Table of contents

The Green's functions for charged particles of spin zero and 1/2, which are subjected to the action of the field of an electromagnetic plane wave, are calculated in the path integral formalism. It is also shown that in the case of spin 0, the semi-classical Green's function obtained via a canonical transformation, is accurate. These Green's functions are obtained under a compact form. The waves in the case of spin 0 and the wave functions in the case of spin 1/2 are then deduced.

In many processes of interest in physics, chemistry and biology small particles come together to form large structures. Very often these structures have a disorderly nature that can be described quite well in terms of the concepts of fractal geometry. The fractal geometry of small particle aggregates plays an important role in their physical behavior including the kinetics of the aggregation process itself. In many cases the kinetics of aggregation can be described by a mean field Smoluchowski equation. The geometric scaling properties (fractal geometry) of the aggregating clusters determine the scaling symmetry of the reaction kernel which in turn determines the asymptotic form of the cluster size distribution and the growth of the mean cluster size. In most simple systems the asymptotic cluster size distribution can be described by the scaling form N_s(t) ~ s^−θf[s/S(t)] where N_s(t) is the number of clusters of size s at time t and S(t) is the mean cluster size at time t. This scaling form is superuniversal and can be used in circumstances where the mean field Smoluchowski equation does not provide an adequate representation of the aggregation kinetics. This scaling form also describes the aggregation kinetics for non-fractal systems such as the coalescence of particles and droplets. In this review recent advances in the application of fractal geometry and simple scaling ideas to aggregation, coalescence and fragmentation processes are described.

We recover the known and find some nontrivial new "exactly solvable" subspaces in the parameter space of a generalized Ising model in magnetic field formulated on the Kagome lattice.

A spectroscopic analysis of light in the 2000-6000 Å wavelength range emitted by Kr⁷⁺ and Kr⁶⁺ ions after charge exchange in 120-keV Kr⁸⁺-He and Kr⁸⁺-H₂ collisions is performed. Transitions with Δn = 0 and Δn = 1 for n = 6 and 7 states of Kr VIII following single electron capture are identified and their emission cross sections are determined. Fine structure splittings of the 3d¹⁰6p²P, 3d¹⁰6d²D and 3d¹⁰6f²F terms are measured and compared with theoretical predictions. As in Ar⁸⁺-He and Ar⁸⁺-H₂ collisions, strong lines due to double electron capture are observed both in Kr⁸⁺-He and Kr⁸⁺-H₂ collisions. They are identified as Rydberg transitions of the type 4snl-4sn'l' in Kr VII.

This paper addresses the question whether ion storage rings advantageously could be used for studies of dissociative recombination of molecular ions. We have used a particular ion, HeH⁺, and a particular storage ring, CRYRING, in a case study. Vibrational relaxation times in ground state HeH⁺ have been calculated by means of an electric dipole moment function obtained from multi-reference CI wave functions. Parameters for CRYRING, including its electron cooler section, have been used to estimate storage times for HeH⁺, and expected count rates in a dissociative recombination experiment. It is shown that the expected storage time of HeH⁺ is two orders of magnitude larger than the vibrational lifetimes, hence experiments with vibrationally cooled ions can be anticipated. The expected count rate is such that three orders of magnitude less ions than normally used in CRYRING (10⁹) is sufficient.

Alignment effects at electron excitation measurements of atomic lifetimes have been studied at 20 keV energy using the High Frequency Deflection technique and a plastic polarizer. Disalignment associated with radiation trapping is observed directly for the first time. It has been pointed out that our previous results of the lifetime of the Ar 2p_i levels might possibly have been influenced not only by radiation trapping itself but also by this "radiative disalignment". However, this influence has been found to be negligible thanks to small intrinsic alignment in almost all lines of noble gases investigated.

The energy splittings and wave function of a hydrogen atom in crossed uniform static electromagnetic and non-resonant monochromatic electric fields of arbitrary mutual orientation are obtained within the "one-shell" approximation. The intensities of the Lyman lines are also obtained. A special analytical method is used. Relativistic corrections and spin-orbit interactions are not considered.

A theory of neutron scattering by nuclei in a molecule, accompanied by an electronic transition, is formulated with attention to gauge potentials and geometric phases in the Born-Oppenheimer scheme. Non-degenerate and nearly degenerate electronic levels are considered. For nearly degenerate levels it is shown that, the cross-section is free of the singular structure which characterizes the corresponding gauge potential for the phase, and much larger than for well separated electronic states.

Relativistic multi-configuration Hartree-Fock calculations have been carried out for the energies of the nickel-like 4d to 4p X-ray lines which are potential lasing lines. Measurements of a set of these transition energies have also been made. Predicted wavelengths, covering the range of atomic numbers from Z = 46-92, have been derived by adjusting the ab initio energies by experimentally derived empirical constants.

The algebra involved in the small amplitude expansion of the Vlasov-equation is much simplified by treating the small amplitude parameter ε as a parameter of evolution and defining the corresponding ε-Hamiltonian S. This is exemplified by a new simple derivation of a Manley-Rowe symmetric formula for the coupling coefficient governing resonant interaction of three electromagnetic waves in an inhomogeneous plasma.

A system of equations describing the two-dimensional nonlinear evolution of the two-stream and gradient-drift instabilities in the E-region of the Earth's ionosphere is derived, taking into account turbulent ion viscosity and the nonlinearity associated with the ion inertia. The linear instabilities are briefly re-examined. Regular nonlinear wave forms are found for both instabilities in the one-dimensional limit. Estimates of characteristic values of amplitudes and wavelengths are also presented.

The dynamics of a fusion plasma is described by means of coupled partial differential equations with due regard to boundary conditions. The set of coupled equations for the temperature T and the density n allows for studies of the dynamic variables T and n in terms of expansions in the radial coordinate divided by time-dependent scale-lengths (dynamic widths) of the profiles of T and n, respectively. The scale-lengths may even be regarded as approximately constant in the process of evolution, leading to a description for the central values of temperature and density by two coupled nonlinear dynamic equations, accounting for the effects of diffusion, sources (alpha particle heating and particle injection), losses (bremsstrahlung radiation) as well as pinch effects (off-diagonal diffusion). The coupled equations provide information about equilibria, scaling laws and the dynamic evolution of the system. The results obtained by the simplified radial expansion technique are supported by direct numerical analysis of the coupled equations for temperature and density, and compare favourably with estimates obtained from model experiments simulating processes in a burning fusion plasma.

The characteristic Debye temperature, Ω_D, is one of the model parameters used in the recent theoretical investigation of the effect of superconducting fluctuations on the thermoelectric and electrical conductivity properties of superconductors [Sov. Phys. JETP 71, 325 (1990)]. We apply the results of this model and outline a procedure to extract Ω_D using experimental data on thermoelectric power and electrical resistivity. The value of Ω_D derived by this method is found to be reasonably close to the results independently obtained by heat-capacity studies on a similar Bi-based polycrystalline material. On this ground we suggest that our study provides experimental verification of some of the features of the above theoretical model.