Table of contents

The problem of `quantum chaos' in many-electron atoms is described. Arguments are presented concerning its occurrence in helium. They suggest that very-high-resolution experiments near the double-ionization threshold are required. The situation is contrasted with the one in heavier atoms, where three conditions are given which would be favourable to the emergence of `quantum chaos'. On the basis of these three conditions, suitable spectra are suggested, and a promising example in the alkaline-earths is given.

An exact quantum method is introduced for the inversion of the bound - free continuum spectrum originating in a single discrete vibrational level. It allows one to obtain an unknown bound-state potential and the transition operator from two observed continuum spectra originating on different vibrational levels of that state and a knowledge of the repulsive final-state potential. This procedure is tested numerically with a couple of well known potentials: an exponential and a Morse potential. A comparison of the exact and the reconstructed potentials is discussed in order to illustrate the numerical limitations of this method.

Simple analytic two variational parameters wavefunctions for the ground state of , He, , , atom (ions) are proposed. These functions fulfil the cusp conditions at the singularities of the Coulombic field, and include the correct behaviour for large interparticle separations. The accuracy of the calculated energies is found to be about . These functions should be useful for the computation of the cross section of inelastic processes involving two-electron systems.

We have measured the photoionization-excitation-to-photoionization ratio for (n = 2 - 6) at several photon energies from 90 to 900 eV. By extrapolating these values we could determine the asymptotic high-energy ratios for (n = 2 - 5) which agree with theoretical predictions. We show that the satellite-to-main-line ratios are consistent with experimental double-to-single photoionization ratios and agree well with recent measurements.

This letter concerns low-energy electron excitation from the ground state of xenon to the lowest four excited levels ( and ). We report here on the first results from Breit - Pauli R-matrix theory which investigates coupling to the 6 p and 5 d levels: specifically, in 5-, 15- and 22-level calculations. Differential cross sections at 15 eV are compared with other theories and with experiments. Our present 22-level R-matrix calculation represents the most elaborate on this system to date and gives reasonable agreement with experiments, though some discrepancies remain. We note that perturbative approaches such as recent distorted-wave calculations agree less well with experiments, and we conclude from this and from other evidence that such methods, as currently formulated, are not reliable for describing low-energy scattering from neutral systems. On the other hand, the R-matrix method appears to be capable of systematic improvement via the introduction of further states and pseudostates.

The emission probability of quasimolecular x-rays in - Ar collisions is calculated in first order with respect to the interaction with the radiation field. For the calculation of the dynamic electronic wavefunction on the level of time-dependent Dirac - Fock - Slater a basis of many-electron two-centre Dirac - Fock - Slater wavefunctions is used and radial as well as rotational couplings are included. The calculated spectra as functions of impact parameter and energy are in good agreement with the experimental data.

We report here on an (e, 2e) measurement at relativistic electron energy (300 keV) on the K shell of copper . Using coplanar asymmetric kinematics the angular distribution of the relative triply differential cross section was measured and is compared with a calculation using relativistic distorted-wave Born approximation. We find a distinct structure in the recoil region which is in reasonable agreement with the theoretical data.

The experimentally observed double structure of the triply differential cross section in the recoil region of the ionization of the copper K-shell by relativistic electrons is analysed by calculations based on the relativistic distorted-wave Born approximation. We study separately the influence of the atomic potential on the incoming and outgoing electrons. Evidence is presented in support of the interpretation that different mechanisms account for the two maxima in the recoil regime.

A narrow S-wave resonance has been found in the positron - helium system at about 30 eV, using the close-coupling approach, in excitation and rearrangement cross sections to He(1s2s), He(1s2p), Ps(1s) and Ps(2s) states by employing different combinations of the following basis functions: He(1s1s), He(1s2s), He(1s2p), Ps(1s) and Ps(2s), where Ps stands for the positronium atom.

We show, by an exact numerical simulation, how to prepare a non-spreading electronic wavepacket in Rydberg atoms, using the nonlinear interaction of the Rydberg electron with a circularly polarized microwave field. The wavepacket can be prepared by a mixed diabatic/adiabatic switching on of the microwave field, which is studied in detail for realistic conditions.

