Table of contents

A quantum treatment for nonlocal factorizable potentials is presented in which the Weyl-Wigner quantum phase space description plays an essential role. The nonlocality is treated in an approximated form and allows for a Feynman propagator that can be handled in standard way. The semiclassical limit of the propagator is obtained which permits the calculation of the transmission factor in quantum tunnelling processes. An application in nuclear physics is also discussed.

Using only elementary algebra, we find that period 3 cycles in the tent map exist whenever the parameter r is larger than or equal to a minimum value r_3m. There are two distinct 3-cycles for each value of r except when it is equal to r_3m in which case there is only one. The cycle elements are explicitly given as functions of r.

We study the decays Z⁰ → H⁰f and W^± → H⁰ff' allowing anomalous ZZH and WWH couplings. We compute the invariant pair-fermion mass spectrum, the fermion f( or f') energy spectrum, and the total decay rate. Some deviations from the standard model result can be observed in the first two of these observables.

In continuation of our previous work on doubly-excited ions with three and four electrons we present the first results on optical transitions in the term system of doubly-excited ions with five electrons. Transitions between such sextet states were identified in beam-foil spectra of the ions nitrogen, oxygen and fluorine. Assignments were first established by comparison with Multi-Configuration Dirac-Fock calculations. Later assignments were aided by Multi-Configuration Hartree-Fock calculations (see the contribution by G. Miecznik et al. in this issue). Decay curves were recorded for all six candidate lines. The lifetime results are compared to theoretical values which confirm most of the assignments qualitatively.

In the present work we study the 1s2s2p³⁶S^o → 1s2s2p²3s⁶P^e and 1s2s2p³⁶S^o → 1s2s2p²3d⁶P^e transitions energies and probabilities in the boron isoelectronic sequence, including B I, C II, N III, O IV, F V, Mg IX and A1 IX. Extending the calculations to Be^-, we also confirm the bound character of the excited 1s2s2p³⁶S^o state and predict the electron affinity EA = 1.29783 eV for Be(1s2s2p²⁵P). The calculations are carried out using a semirelativistic multiconfiguration Hartree-Fock method and the transition properties are analyzed mainly in the light of correlation effects. The present results are compared with recent experimental studies, indicating an overall good agreement for the transition energies, but a larger discrepancy for the transition probabilities.

The energy of the Li^– 1s²2s² state is calculated with a configuration interaction (CI) wave function using a 1s²-core plus correlation method. Relativistic and mass polarization corrections are included. The energy upper bound obtained in this work is substantially lower than that of the Sims et al. [Phys. Rev. A13, 560 (1976)] where an elaborate Hylleraas wave function is used. From our energy upper bound and the core deficiency correction we found that the Li 1s²2s electron affinity is greater than 0.6171 eV. Our extrapolated result, 0.6174(2)eV, agrees with the results, 0.6173(7)eV and 0.6176(2)eV from experiment.

The oscillator strengths of all allowed transitions between the singly excited states of Be II and Be III with principal quantum number up to n = 11 were calculated within the Coulomb approximation with a Hartree-Slater core (CAHS) approach. The results were subsequently combined to obtain the radiative lifetimes of all excited states and are presented here.

The empirical pseudopotential method is used to compute the electronic charge densities at the Γ and X points of the valence and conduction band edges in GaSb. These charge densities are used to study the modification of the bonding properties of GaSb with respect to the lattice constant variations.

Electronic properties near interfaces of transition metals are investigated by a model calculation based on the Hubbard model. It is shown that the binding energy increases when the metals with narrower band widths or larger work functions are in contact. Effects of impurities at the interface are also examined. It is shown that two peaks corresponding to the energy level of the impurity atom get broadened and shifted and that the stronger binding is constructed as the concentration of the impurity decreases.

This paper presents a review of the distribution, nature and properties of dust particles in space, their charging due to plasma and other currents and the effects of their presence on plasma behaviour.

Dust grains immersed in plasma become charged. The charge is determined by the plasma characteristics, by secondary and photoemission from the grain, by grain velocity, and at any given instant by the past time history of the charging currents. This charge affects the Coulomb drag on a grain moving through the plasma. It affects the motion of the grain in an electromagnetic field of a planetary magnetosphere, and it is involved in the formation of the spokes in Saturn's rings and in the erosion of the rings by micrometeorites. And finally it affects the coagulation rate of dust into larger bodies.

We show that a dust test particle moving in a periodic orbit in electrostatic fields, as those due to planetary rings, will experience a net deceleration also in the absence of any dust-dust collisions. The varying charge on the moving dust, as it moves in and out of regions of differing electron and ion densities (due to changes in the ring electrostatic potential), will be out of phase with the equilibrium charge in a way which leads to a net braking of the particle. This effect has been shown to damp the coherent oscillations of electrostatically supported dust rings [1] and to damp the oscillatons of levitated dust particles in plasma sheaths at surfaces of solid bodies [2]. We show that this effect will lead to a damping of internal random velocities in a planetary ring, at a rate which in many cases can be much faster than that due to dust-dust collisions. For moderate radial motions of dust test particles relative to a ring we also find that there can be an efficient braking and pick-up of particles already at the ring edges.

