Table of contents

A new method is proposed for calculating the widths of atomic and molecular resonances. The method uses only square-integrable functions to approximate the nonresonant scattering solutions and employs Stieltjes-moment-theory techniques to extract a continuous approximation for Gamma (E) from a discrete representation of the background continuum. The method has been applied to several well known resonances in He, He^- and Mg^- with encouraging results. The proposed method is easily applied to molecular problems.

For original article see ibid., vol.10, p.L653 (1977). The authors remarks on the halfwidth of the polarisation curve and the utility of the process discussed as a source of polarised electrons are corrected.

It is shown that a thermionic detector can be applied with success not only in Doppler-free two-photon spectroscopy but also in saturation spectroscopy. Without changing the experimental set-up, the fine-structure splittings of some Cs n²D_5/2,3/2 levels (18<or=n<or=23) are determined by two-photon spectra (6²S_1/2^-n²D_5/2,3/2) and parts of the saturation spectrum of the 6250 AA band of Cs₂ are recorded simultaneously.

A rate is derived for n-photon absorption which includes all atomic and laser linewidths and experimentally check the laser linewidth dependence for two-photon absorption.

A logarithmic angular dependence at small angles is obtained for the amplitude of elastic electron scattering by excited hydrogen atoms.

In a crossed-beam experiment polarised potassium atoms have been ionised with a beam of polarised electrons. A measurement of the ionisation for the two relative spin orientations yields the asymmetry factor A which is related to the total interference cross section for ionisation. The measurements extend over an energy range from 6 to 80 eV. The measurements of A cannot be compared directly with theoretical results since no calculations of the interference cross section have been made for potassium. However, theoretical values of A for lithium and sodium exist and, when plotted against reduced energy units, it is apparent that for energies less than about five times the ionisation energy, the measurements disagree with theory. At higher energies the agreement is satisfactory.

The first ionisation potentials of the light atoms up to krypton are computed by means of Slater's transition-state method for the following local-density functional models: Slater's exchange potential, the X alpha and X alpha beta methods and the exchange correlation potential due to Hedin and Lundqvist (1972). By taking into account the experimental multiplet structure of the atoms and the corresponding ions, a direct comparison can be made between experiment and theory. For the four potential models, this shows systematic trends, which are explained. In addition, comparison is made with Hartree-Fock results. It is concluded that the best overall agreement is found for the Hedin-Lundqvist potential.

Transition probabilities have been calculated for two-electron one-photon K_{alpha alpha} transitions (2s2p to 1s²) and single-electron K_alpha ^h hypersatellite transitions (2p to 1s) for ions with two K-shell vacancies in the initial state. The ions studied are N, Ne, Al, Cl, Ca, Fe and Ni. The K_{alpha alpha} and K_alpha ^h rates were calculated within a single-particle atomic model, allowing for the relaxation of the single-particle orbitals when passing from the initial to the final state. The LS-coupling scheme and non-relativistic single-configuration Hartree-Fock wavefunctions were used to calculate oscillator strengths in the dipole-length approximation.

The profiles of the emission lines of Cs perturbed by Xe have been calculated using Anderson and Talman theory (1956). A square-well potential has been chosen which provides an analytical autocorrelation function that allows a great number of precise and fast calculations. Periodic red satellites centred at multiples of the depth of the well, have been found. The variations of their amplitude and position with density and the parameters of the potential are investigated. The present paper is restricted to the study of the satellites but their influence on the main line parameters will be developed in a further paper.

Using a CW Nile-blue dye laser the authors have measured the hyperfine magnetic constant A for the 2p₁₀ level of ²¹Ne by the level-crossing technique and found A(2p₁₀)=-2.711+or-0.007 mK. This value is used, together with other experimental determinations of the hyperfine constants for the levels of configurations 2p⁵3s and 2p⁵3p, to improve a previous semi-empirical calculation by Liberman (1973) of the hyperfine A constants for the levels of the lowest configurations of ²¹Ne.

A model-potential method is used to compute one- and two-photon ionisation cross sections for ground- and excited-state sodium atoms. The inhomogeneous-differential-equation method, suitably modified for use in resonance regions, is used in the two-photon calculations. The author calculates a generalised cross section of the order of 10^-48 cm⁴s for two-photon ionisation of the 3p level at the Na I resonance transition wavelength.

