Table of contents

The hyperspherical expansion in the He atom problem is studied. The methods used permit a great number of basis hyperspherical harmonics to be retained in a simple way. The E_B value obtained for K_max=40 is 2.9018 au. The extrapolation to K_max= infinity gives E_B=2.9038 au. A new basis is proposed having technical advantages similar to those of HH but which ensure a faster convergence.

For the 5d7d¹D₂ perturbing state of barium hyperfine structure and isotope shifts are reported. From these measurements the amplitudes of the exactly LS-coupled 6snd ¹D₂ and 6snd ³D₂ components of the 5d7d ¹D₂ state vector are derived. These admixture coefficients are in excellent agreement with amplitudes predicted by a recent three-channel quantum defect analysis (the authors, 1982). On the contrary, the results are in disagreement with amplitudes derived previously from Stark-shift measurements.

The impact shifts of the resonance lines of lithium in the presence of He, Ne, Ar, Kr and Xe are reported. The results are compared with the predictions of a semi-classical collision model using the Pascale and Vandeplanque interaction potentials (1924).

The authors report the result of a theoretical study on the photoionisation of the 2p subshell of the sodium atom with its valence electron either in its ground state or at various different stages of excitation. The contribution from important many-body interactions to the photoionisation cross section is examined. The calculated cross section and the angular distribution of the ejected photoelectron are presented.

To study the modifications of lifetimes near perturbed levels observed for the A 0_u⁺ state of ¹³⁰Te₂ the authors have made preliminary measurements concerning lifetimes of the unperturbed levels v'=16 (J=53, 87, 103) and v'=17 (J=103) at zero pressure and quenching cross sections by laser-induced fluorescence.

K X-ray emission cross sections have been measured to an uncertainty of +or-6% for 1 to 3 MeV deuterons incident on thin layers of selected elements with atomic number (Z₂) from 22 to 32. The experimental technique is outlined and the results compared with the predictions of modifications to the plane-wave Born approximation (PWBA) and the semiclassical approximation (SCA). Agreement is better with the PWBA, corrected for 'binding energy' and 'Coulomb' effects, with the theory underestimating the data by only 12% on the average. This deviation exhibits negligible projectile energy or Z₂ dependence.

Distributions of captured electrons in the reaction A^q++He to A^(q-1)+(n,l)+He⁺ over the final-state quantum numbers n and l are measured using a beam spectroscopy method at the energy of 1.0q keV. Projectile ions A^q+ are Li-like species of carbon (q=3), nitrogen (q=4) and oxygen (q=5).

The problem of extracting selective information on the distribution of final-state (nl) population following high-energy electron capture is addressed. As a prototype reaction, the authors study the quasihydrogenic system C⁴⁺(1s²)+T going to C³⁺(1s²nl)+T(?) at energies 2<or=E<or=5 MeV, where T=H₂ or He. Theoretically, two multiple scattering approaches (IA and CDW) are generalised to include capture to high-lying states (nl arbitrary), and experimentally the EUV emission spectra subsequent to the capture process are examined. The experimentally deduced cross sections for final states 3<or=n<or=10 and l=0, 1, 2 are then compared with theory. The data satisfy the n^-3 law and the experimental trends are equally well reproduced by the IA or CDW calculations. In contrast, the first and second Born cross sections are found to be inadequate to represent the data. This in turn gives further evidence of the inadequacy of the latter theories and provides a measure of the importance of multiple scattering effects in capture processes. To the authors' knowledge, these results represent the first quantitative comparison between theory and experiment in this high-energy regime and at this level of discrimination.

A modification of the linear algebraic equations method is described which ensures a variational bound on the phaseshifts for potentials having a definite sign at all points. The method is illustrated by the elastic scattering of s-wave electrons by the static field of atomic hydrogen.

The two-potential coherent approach of Hayashi and Kuchitsu (1976) (in which multiple scattering within the molecule is allowed) is applied to calculate elastic differential, integral and momentum transfer cross sections for e-CO₂ scattering at 50, 70, 90, 300, 400 and 500 eV. Agreement with experiment is very good at all energies.

Analysis of rotational branch structure in high resolution electron energy-loss spectroscopy is greatly facilitated by a high j approximation to the Clebsch-Gordan coefficient. A more accurate approximation than Read's (1972) is found for molecules in the Sigma state. When assimilated into the theory of Chang (1977), the resulting expressions for the branch differential cross sections for N₂ and CO turn out to be easily evaluated by hand. In both cases, good agreement is found with experiment in both the shape and the magnitude of the cross sections at an electron energy of around 2 eV.

Matrix calculations are carried out for different ranges of the Yukawa interaction for eight particles distributed in the N=2 harmonic oscillator shell. The eigenvalue spectra, corresponding to an exact symmetry subspace of dimensionality 287, are analysed for fluctuation properties such as near-neighbour spacing distributions and short- and long-range correlation measures, Q and Delta ₃ respectively. Both short- and long-range ordering decrease as the range of the interaction is increased or decreased from the nuclear range.

