Table of contents

The sequence of functions phi ^(N)(x), converging to the solution of the Thomas-Fermi equation for a neutral atom phi (x), is constructed. The function phi ⁽³⁰⁾(x) approximating phi (x) and phi '(x) with an accuracy of nine significant figures for x in (0; infinity ) is presented.

Complete fourth-order Moeller-Plesset perturbation theory (MPPT) calculations for the quadrupole (Q₂) and hexadecapole (Q₄) moments of N₂ are reported. The authors' fourth-order MPPT values are Q₂=-1.171 ea²₀ and Q₄=-5.8 ea⁴₀ at a bond length of R=2.073 42 a₀. Taking basis-set truncation and vibrational corrections into account, these values are in good agreement with experiments. Preliminary values for the longitudinal components of the quadrupole polarisability, mixed dipole-quadrupole hyperpolarisability and dipole hyperpolarisability are C_zz,zz=33.64 e²a⁴₀E^-1_h, B_zz,zz=-215 e³a⁴₀4 E^-2_h and gamma _zzzz=1173 e⁴a⁴₀E^-3_h, respectively.

Natural radiative lifetimes of ytterbium in the 6sns ¹S₀ (n=12-22) Rydberg sequence have been measured using stepwise excitation and the fluorescence decay monitoring method. The lifetimes are perturbed by 6p² and 4f¹³5d6s6p configurations near n=12 and 19. The lifetimes of two perturbers were also measured.

The deviation from first-order perturbation theory in the description of the impact parameter dependence of L-subshell ionisation probabilities has been estimated by model calculations of 0.9 MeV amu^-1 Ne on Yb and Pt collisions. The applied model takes into account the strong distortion of the L shell by solving a truncated set of coupled equations which describe the time evolution of the L-substate amplitudes. According to the model the subshell couplings lead to a large reduction of the L₁-subshell ionisation probabilities, but they alter the L₃ probabilities to a lesser extent. As a result of crossing of the probability curves predicted by the relativistic first-order theory at small impact parameters disappears, in accordance with the experimental observation of Dexheimer et al (1986). The possibilities of further improvements in the theoretical description are discussed. The evaluation procedure applied by Dexheimer et al to extract the ionisation probabilities from the measured X-ray yields is also analysed as a source of the remaining discrepancies between experiment and theory.

The ionisation of highly excited Rydberg atoms in collisions with ground-state atoms is considered. The stationary diffusion-like mechanism of the ionisation is presented. The investigation is based on the Fokker-Planck equation. Analytical expressions for the probabilities of stationary diffusive ionisation are obtained and applied for the explanation of experimental results on the ionisation of highly excited Rydberg states of caesium in collisions with ground-state Cs atoms. It is concluded that the diffusive mechanism is the main mechanism for collisional ionisation of Rydberg atoms with n>or approximately=25-30.

The authors show that the effects of saturation on the ionisation probability at small impact parameters can be exhibited in ion-atom collisions where simultaneous electron capture and ionisation occur. Such effects show up for this process because capture probabilities are only appreciable at small impact parameters, whereas saturation effects hardly appear in a simple ionisation process where significant contributions come from large impact parameters. When such effects are accounted for accurately, good agreement with experiments can be obtained within an independent-electron model.

Relative electron capture cross sections have been measured for OCS³⁺ ions colliding with atomic and molecular targets at 15 keV impact energy. Translational energy change spectroscopy of product ions is utilised to identify specific electron capture channels. A reaction window is observed which has a maximum when avoided crossings occur in the region of 6 AA.

First-order many-body theory (FOMBT) has been used to calculate the differential cross sections (DCS) and electron impact coherence parameters (EICP) associated with excitation of the 3¹P, 3¹D and 3³D states of helium for incident electron energies of 30, 40, 45 and 60 eV. No direct measurements of the DCS for excitation of the individual 3¹P, 3¹D and 3³D states have been reported but the sum of the theoretical DCS for excitation of these three states is in excellent agreement with that determined from recent electron energy loss data at 30 eV. The EICP predicted by FOMBT for excitation of the 3¹D state are in good agreement with the recent measurements of Beijers et al (1986, 1987) but differ from FOMBT are qualitatively different from those obtained using the multichannel eikonal approximation. More accurate and extensive measurements will be needed to determine which of these two theories better describes the electron scattering process.