Photoionisation cross sections for the ground level and some excited ns levels (n up to 14) of neutral sodium have been computed for low photoelectron energies. Starting from a single-particle central-field model, perturbation theory is used to estimate the contribution of potential corrections and core-polarisation effects. For the ground level in the agreement between our results and previous data (experimental and theoretical) is greatly improved by the inclusion of these corrections. The evolution of cross sections and core-polarisation effects along the ns Rydberg series is investigated; core-polarisation effects have larger relative magnitude for the ground level and the low excited levels than for the high excited ones.

The introduction of a realistic velocity distribution into the binary-encounter approximation (BEA), both for K shells and L subshells of target elements other than hydrogen, leads to the same scaling rules for the proton impact ionisation cross section as those obtained in the plane-wave Born (PWBA) and semiclassical approximations (SCA). K shell ionisation cross sections for the same element calculated with the BEA, PWBA and SCA differ by less than 20% in the region of proton energies currently employed.

The Coulomb deflection of a projectile due to the target nucleus and the increase in the binding of a target electron due to incident protons have been incorporated in a binary encounter model for proton impact K-shell ionisation of atoms. The modified expressions have been used to calculate K-shell ionisation cross sections for different atomic systems. The cross sections have also been calculated by using Vriens' expression (1966, 1967) with a Hartree-Fock velocity distribution for the bound electron. These results have been compared with other theoretical calculations for the bound electron. These results have been compared with other theoretical calculations and the available experimental data. The modified model gives good results for the ionisation cross sections for low-energy protons and results based on Vriens' expression using the Hartree-Fock velocity distribution agree well with the experimental results at high incident energies.

The production of 2s vacancies in collisions of 0.3-400 keV Ne⁰, Ne⁺ and Ne²⁺ with Ne has been studied by measuring the emission cross sections for the Ne II (2s2p⁶) and Ne III (2s2p⁵) states using VUV spectroscopy. The experimental data show the presence of different reaction mechanisms, the origins of which are discussed within the framework of the MO model.

Total cross sections for the process He²⁺+H(1s) to He⁺( Sigma n,l)+H⁺ involving capture into all final bound states of He⁺ have been determined for ³He²⁺ ions in the range 1.5-9.0 keV using a furnace-target technique previously employed for similar measurements at higher impact energies. Measured cross sections are considerably smaller than those measured previously by Fit et al. (1962) and are in better accord with recent theoretical estimates. A likely explanation for the discrepancy is given in terms of the corresponding cross sections for electron capture in He²⁺-H₂ collisions which have also been determined.

Measurements of the sigma ₂₁ cross sections for Ne²⁺ ions in targets of helium, neon, argon, krypton and xenon have been made with an absolute accuracy of about 5% in the energy range between 60 and 200 keV. The two-state theory, in the form given by Rapp and Francis (1962) is able to account for the energy variation of the cross sections in all these targets when the states of the product ions which have unsuitable atomic structures are excluded. The magnitude of the cross sections from the theory is smaller than experiment of all the targets, the discrepancy being worse for the heavier targets. An improvement can be obtained in the magnitudes of the theoretical cross sections by scaling down the input parameters by factors which depend on the radial quantum number of the transferred electron in order to compensate roughly for the inadequacies of the1s electron orbits which are assumed in the Rapp and Francis theory.

It is shown that the condition for a root to be invariant under a dilatation transformation (complex-coordinate rotation) is that it satisfies the complex virial theorem.

For pt.I see ibid., vol.11, no.8, p.1475 (1978). In the present text two different perturbation methods are proposed, the implementation of which facilitates the computation of resonance parameters within the framework of the coordinate-rotation method. Additional physical insight into the application of dilatation transformations in connection with finite-basis techniques is gained. The virial theorem for resonances derived in the companion paper supplies a rigorous criterion for determining the best solution (in a variational sense) obtainable at a given level of the approximation. This is a generalisation of the well known scaling relationships for wavefunctions, investigated by Lowdin, to include the case of resonance states. The test system is the first ¹S resonance of the He⁺+e system for which there is ample numerical data from previous standard coordinate-rotation calculations.

A variational method is described and used to calculate bound states of an electron-polar-molecule system in which the molecule is regarded as a rigid rotor and its interaction with the electron is described by a cut-off dipole potential. Energies are computed as a function of the dipole moment, cut-off radius and moment of inertia of the molecule.

Calculations of elastic and rotational excitation cross sections for electron scattering by LiF are presented. A model potential is used and the cross sections computed using the close-coupling and a number of other theoretical methods. The accuracy of the various methods is assessed and a comparison with experimental data shows close agreement at an energy of 5.4 eV.