the Coulomb interaction.

The lower bound formulae of Temple, Weinstein and Stevenson (1973) are known to give rather poor estimates of the energy when the wavefunction has been calculated by minimization of the Rayleigh upper bound. Recent studies for atoms and molecules have shown that gaussian wavefunctions give particularly poor lower bounds, and this has been explained in terms of the incorrect behaviour of such wavefunctions at and near a nucleus. The authors examine the accuracies of the lower bounds for a series of cusped-gaussian wavefunctions, and discuss the significance of the cusp condition at a nucleus. Numerical evidence for the proposition that -(H²)^1/2 may in practice be expected to be a lower bound for a wavefunction calculated by minimization of the upper bound is presented.

The gauge invariance of the matrix elements of electromagnetic interaction is a property that is usually taken for granted. The author describes a unified derivation in which the dependence of the matrix elements on the gauge in which the electromagnetic potentials are written is exhibited explicitly. The necessary and sufficient condition for the transition matrices for all multipoles to be gauge invariant is that the transition matrix for longitudinal photons should vanish identically. This imposes conditions on the initial and final wavefunctions which are automatically satisfied for a single-particle model but may not necessarily hold in, say, the Hartree-Fock model. For electric dipole transitions, it is shown that the Coulomb gauge leads to the dipole velocity form of the matrix element in the nonrelativistic limit and that a different choice is needed to give the dipole length form. Arguments are advanced suggesting that the dipole velocity form should be given a privileged position in approximate calculations of atomic and molecular transition probabilities.

The spectrum of the helium-like boron ion B IV has been obtained by using the laser-impact technique. It has been recorded in the 250-4500 AA wavelength region. The ionization energy has been determined to be 2091976+or-20 cm^-1, by means of the theoretical values for the np ¹P energy levels. Experimental values of the Lamb shift have been determined for the ground state (-93+or-20 cm^-1) and for the two first excited levels 2s ¹S and 2s ³S (-8.0 cm^-1 and -8.6 cm^-1 respectively). The term system is derived from twenty two new lines and extended by using Ritz formulae and other semi-empirical formulae. The results are compared with theoretical calculations of ionization energies.

The transition probabilities for L₂-L₃X Coster-Kronig transitions at Z=63, 65, 73, 80 and 81 are measured by observing the ratio of K alpha ₁ and K alpha ₂ X-rays in coincidence with L alpha X-rays during the radioactive decays of ¹⁵¹Gd, ¹⁵⁹Dy, ¹⁸¹W, ¹⁹⁸Au and ²⁰⁴Tl, and ²⁰³Hg respectively, employing Si(Li) detectors. A comparison of the experimental results with the existing theoretical predictions indicates that there is general agreement with the recent calculations by Chen and Crasemann (1973).

Cross sections for K-shell X-ray production in collisions of Ar with Ar, HCl and Cl₂ have been measured in the energy range 0.25-2.2 MeV. These experiments show unambiguously that K-shell ionization does occur in symmetric systems with an atomic number larger than 10, under adiabatic and single collision conditions. Yet, the cross sections are so small that the results are not necessarily in contradiction with the molecular model. Observed differences in cross sections and spectra for Ar-Cl₂, as compared with Ar-Ar, Ar-HCl, are speculated to be due to double scattering the Cl₂ molecule. Ar-2p vacancies created in the first collision can, during collision with the second Cl-atom of the same molecule, lead to: promotion of Cl-K electrons via 2p pi -2p sigma rotational coupling; promotion of Ar-K electrons via 2p pi -1s sigma rotational coupling: the production of MO X-rays. These speculations are consistent with experimental results. A calculated cross section for K-shell ionization via 2p pi -2p sigma rotational coupling, is shown to be in good agreement with the Cl-K ionization cross section in Ar-Cl₂ double scattering deduced from the experimental results.

The problem of the interaction of an atomic particle (atom or ion) with a solid surface is considered. The electron transition probabilities of resonant ionization and neutralization processes are determined by a non-perturbative method, which provides asymptotically correct results. The transition rates, as well as mean transition distances for these processes are also calculated. Parameters determining the transition probabilities are given for several atoms.

Electron-photon angular correlations were measured by delayed coincidences between electrons scattered inelastically from helium and 58.4 nm photons emitted in the decay of 2 ¹P state. The ratio of the differential cross sections for exciting the degenerate magnetic sublevels and the relative phase of the corresponding excitation amplitudes for electron scattering angles between 16 degrees and 40 degrees and for incident electron energies in the range 40 to 200 eV is deduced. The data show that a high degree of atomic orientation is produced by collisions in this range of energy and angle. The orientation increases rapidly towards its theoretical limit as the scattering angle is increased, and higher incident energy produces, in general, greater orientation at a fixed scattering angle. The data also show that the alignment of the atomic dipole radiation pattern can depart significantly from the direction of linear momentum transfer at the larger scattering angles. The results are compared with the predictions of the first Born and Glauber approximations, and good agreement is obtained with a recent distorted wave calculation.