The qualitative properties of the generalised spheroidal wave equations for a hydrogenic system in half space obtained previously are studied. Geometrical and dynamical symmetry properties are discussed briefly. The behaviour of the energy eigenvalue and the eigenvalue of a constant of the motion, Omega , in the limiting cases d=0 and d= infinity are investigated, where d is the distance between the centre of the system and the boundary surface. The property that the number of nodes of the wavefunction in each coordinate is conserved is used to find the correlations between the quantum numbers as well as the energy eigenvalue at d=0 and those at d= infinity .

For pt. I see ibid., vol.20, p.4275 (1987). The generalised spheroidal wave equations for a hydrogenic system in half space are solved exactly. The eigenvalues of the lowest twenty-two physical states are obtained and presented in tabular form and/or in the form of curves. The results are analysed and also discussed along with the non-crossing rule of von Neumann and Wigner.

An L² method for calculating electronic Coulomb scattering wavefunctions and phaseshifts is presented which has been designed for being incorporated in quantum chemical program systems. It is based on simple matrix operations and a recursive solution of the Schrodinger equation by means of the Lanczos tridiagonalisation. In combination with a finite basis set of harmonic oscillator functions, calculations for non-spherical systems (molecules) are feasible. Results for the H and Li atoms are discussed.

The non-locality and non-linearity of the atomic relativistic Hartree-Fock (RHF) equations have hampered the formulation of a consistent non-relativistic reduction. In the paper a reduction technique is presented that yields an RHF equation for which all terms are correct to second order in m^-1. The results and techniques presented should be of use for practical calculations of atomic X-ray transition rates and energies.

The average static dipole polarisability of the ground state of titanium is calculated. The polarisability is expressed in terms of the first-order correction in the wavefunction due to the static electric dipole perturbation, which is determined variationally as a configuration interaction expansion. Near-degeneracy effects are included. The contribution to the total polarisability from the replacement 4p² to 4pnd is discussed. The importance of including pseudo-orbitals specifically determined to describe the polarisation of 3d is also discussed. The author has also shown that quite an accurate value for the polarisability can be obtained using truncated expansions for the wavefunction composition.

Within the framework of the eigenchannel R-matrix method, theoretical calculations of the multichannel quantum defect (MQDT) parameters have been performed for ^1.3P^o, ^1.3D^e and ^1.3S^e spectra of Sr. For the singlet spectra, both discrete and autoionisation regions below the Sr⁺ 4d threshold are investigated, while the analysis of the triplets is restricted to the bound spectra below the Sr⁺ 5s threshold. Near the Sr⁺5s threshold, the calculated parameters are in good agreement with those previously fitted to spectroscopic data. The main improvements with respect to the empirical MQDT studies concern evidence of the large energy dependence of the parameters and identification of isolated perturbers of the ¹D₂ and ¹S₀ spectra. In addition, the energy levels and the spectral intensities are accurately reproduced and channel mixing and correlation effects in doubly excited states are analysed in detail. A close similarity is found between the 5snp-4d np ¹P^o mixing in Sr and the msnp-mpns ¹P^o mixing in the light alkaline earths Be and Mg. Such near invariance does not hold for the ¹D^e and ¹S^e spectra.

Various types of electron density have been calculated for the H₂ molecular using accurate wavefunctions expressed in terms of explicitly correlated Gaussian-type geminals. The difference density (with respect to the densities of free atoms superimposed at the molecular geometry) has been averaged over vibrations and rotations. The other densities considered include the difference density with respect to the Hartree-Fock density, the radial density, the density along the molecular axis and the density describing the correlation hole.

Multiconfiguration Hartree-Fock studies of the (²D)nd ³P^o Rydberg series of S I have been performed. As predicted by other theories, the 3s3p⁵³P^o level is well below the first 3p⁴⁴S ionisation limit. The component of this configuration accounts for much of the oscillator strength for transitions to the Rydberg series from the ground state. These calculations showed there was a confluence of three ³P^o Rydberg series near the states (²D)6d, (²P)3d and (²P)5s resulting in highly mixed states.