We conclude that when the collisionless braking of random velocities dominates over dust-dust braking, an increased rate of collapse of the ring to its minimum electrostatic thickness may occur and possibly also an increased radial stability of the ring. The pick-up effect at the ring radial edges is a potentially imortant factor in forming their structure.

A review is given of the orbital motion limited (O.M.L.) theory of cylindrical and spherical Langmuir probes. In many cases the O.M.L. theory is invalid and the second orbital motion theory presented here, that of Bohm, Burhop and Massey, shows that the concept of an absorption radius must be introduced. The extensive numerical extensions to this theory are briefly discussed.

Recent experimental work is referred to in which measurements of ion currents to cylindrical probes showed better agreement with the ABR (radial-motion) theory than with the calculations of Laframboise. It is suggested that the mean free path must be greater than the probe radius by a large factor if the calculations of the Laframboise are to apply; the numerical value depends on the ratio of probe potential to ion temperature.

Linear properties of low-frequency electrostatic and electromagnetic modes in dusty plasmas are studied. The wave spectra in the presence of static and non-static charged dust grains are presented. The relevance of our investigation to astrophysical and cometary plasmas is pointed out.

The existence of a new low-frequency electrostatic wave in an unmagnetized collisionless dusty plasma is pointed out.

Plasma density fluctuations, due to the presence of massive, charged dust particles, can alter the usual dispersion properties of waves as shown, in a particular case, by de Angelis et al. [1]. Here a general dispersion relation is derived, as an average over a random distribution of dust particles, and the possibility of complex solutions (wave damping) is pointed out.

Two-stream instabilities in an unmagnetized multi-species dusty plasma are investigated. Four different plasma models are considered. The effect of the dust particles on the instability growth rate and the threshold drift velocity for excitation of the instability are examined.

Low frequency density waves in a planetary ring, will be damped if there is a significant time delay in charging of dust particles. This damping can in many cases be more important than damping due to dust-dust and dust-plasma collisions. We have in this paper derived the response in plasma potential and dust particle charge when the dust density is varied periodically with frequency ω. This response is then applied to oscillations of dust particles in Jupiter's and Saturn's tenuous rings in the direction normal to the central plane of the rings. For tenuous rings we find analytically expressions which approximate the eigenfrequencies and timescales of damping for the oscillation. These expressions are compared with numerically solutions of the original set of equations.

A simple qualitative picture for scattering of waves by a single dust particle is presented. Attention is focused on linear as well as nonlinear transition scatterings in dusty plasmas.

Spherules of pure magnetite, with radii ≲10 micron and number density 10⁻⁵ cm⁻³ are known to be present in the Earth's magnetosphere. Rotating charged dust particles, known to exist in many space environments, also constitute a distribution of magnetic dipoles. We consider the case when these particles are in an ambient plasma and calculate the scattering cross-section for an electromagnetic wave. It is found that enhancements over scattering from plasma thermal fluctuations are possible when the dipoles are aligned in an external magnetic field (e.g. the Earth's field) for waves of wavelength much larger than the plasma Debye length.

A calculation of the scattering cross section of charged dust particles in a plasma is carried out for an incident electromagnetic wave with frequency much larger than the electron plasma frequency. The present derivation employs the dressed test particle theorem of Hubbard and Rostoker. A critical discussion on the applicability of conventional plasma theory - as employed here - is given. It is shown that there is a range of values of the relevant parameters for which the underlying assumptions implied by the plasma approximation are applicable. The results depend crucially on neglecting the collective interactions of the dust particles among themselves. This is justified when the number of dust particles in a Debye sphere is less than one. The calculation is applied subsequently to the case of charged dust in the earth's mesosphere in connection with polar mesospheric summer echoes. Scattering enhancements comparable to observations at 224 MHz are possible provided that the mesospheric dust particles attain charge numbers of several hundred. However, the dependence of the scattering cross section on the radar frequency as calculated here seems too weak to explain the observations.

We discuss to what extent small scale density inhomogeneities in the dust distribution may influence radar backscatter in the summer mesopause. We show for a reasonable range of parameters that falling dust interacting with a neutral gas vortex cannot penetrate to the centre of the vortex. The size of the hole in the dust space density distribution around the vortex centre depends on the vortex size and rotation speed and on the free fall velocity of the dust. If the dust contains a non-negligible fraction of the space charge (this requires that the dust is charged by the photoelectric effect), a substantial gradient in the positive charge density across the dust hole edge results. The positive charge density profile in the thin boundary layer will depend on the size distribution of the dust grains. A corresponding gradient in the electron density will appear and we discuss the conditions under which it will lead to a radar reflection of the magnitude observed in the summer polar mesosphere (PMSE - Polar Mesospheric Summer Echoes). This mechanism appears to have the potential of explaining the observed characteristics of the radar echoes such as the strong wavelength dependence and the narrow and sometimes complex and composite spectral signal profiles.