Siegert's representation (1960) for the grand canonical partition function of a fermion system with two-particle interactions serves as a starting point for a perturbation expansion around stationary points. It is shown that, in general, the latter are given by solutions of the time-independent Hartree equation. Introducing more general random fields, exchange terms are obtained in the stationarity equation. The procedure is extended to relativistic systems. A perturbative expansion for e.g. the ground-state energy of the N-particle relativistic bound-state problem is obtained which allows, contrary to 'Hamiltonian methods', a straightforward application of standard regularisation and renormalisation procedures.

For pt.I see ibid., vol.15, no.23, p.4293 (1982). The one-parameter non-uniqueness of stationary electron configurations in atoms can be used to single out a mean-field equation yielding the exact total energy. This equation is Hartree-like and contains exchange terms with a strength parametrising electron correlations, radiative corrections and further perturbative contributions. A numerical study of this equation is presented for the relativistic case.

L-shell correlation energies are computed for the nonrelativistic states of 2s²2p², 2s2p³ and 2p⁴ of Fe²⁰⁺. These results are combined with Pauli approximation intermediate coupling calculations to derive residual correlation corrections to relativistic multiconfiguration Dirac-Fock calculations. The excitation energies are significantly improved, and it is concluded that such hybrid schemes may be considered reliable to within 2000 cm^-1, at least for ions at this stage of ionisation.

Electron momentum density contour maps of the first-row diatomic hydrides are determined from near-Hartree-Fock wavefunctions. The total and molecular orbital momentum density distributions are studied in terms of the binding in the molecules; trends are discussed and comparisons with the corresponding position space charge density maps of the same series of molecules (Bader et al., 1967) are made. Momentum density difference maps (for molecules and isolated atoms) are then presented to show the redistribution of electron momentum density upon molecular formation. There is a distinctive trend in the difference maps as atom A in AH goes from Li to F that may again be related to molecular binding.

An approximation scheme valid for high field strengths and arbitrary detuning is applied to the calculation of fluorescent spectra for various numbers (n) of emitting atoms. The presence of detuning is shown to prevent the possibility of solving this problem in closed form for arbitrary n. The one- and two-atom spectra are derived explicitly and compared with the known exact results.

A beam of Mn⁺ ions in the ground level 3d⁵(a⁶S)4s a ⁷S₃ and metastable level 3d⁵(a⁶S)4s a ⁵S₂ (9472 cm^-1) was produced in a discharge of Mn vapour. The ions were selectively excited by the frequency-doubled radiation of a pulsed dye laser to the levels 3d⁵(a⁶S)4p z ⁷P_J (J=2, 3) and 3d⁵(a ⁶S)4p z ⁵P_J (J=1, 2, 3). The radiative lifetimes of these levels were measured by the time-resolved observation of the re-emitted fluorescence. The results are compared with the other experimental and theoretical values.

The complete electron spectra caused by photoionisation of Li and Na vapour in the 1s and 2p shells respectively, have been investigated in the region from 5 eV above threshold up to about twice the binding energy of the ionised electron. Even though the contribution of molecules to the vapour pressure was only of the order of a few per cent, molecular features are found in the experimental spectra with intensities comparable with the atomic structures. The interpretation of all features observed in the spectrum is given. In specific energy regions, where the molecular contributions do not disturb the atomic ones, a detailed study of the fine-structure branching ratio and of the satellite structure accompanying these ionisation processes has been made. The results of this investigation are compared with other experimental and theoretical data.

According to laser theory the lineshape of a laser broadened by Ornstein-Uhlenbeck phase fluctuations is non-Lorentzian. The equations describing the interaction of such a laser with atomic systems are cast into a form which has the same structure as the density-matrix equations in the absence of fluctuations but with modified detunings, damping parameters and interaction matrix elements. By these means the authors derive substitution rules for taking into account the effect of these non-Lorentzian lineshapes which generalize those already known for Lorentzian lineshapes arising from Wiener-Levy fluctuations. The theory is applied to two-photon ionisation and analytic expressions are obtained for the rate of this process. For the extended two-level model the authors' results agree with those of Yeh and Eberly (1981) in the appropriate limit, but they also consider a more general model which leads to enhanced single-photon ionisation rates.

The rotational structure in the ² Sigma ⁺-² Pi _3/2 subsystem and the B-X system of the SbO molecule, photographed earlier under high resolution, has been reanalysed. It is concluded that all earlier reported rotational analyses are incorrect and the B² Sigma ⁺ state has an appreciable spin splitting. New molecular constants for the two combining states are presented.