In the asymmetric doubly excited states of the two-electron atom one electron is excited much more than the other. The characteristic separation of the strongly excited electron from the atomic nucleus significantly exceeds that for the weakly excited electron . The electron - electron interaction is approximated by the first non-trivial (dipole) term of its expansion over . The same approach is easily extended to the general Coulomb three-body problem with the particles of arbitrary mass and charge. The dynamics of three-body states with and symmetry is analysed in quantum, semiclassical and classical approximations in comparison with the S and states considered previously. Mathematically, the problem is reduced to two coupled three-term recursion relations which were not studied previously. The exact and approximate (semiclassical) degeneracies of the levels with different values of the total orbital momentum L are revealed, and the energies of the `planetary atom' states are estimated.

Accurate static dipole and quadrupole polarizabilities and hyperpolarizabilities which incorporate the effects of electron correlation have been calculated for boron from MRDCI and CCSD(T) treatments with large Gaussian basis sets. Frequency-dependent dipole and quadrupole polarizabilities at real and imaginary pulsations have also been determined for the ground state using our time-dependent gauge-invariant method. Dynamic values presented here are new.

A new expression for the electron self-energy in a strong Coulomb field is obtained without expansion in powers of ( is the fine structure constant, Z is the charge of the nucleus). This expression contains the multiple commutator expansion, which differs from the expansion and converges rapidly even for very high Z values. The renormalization procedure requires the proof of a new sum rule. This proof is given explicitly for Z = 1 and implicitly for all Z values for the state. The numerical calculation of the Lamb shift for different Z values is performed and comparison with the known results made.

The spectrum of has been treated by the complex coordinate rotation method within an extensive basis sets of -correlated configurations. The energy position and width obtained for the lowest shape resonance are in very good agreement with the available experimental and theoretical data. The resonant parameters for five 1s, n = 3,...,7, Feshbach states, forming a regular two-electron ionization ladder, confirm a recent theoretical prediction of Themelis and Nicolaides (1995 J. Phys. B: At. Mol. Opt. Phys. 28 L379). 16 other, hitherto unknown, doubly excited Feshbach and shape resonances have also been discovered in the energy region up to the threshold. The Feshbach part of this spectrum shows regular character. The number of resonances connected with the L thresholds increases with increasing n.

Fluorescence yields are reported for Rydberg series members in He-like ions of N, O and Ne. Results are presented for singlet series members with n values between 3 and 9, i.e. up to the region of overlap with the states belonging to the manifold in these atoms. This data is required, for example, for the interpretation of charge-exchange experiments involving bare N, O and Ne nuclei. Fluorescence yields, averaged over all singlet states, larger than 50% are obtained from about n = 7.

The influence of the plasma coupling between the populations and the coherences on the lineshape is investigated. Ion dynamics is taken into account. The present research is performed within the atomic density matrix formalism. Ion microfield dynamics is simulated by the kangaroo - Poisson stochastic process (model microfield method). Numerical calculations of both lifetimes of radiating states and lineshapes are performed for the spectral doublet (1s - 2s) - (1s - 4p), (1s - 2) - (1s - 4d) of helium-like multicharged ions in hot dense plasmas. It is found that the ion microfield essentially influences the difference of populations of radiating states. Calculation of the lineshape of the doublet (1s - 2p) - (1s - 4d), (1s - 2p) - (1s - 4f) of neutral helium at astrophysical plasma conditions is also performed. The contribution of nonlinear interference effects (NIEF) in both allowed and forbidden components is calculated at various plasma conditions and a comparison with binary adiabatic theory is made. The results demonstrate that it is essential to take account of NIEF in the calculation of lineshapes of multicharged ions, but not essential in the case of neutral helium.

Ion charge state distributions due to vacancy cascades following K-, -, - and -shell ionization are calculated using a Monte Carlo technique. Probabilities P(q) that the de-excited ions become q-fold ionized after a single primary ionization are given as a function of the atomic number in the region Z = 10 - 60. The calculations are accomplished by tracing successive radiative and non-radiative transitions and electron shake-off as an additional effect. Thereby, radiative and non-radiative transition rates and shake-off probabilities have been calculated from relativistic wavefunctions.