Fully quantal close-coupling calculations of the cross sections for fine structure and depolarization transitions in Rb(S²P)-Ne collisions are presented. The calculations proceed by analogy with collision-induced rotational excitation (Reid and Dalgarno (1970)). They were performed using the interaction potentials of Baylis (1969) and of Hidalgo and Geltman at both high and low energy. The quantal calculations using the Hidalgo-Geltman potential are compared with the Hidalgo-Geltman semi-classical calculations and are found to be in reasonable agreement. The Baylis potential gives good agreement with experiment for the depolarization cross sections and the low-energy inelastic cross section. Improvement in the repulsive potential should improve the high-energy inelastic results. The results suggest that Nikitin's second mechanism (1967) (Coriolis coupling between the Pi quasi-molecular states at short interatomic distances) is to be favoured over the first (coupling between the Pi _1/2 and Sigma _1/2 states at intermediate distances) for Rb-Ne collisions.

Differential cross sections for H⁺-He(1s²) elastic and inelastic collisions in the keV-energy region are calculated using various approximate schemes.

The Kohn variational method has been applied to the zero energy positron-helium collisions. Results show that singularity persists in scattering length values, for variant IV of Peterkop and Rabik (1971), which may suggest that this method is not, after all, reliable.

Five different ion sources were investigated to find one which produced currents of de-excited H₃⁺ ions which are adequate for crossed beam experiments. An inclined beam technique was then used to measure absolute cross sections for energies between 15 and 22 eV, for the formation of protons by collisions between electrons and H₃⁺. From the shape of the excitation function it was established that the H₃⁺ ions had negligible internal energy and that they had two electronically-excited states with energies 15 and 19.2 eV above the lowest vibrational ground state. These energies are in satisfactory agreement with Kawaoka and Borkman's (1971) calculations of the energies of the ³E' and ¹E' states of equilateral H₃⁺.

Energy differences, and differences in kinetic energies, nuclear attraction energies and interelectronic repulsion energies are given for the lowest ^1,3 Pi states of H₂, HeH⁺, and LiH⁺⁺, and an analysis of the results in terms of 1/Z-expansions is presented. If Z is used to denote the charge of the nucleus of higher atomic number, then it is found that at low Z the difference in interelectronic repulsion is dominated by higher-order terms, and that the often-quoted statement that the singlet-triplet energy difference is twice an exchange integral is true only for high values of the nuclear charge Z.

A method has been derived to find the potential of diatomic molecules from the given experimental eigenvalues and rotational constants. The potential is found by computing the coordinates of the turning points. The method is different from the semiclassical RKR method and is based on simple and straightforward quantum mechanical principles. The present method is applied to the state B¹ Sigma _u⁺ of the H₂ molecule. The results are compared with other results of the same state and show a marked improvement.

It is shown that the presence of the sound waves causes the ionization balance to be altered from the quiescent plasma condition and the effect on excitation is also considered. The treatment covers isothermal and adiabatic sound waves in three plasma conditions, viz., (i) Uniform high density plasma in local thermodynamic equilibrium (LTE), (ii) Uniform low density plasma (non-LTE), (iii) Low density plasma of uniform pressure and a temperature gradient. The results show that the presence of a sound wave can cause quite large changes in the ionization balance depending on the magnitude and frequency of the waves as well as the atomic parameters. The intensities are modulated with the same frequency as the waves and the time or space averaged intensities can also be significantly modified. In the case with the temperature gradient the counter-acting effects of ionization balance and excitation are shown to reduce the extent to which the time averaged intensities are changed. The theory has been developed because of its possible application to the interpretation of the solar spectrum arising from the transition region between the chromosphere and corona where one of the proposed mechanisms for heating the corona requires propagating sound waves.

The equation of mass transport of a weakly ionized gas in a uniform electric field is solved giving initial corrections to the diffusion equation. The corrections arise because account is taken of the effect on the ion velocity distribution of both small density gradients and non-steady state. The Green's function in unbounded space of the resulting equation is found for two situations, one in the limit of vanishing electric fields and the other for finite fields. Generally initial deviations from the diffusion equation result in a skewed density distribution. The analysis is applied to the interpretation of drift velocities in drift tube experiments.