The information supported by the lowest adiabatic eigenstates resulting from ab initio MO-CI calculations using finite basis sets with diffuse AO many be transformed into a small effective Hamiltonian through a unitary transformation recently proposed. This diabatisation procedure of ab initio MO-CI potential curves is applied to the lowest ² Sigma ⁺_u and ² Sigma ⁺_g states of H₂^-. In both cases one of the vectors supporting the effective Hamiltonian has large components on the (H^-H+or-HH^-) description taken from the bound asymptotic limit. It is rather spatially concentrated, of predominant valence character and may be considered as a description of the resonant state. Its mean (diabatic) energy varies smoothly with the interatomic distance, becoming unbound for r(1.6 AA for ² Sigma ⁺_u and r(2.5 AA for ² Sigma ⁺_g. The diabatic potential curve of the resonant state is almost independent on the basis set. In contrast, the other diabatic potential curves (a sampling of diffuse states) are parallel to the ground-state potential curve of the neutral molecule, and their position is very sensitive to the basis set. An estimate of the width of the resonant state is proposed. The results are in good agreement with the experimental evidence for both symmetries and with most refined calculations by Domcke and co-workers.

Line profiles of the resonance lines of Ba⁺ (455.4 and 493.4 nm) were observed in emission from a flow lamp. Broadening due to helium and argon perturbers is reported and discussed in the context of other group II metals ions.

The transport of laser radiation, resonant with the optically deep H- alpha transition in a well diagnosed, partially ionised hydrogen plasma was investigated experimentally. The results were compared with the numerical solution of a one-dimensional radiation transport model which included all the significant collisional and radiative rates for the first five levels of the hydrogen atom. The result was a substantial disagreement between theory and experiment for the two plasma conditions investigated; i.e. N_e=5*10¹⁴ cm^-3, T_e=0.8 eV and N_e=8.5*10¹⁴ cm^-3, T_e=1.14 eV. No reasonable mechanism that would account for the disagreement is forthcoming.

The photoionisation spectrum of atomic arsenic prepared by successive abstraction reactions involving H atoms and AsH₃, has been obtained from its ionisation threshold at around 1266.6 to 745 AA. A number of s-like and d-like autoionisation resonance series have been identified converging to ³P₁ and ³P₂ of As⁺. At least one of the d-like series is broad and asymmetric. In addition, at higher energies a deep window resonance series is seen, involving inner s-shell excitation to . . . (⁵S)np ⁴P states. The quantum defect for this series is in good agreement with recent Hartree-Slater calculations.

In the framework of a non-relativistic single-electron model, photoionisation cross sections from nl states (n<or=20, 0<or=l<or=4) have been computed for the Rb, Cu and Ag sequences. The evolution of non-hydrogenic behaviour of photoionisation near threshold is studied along the sequences, and emphasis is put on the occurrence of minima in the photoionisation cross section curves. Systematic trends along a sequence and the comparison of the behaviour along the different K, Rb, Cu and Ag sequences are analysed in terms of the quantum-defect theory. Through the principle of detailed balance, scaled radiative recombination coefficients alpha '_nl(T)' for Sr⁺-Y²⁺, Cu-Ga²⁺ and Ag-Sn³⁺ have been obtained within the scaled electron temperature range 500<or=T'<or=5000 K, and compared with the corresponding hydrogen results. Markedly non-hydrogenic features and systematics of recombination along isoelectronic sequences have been outlined.

A general calculational method is proposed to investigate the response of an electron residing in a one-dimensional potential well to an intense laser field. The numerical technique is based upon a pseudospectral solution of the time-dependent Schrodinger equation and is capable of incorporating the spatial and temporal aspects of the electromagnetic field. The intensity and frequency dependence of the ionisation rate along with the ejected-photoelectron spectrum are calculated for a one-dimensional cut-off harmonic-oscillator potential well.