We have combined a laboratory frame independent particle approach with a body-fixed frame collective coordinates approach to derive new exact parametrizations of the triple differential cross section for double photoionization. The latter disentangle the kinematical from the dynamical effects to the largest possible extent. In addition, they provide an expansion of the so-called correlation factor with respect to the configurations of the electronic pair. The present approach is particularly suitable for the physical analysis of experimental data, as illustrated by the applications reported in the companion paper.

We use the general formalism established in the companion paper I to analyse recent measurements of the triple differential cross sections for double photoionization of He and Ne, for equal energy sharing and for symmetry of the residual ion. A dynamical factor, which depends on the energy and on the mutual angle between the two electrons, is extracted from the experiments without relying on any dynamical approximation. This factor is expanded with respect to the one-electron angular momentum , up to a maximum value , which measures the degree of angular correlation attained by the electron pair. We discuss the physical meaning of , and the dependence of the dynamical factor on the target, which is observed when comparing helium and neon results.

The R-matrix method is used to investigate electron-impact excitation of neutral carbon over an energy range of interest for fusion plasma modelling. Two independent calculations are carried out. In the first, all levels of carbon with are included in the expansion of the total wavefunction and cross sections including exchange are calculated for collision energies from threshold to 150 eV. In the second, all levels with are included in the expansion and spin-allowed cross sections excluding exchange are calculated from threshold to 60 eV. Cross sections and effective collision strengths are presented for important transitions.

We demonstrate a number of two-colour spectroscopy techniques where the first step is the photoassociation of laser-cooled and trapped sodium atoms to form bound states of . High-resolution spectra of are obtained. Spectra of the `purely long-range' state demonstrates the use of two-colour spectroscopy to open up an ionization channel for detecting the occurrence of photoassociation. The utility of photoassociation as a technique for producing cold molecular samples in a well defined rovibrational state is demonstrated with spectra showing and (Condon internal diffraction) transitions after the photoassociation. Starting from states in the and potentials, these transitions include upward transitions to autoionizing potentials dissociating near 3P + 3P and downward transitions back to the 3S + 3S ground-state potentials. Spectroscopic constants for six levels of a doubly excited state of are given.

A Hamiltonian is proposed to describe the coupling between vibration and rotation in a molecular system. The time behaviour of such a system exhibits both regular and irregular motion for different energies and different values of the coupling parameter. There is a dramatic manifestation of the transition between the two types of dynamics that define parametric regions of regular and irregular behaviour. The Lyapunov exponent, phase portraits, Poincaré sections and power spectra are calculated. The computer simulations show that the vibrational anharmonicity favours the regular behaviour of the system.

Cross sections for the dissociative recombination of ions have been measured in the energy range from 0.01 - 1.0 eV. The large values measured for low-energy electrons are supported by an earlier extensive quantum mechanical study by Talbi and co-workers which is reviewed. A broad maximum has been found in the region from 0.3 - 0.8 eV and this is attributed to the opening up of a second product channel leading to CH + O.

A new method for calculating equilibrium and transport properties of mixtures containing heavy globular molecules is proposed. The interaction between equal and unequal molecules is described by means of isotropic temperature-dependent potentials (ITDP). The deviations of the calculated mixed and interaction second virial coefficients from the corresponding experimental values are 3 - 5 times lower than those obtained when the traditional extended law of corresponding states is used. The most accurate measured mixture viscosity data have been reproduced by means of the same potential parameters within an accuracy of better than 1%. The effective parameters of the isotropic potentials for the interactions between equal and unequal molecules are given, to enable accurate calculations at arbitrary temperatures and proportions of the constituents. and are plotted as functions of the temperature and the mole fractions of the components and the graphs can be used for approximate evaluations.

The rotational excitation cross sections and rate constants for He - collisions are calculated in coupled state approximation by the R-matrix propagation method. The results are compared with other theoretical results as well as with experimental data. It is found that the present results are better than other theoretical data.