Photoabsorption and fluorescence cross sections of CS₂ have been measured in the 1060-1520 AA region using synchrotron radiation. In the 1060-1200 AA region the absorption is smooth and continuous, except that a strong absorption band ( sigma _a=2.1*10^-16 cm²) shows at 1117 AA. For wavelengths longer than 1200 AA, the absorption spectrum shows the structure of Rydberg states. The fluorescence in the 1900-3000 AA region starts to appear at 1335 AA. This fluorescence is mainly the CS(A¹ Pi to X¹ Sigma ⁺) transition in the 2400-2800 AA region. The fluorescence in the 1900-8000 AA region starts to appear at 1490 AA. In addition to the CS(A¹ Pi to X¹ Sigma ⁺) system, the fluorescence is probably composed of the transitions of S(¹S₀ to ³P₁) at 4589AA and of CS(d³ Delta , a'³ Sigma ⁺, and a ³ Pi to X¹ Sigma ⁺) at 3000-4000 AA. The quantum yields for the production of fluorescence have maxima of 13 and 7.5% at 1235 AA for the fluorescence in the 1900-8000 and 1900-3000 AA regions, respectively.

A scaling law that describes the most probable vibro-rotational excitation in ion-molecular collisions has recently been extended by Sigmund (1978) to cover polyatomic targets. The predictions of this scaling law are examined for collisions of Cl^- and K⁺ with the targets O₂, N₂, CO, CO₂, and CH₄ in the energy range 50-200 eV. The experimental results do not all scale according to the theory. The study does demonstrate the usefulness of the scaling variables when examining the most probable vibro-rotational excitation in ion-molecule collisions. A collection of isoelectronic scattering results is presented.

The total probability for electron capture from CH₄ by 200-2000 keV protons scattered through 15 or 20 degrees in the laboratory system by the carbon nucleus has been measured. The probability decreases strongly with increasing proton energy, and a clear structure is seen around 400 keV. Complementary differential coincidence measurements of capture by protons from the K shell of carbon (CH₄) show that the structure is caused by the K-shell capture component of the total capture probability, which becomes significant in the energy range 200-500 keV. Above 1 MeV, the K-shell capture component dominates the total capture probability. The angular dependence (10-50 degrees ) of the total capture probability was determined at 500 keV, where the K-shell capture component at 20 degrees contributes with (80+or-15)%. An experimental measure of the widths of the impact parameter distributions for K-shell ionisation and capture, respectively, as functions of the collision energy, was obtained on the basis of the pertinent experimental total cross sections and measured probabilities for small impact parameter collisions with nearly straight-line trajectories. The width of the K-shell ionisation distribution increases with increasing projectile kinetic energy, whereas the width of the K-shell capture distribution exhibits a maximum. Particular attention has been paid to the capture probabilities in an energy region around the elastic scattering resonances ¹²C(p,p)¹²C near 1.7 MeV.

The asymptotic theory of resonance charge exchange between a ground-state diatomic molecular ion and its neutral parent is presented. The parameters of the valence electron wavefunction and asymptotically precise exchange interaction potential are calculated. The role of rotational transitions is discussed. The vibrational excitation transfer is taken into account and the coupled equations, describing the charge exchange process between diatomics, are solved both in limiting cases and numerically. The total charge transfer cross sections are calculated for many diatomic systems and the results are compared with experimental data.

It is proposed to use the adiabatic formalism in combination with the S-matrix description on the interaction between electrons in the problem of electron scattering on atoms and multiple-charged ions. In the present paper the rules of construction of the scattering amplitude are formulated on the basis of Feynman diagrams. The relativistic version of the Born approximation is given. For the transitions 1s-1s and 1s-2s the contributions of retardation and magnetic interaction in the differential cross sections are estimated. The numerical results for elastic and inelastic electron scattering by hydrogen-like ions with charge Z from 1 to about 50 at incident energies from 10 eV to 250 keV are presented.

For pt.III see Phys. Rev. A, vol.16, p.80-108 (1977). A non-perturbative approximation, suitable for electron scattering from both weakly and strongly polar molecular, has been proposed. The coupling in the scattering equations due to the presence of the non-central electron-dipole interaction is removed by merely shifting the relative positions of the rotational levels but without either making them degenerate or neglecting their energies. This method has been used to simplify application of the frame-transformation theory (FT) to electron scattering from polar systems. The problem in the outer region of the FT can now be solved without numerical integration and the solution written in a form suited for an R-matrix treatment of the molecular core. The proposed procedure achieves very high level of efficiency and economy of calculation without much sacrifice of accuracy. This method has been applied to electron scattering from weakly polar carbon monoxide. The integrated cross sections for various rotational transitions have been calculated from 0.005 to 10.0 eV and compared with previously obtained accurate results. The usefulness of this method for electron scattering from strongly polar neutral and ionic systems has been discussed.

Satellite lines emitted by a three-level atomic model in the presence of longitudinal electrostatic plasma waves and a non-resonant laser radiation field are investigated by calculating the autocorrelation function of the emitted light wave up to fourth order in the perturbation energy of the atomic system. Both the plasma wave and the radiation fields lead to a shift of the second-order Baranger and Mozer (1961) plasma satellites and of the allowed line. The intensities of the plasma satellites are enhanced by the laser radiation field. Under certain frequency conditions satellites pertaining to the radiation field appear in absorption. The same phenomenon occurs for the plasma satellites when the atoms are subjected to a single-mode plasma wave field.