The charge distributions of Xe ions as a result of photoionisation have been studied experimentally and theoretically. The initial vacancies are produced by 4.1-8.0 keV synchrotron orbital radiation and the charge distribution of ions was measured with a time-of-flight mass spectrometer at various photon energies. The theoretical estimation of the charge distribution was made by the use of the Monte Carlo simulation. The calculated charge distributions as a function of incident photon energy are in good agreement with the measured results.

In the spectral region 560-610 nm the multiphoton double ionisation of Ba is dominated by sharp resonances of incompletely determined origin. By selectively populating specific low lying states of Ba⁺ with a secondary laser system the authors show unambiguously that the multiphoton double ionisation of Ba proceeds via real Ba⁺ intermediate states. Specifically, by comparing multiphoton double ionisation spectra with and without the population of selected Ba⁺ states the authors can identify the initial Ba⁺ states for multiphoton double ionisation as the Ba⁺ 6s_1/2, 5d_3/2 and 5d_5/2 states. The wavelengths of the observed Ba²⁺ features can be assigned with confidence as multiphoton resonances to Ba⁺ intermediate states, and these assignments are confirmed in some cases by the wavelength of the Ba²⁺ photoionisation threshold and the angular distributions of the electrons ejected in the production of Ba²⁺.

The statistical fluctuations of the number of ion pairs created by monoenergetic photons in several polyatomic gases and gas mixtures were derived by iterative deconvolution of measured pulse height spectra obtained by means of the proportional counter. The response of the proportional counter to the unit charge (the single-electron spectrum) has been determined precisely, making possible the measurement of the number of electrons created per absorbed photon. W values (mean energy per ion pair), generalised Fano factors and primary ion pair distribution characteristics have been derived as functions of incident photon energy for ten polyatomic gases, mostly alkanes, and two tissue-equivalent gas mixtures. Monoenergetic photons having an energy equal to 0.277 keV (carbon K_alpha line), 1.49 keV (aluminium K_alpha line) and 5.89 keV (⁵⁵Fe) have been used throughout the experiment. It is shown that the primary distribution of ion pairs in all investigated gases and gas mixtures is asymmetrical and more peaked than the Gaussian distribution for low-energy incident photons, approaching the Gaussian shape for 6 keV photons.

NO⁺ ions produced by electron impact on either NO₂ or NO were observed to photodissociate into N⁺(³P) and O(³P) when irradiated by light from an argon-ion laser having wavelengths of 514.5 and 476.5 nm. The translational energy spectra of the photofragment N⁺ ions, which give information on the translational energy released, reflect absorptions from more than one long-lived NO⁺ excited electronic state. Assuming single-photon absorption, these states are tentatively identified.

Elastic and inelastic cross sections, differential in energy loss and scattering angle, have been determined from the energy loss spectra of 1.5-25 keV He⁺ scattered from atomic hydrogen at scattering angles from 5'-2 degrees (laboratory frame). Energy loss spectrometry does not allow the study of electron capture processes. The experimental results compare favourably with the experimental and theoretical data obtained at low incident energies by other authors, but for the higher energies, the results exhibit a strong disagreement with all the calculations, except the ones of Maidagan and Rivarola (1983).

For pt.I see ibid., vol.20, no.13, p.3125 (1987). The authors report quantal and classical calculations of single-electron ionisation and direct excitation in collisions between He²⁺ ions and neutral Li. Calculations by both methods have included a K-shell correction to the ionisation and in both cases the interaction between the active electron and the lithium core was represented by an effective potential described earlier in I. Quantal calculations have been performed using close-coupled atomic-orbital expansions with up to 65 pseudostates in the basis, within the impact parameter formalism described in I. The range of impact energies treated in this work was from 22 to 10000 keV lab. The authors propose a semi-empirical method for estimating a correction due to the finite size of the basis, based on a combination of the close-coupled and first Born ionisation results. CTMC calculations have been carried out in the impact energy range from 40 to 2000 keV lab.