Charge state dependence of L-shell x-ray production cross sections in bombarded by 4 - 14 MeV ions with charge states from q = 3+ to 8+ was measured using a Si(Li) x-ray detector with a resolution of 96 eV at 1 keV. An ultra-thin copper foil was used to ensure single-collision conditions. The data for the total L x-ray production cross sections are compared to the predictions of the first Born and the ECPSSR calculations for L-shell ionization converted to x-ray production cross sections using a single-hole fluorescence yield. Except at the lowest projectile velocity, the ECPSSR theory gives satisfactory agreement with the data while the first Born theory overpredicts all the data in the investigated energy range by almost two orders of magnitude. Measurements of the charge state dependence of the target L-shell x-ray production cross sections allowed the separate contributions of the electron capture (EC) and the direct ionization (DI) to the inner-shell ionization to be determined. The EC contributions were extracted from the x-ray measurements with two, one, and no K-shell vacancies in the oxygen ions. These EC cross sections are compared with the results of an OBK approximation and the ECPSSR theory, and found to be significantly smaller than both EC calculations.

The electron impact approximation (EIA) for electron loss or target ionization in encounters with heavy atoms or ions is extended to relativistic collision velocities. The theory is formulated in the single-particle semiclassical approximation which is valid for collision energies up to some hundred GeV . Predictions are made for the doubly differential electron loss cross section in H +Xe collisions and are contrasted to results from the first-order Born approximation. For the ionization of carbon by 13.6 - 93 MeV incident and ions the EIA is compared with available experimental data. Whereas the theoretical angular and velocity dependence of the energy-integrated binary encounter peak yield is generally in good accord with experiment, the peak shape is only correctly predicted for the thinnest targets.

Symmetric (e, 2e) experimental studies on helium over a very wide range of scattering geometries at energies from 1 to 50 eV above the ionization threshold are parametrized in terms of a set of universal irreducible tensorial angular functions. Measurements from the Manchester and Paris experimental groups are used in this parametrization, which provides a complete picture of the symmetric ionization process. The use of the parametrization technique for deconvolution of the experimental angular resolution from measured results is discussed.

We have studied the inner-shell excited states of argon below the 2p thresholds for electron-impact excitation in the range of the incident energy . We carried this out through the measurement of the electrons emitted during the decay of the states. The corresponding satellite peaks in the spectra of the emitted electrons were separated from the normal (diagram) LMM Auger peaks by a special evaluating process. We observed the satellite peaks coming from the , and transitions at all applied incident energies. The intensity of the satellite peaks increased approaching the ionization threshold (). Nevertheless in the range - 1700 eV we could identify more satellites due to the lower continuous background and the smaller post-collision interaction effects.

We present analytical and numerical results on the cross section of the two-photon bremsstrahlung (2BrS) of a non-relativistic projectile scattered in a point Coulomb field. The effect of the radiation retardation is taken into account.

The exact analytic evaluation of the point Coulomb two-photon non-dipole free - free matrix element, which characterizes the amplitude of the 2BrS process, is carried out following a method of momentum space integration developed by Gavrila. The obtained formulae are the generalization of the expressions derived earlier by several workers within the framework of the non-relativistic dipole approximation. Results of numerical calculations are compared with predictions of other theoretical approaches and with the experimental data on 2BrS.

Msezane and colleagues have developed a `universal formula' to interpolate between the optical oscillator strength (OOS) and generalized oscillator strengths (GOS) as a function of the square of the momentum transfer K. They have inferred regions of applicability of their formula, then made deductions about theoretical and experimental differential cross sections and estimated integral cross sections for optically allowed transitions in atoms and molecules. This comment raises some questions about their work.

The universal extrapolation (not interpolation) formula is justified through a complex angular momentum Regge pole representation of the electron differential cross sections. It is further demonstrated, using the recent forward electron scattering method for optically allowed transitions, that some of the sophisticated theoretical calculations are unreliable at and near zero scattering angles.

In this recent article the following typographical errors occurred:

On page 5291, footnote ^c to table 2 should read: `^c Laboratory-frame microwave spectrum (Saito et al 1989).'

On page 5292, the sixth sentence of the second paragraph on section 3.3 should read: `Furthermore, the CAS reference space had to be reduced to include only those configurations with expansion coefficients 0.01.'

On page 5303, the full reference for Werner and Knowles (1988) should read: `Werner H-J and Knowles P J 1988 J. Chem. Phys. 89 5803'

The publishers apologize for these errors.