Total cross sections sigma ₊₀ and sigma _+- for single- and double-electron capture by protons, and total cross sections sigma _0- and sigma ₀₊ for single-electron capture and single-electron loss by neutral hydrogen atoms in single collisions with atoms of sodium, potassium and rubidium have been measured in the energy range 0.2-5.0 keV. All electron capture cross sections show a maximum at an energy which depends on the energy defects of the reaction. The electron loss cross sections increase monotonically with increasing collision energy. The results are discussed and compared with previous measurements and theoretical calculations. Some of the cross sections show considerable discrepancies with previous measurements.

Absolute differential cross sections sigma ( theta ) for elastic electron scattering from mercury atoms were measured in the energy range from 25 to 300 eV at scattering angles up to 135'. The smallest scattering angles were 2 and 7' at 300 and 25 eV, respectively. A target cell was used in which the pressure could be controlled precisely. The scattered beam passed through a well defined system of two apertures and a spectrometer, which removed inelastically scattered electrons without diminishing the elastic current. At each scattering angle the primary and scattered beam currents and the temperature of the target were measured at various pressures. A suitable extrapolation of these data to zero target density yields at each scattering angle an absolute value of sigma ( theta ) which is not affected by multiple scattering or disturbing ions. In the range of overlap with Bromberg's absolute values at 300 eV, his values are about 10% small than ours. The internal consistency of existing total cross section measurements is checked and by combining the present data with others the scattering amplitudes mod f mod and mod g mod of Mott's theory are extracted.

Close-coupling calculations that include the continuum and higher discrete states by two different methods, optical potentials and pseudostates, are found to be in fair agreement with existing absolute measurements of elastic and inelastic differential and total cross sections for electron-hydrogen scattering at 54.4, 100 and 200 eV. For elastic scattering the calculations essentially agree in absolute magnitude but differ from the experiments by 10 to 20% at different energies. Calculated values are too low for larger-angle inelastic scattering at 100 and 200 eV but agree for smaller angles. A new experiment and a very detailed coupled-channels-optical calculation have been performed in an effort to resolve the discrepancies. The experiment measures accurate ratios of differential cross sections for inelastic (n=2) and elastic scattering of electrons by atomic hydrogen at several scattering angles at 100 and 200 eV.

The differential elastic and vibrationally inelastic cross sections for e^-N₂ scattering are calculated in the energy range from threshold to 30 eV using the R-matrix method. At low energies the cross sections are dominated by the well known 2 Pi _g resonance. In this energy region non-adiabatic effects due to the coupling of the electronic and nuclear degrees of freedom are included. At higher energies the cross sections are dominated by the ² Sigma _u resonance. In this energy region the adiabatic approximation is appropriate. The cross sections are compared where possible with experiment. In general good agreement is obtained but some discrepancies suggest directions for future work.

An optical potential method is used to formulate a model for the post-collision interaction that occurs in electron-helium scattering after excitation and decay of autoionising states. The model is an extension of an earlier description given by Nienhuis and Heideman, and is used to study the effects of post-collision interaction in ejected-electron spectra. The authors present a calculation of angular distributions of ejected electrons from the He**(2s²)¹S autoionising state. It is argued that study of angular momentum exchange during the post-collision interaction requires detailed knowledge of the interfering background of the direct ionisation process.

Exact analytical cross sections for direct radiative recombination (DRR) on nS, nP and nD states with arbitrary principal quantum number n are obtained in the non-relativistic Coulomb dipole approximation. They may be used in the case of DRR on the Rydberg states of N-electrons ions by considering the ionic charge Z_eff=Z-N instead of the atomic charge Z. Numerical values of the cross sections are given for a large range of incoming electron energies and ionic changes, involving nuclear fusion plasma.

The authors use the variational cellular method (VCM) for the calculation of the ionisation potentials (IP) of benzene. The expected precision of the VCM is the same as that of an atomic calculation where charge and potential are spherically averaged. The calculated IP of benzene, if shifted by a constant, are in better agreement with the experiment than those of a Hartree-Fock or a multiple-scattering calculation. The shifted IP have a precision already comparable with those of a configuration interaction calculation. The constant shift of all IP is much too large, but can be understood as resulting from the assumed full symmetry of the molecular ion.