Table of contents

The spectrum of 3d³–3d²4f transitions in Ni VIII was investigated using the extrapolation of the energy parameters in the isonuclear sequence of nickel ions. The earlier analysis of these transitions was revised and extended. Forty four lines were newly classified in the Ni VIII spectrum. As a result, the energies of 13 3d²4f levels were changed and seven energies of this configuration were determined for the first time. The least-squares fitting in a frame of Hartree–Fock calculations confirmed the results of the present analysis.

By applying a special Bäcklund transformation and extended homogeneous balance method, a quite general variable separation solution for the (2+1)-dimensional higher order Broer–Kaup (HBK) system is derived. In addition to some types of the usual localized excitations, some special types of the kink soliton solution, periodic soliton solutions and lattice soliton solutions are constructed by selecting appropriate functions in the general variable separation solution of this system.

The fractional Hamiltonian formulation and the fractional path integral quantization of fields are analysed. Dirac and Schrödinger fields are investigated in detail.

The Schrödinger equation for an electron on the surface of an elliptical torus in the presence of a constant azimuthally symmetric magnetic field is developed. The single particle spectrum and eigenfunctions as a function of magnetic flux through the torus are determined and it is shown that inclusion of the geometric potential is necessary to recover the limiting cases of vertical strip and flat-ring structures.

In this paper, a quantum action-angle variable in two dimensions is defined in the context of the quantum Hamilton–Jacobi theory, and then a quantization rule, which can give the exact bound state energy spectrum without solving the motion equation for the wavefunction, is derived from the singularities of the quantum momentum function. As illustrative examples, the Coulomb potential and the harmonic oscillator are considered.

Ab initio and DFT computations are used to investigate the vibrational normal coordinates of the protonated Schiff base (PSB) 4-cis-γ, η-dimethyl-C₉H₉ NH₂⁺. The ground and the first excited states are investigated. Our results suggests that the torsional motion involving the central C=C bonds that plays a significant role in the isomerization process involves mostly the central part of the carbon skeleton of the PSB. Together with the information coming from the simulated IR spectra these results offer a qualitative description of the dynamics of the system on its first excited state.

This paper presents a model of an irreversible quantum Brayton refrigerator (IQBR) using ideal Bose gases as working fluid. The optimal relationship between the dimensionless cooling rate and the coefficient of performance, and the optimization region (or criteria) for an IQBR is obtained. The effects of heat leakage, irreversibility in two adiabatic processes and the quantum characteristic of the working fluid are discussed.

Within the nuclear Fermi-liquid approach, the memory effect on the Landau–Vlasov–Langevin dynamics is considered. The basic collisional kinetic equation for the Wigner distribution function is reduced to a macroscopic equation of motion for the shape variables of the nucleus. Parametrizing the potential energy of the nucleus at descent from the fission barrier by the inverted oscillator potential, we derive analytical expressions for the mean value, ⟨E_{kin, ps}⟩, and the variance, σ(E_{kin, ps}), of the pre-scission kinetic energy. We show that the memory effect hinders the values of ⟨E_{kin, ps}⟩ and σ(E_{kin, ps}) due to an additional elastic force originating from the memory integral. The hindrance effect increases with the increase of the relaxation time.

K to L and M shell vacancy transfer probabilities were measured in Cr_xNi_1−x and Cr_xAl_1−x alloys. The samples were excited by γ photons with an energy of 59.5 keV from a ²⁴¹Am radioisotope source and K x-rays emitted from samples were detected with a high-resolution Si(Li) detector. Comparisons between present experimental results and theoretical predictions were made.

x-ray emission in LiNbO₃ is confirmed by thermal treatments in a vacuum system by a new cleaning method of the crystal. Detailed single-crystal high-temperature x-ray structure refinements were carried out at 297, 323, 373, 423 and 473 K, far below the phase transition (∼1473 K). The unit cell dimensions a and V show a linear increase with temperature; however, the lattice parameter, c shows only a slight linear increase. The length of Nb–O bonds in adjacent octahedra is almost constant below 423 K. It is suggested that the valence electron in Nb changes in the compound. Therefore, x-ray emission induced by charged particles including electrons can be considered to have a close relation to the electric charge of Nb in LiNbO₃.

An analytical theory for calculating shifts in eigenvalues to Schrödinger problems due to geometrical perturbations is proposed. The possibility of growing practically any nano-heterostructure today makes it interesting to examine the influence of shape and size on, e.g., electronic, optical and magnetic properties. For that, detailed knowledge of shifts in eigenvalues induced by changes in geometry, either intentionally or unintentionally, is important. Several examples are presented so as (a) to verify the geometry-perturbative model against exact calculations and (b) to attack problems which cannot be solved exactly without resorting to numerical partial differential equation (PDE) techniques. The latter include the cases of a particle confined to a three-dimensional cylinder with a sinusoidally varying radius as a function of the axial coordinate in the presence (or absence) of a dc electric field along the cylinder axis.

Two theorems on the Riemannian geometrical constraints on vortex magnetic filaments acting as dynamos in (MHD) flows are presented. The use of Gauss–Mainard–Codazzi equations allows us to investigate in detail the influence of curvature and torsion of vortex filaments in the MHD dynamos. This application follows closely previous applications to Heisenberg spin equation to the investigations in magnetohydrostatics given by Schief (2003 Plasma Phys. J.10 2677). The Lorentz forces on vortex filaments are computed and the ratios between the forces along different directions are obtained in terms of the ratio between the corresponding magnetic fields which also equals the ratio between the Frenet torsion and vortex line curvature. A similar relation between Lorentz forces, magnetic fields and twist, which is proportional to total torsion integral, has been obtained by Ricca (2005 Fluid Dyn. Res.36 319) in the case of inflexional disequilibrium of magnetic flux tubes. This is due to the fact that the magnetic vortex lines are a limiting case of the magnetic flux tubes when the length of the tube is much greater than the radius of the tube. The magnetic helicity equation of the filament allows us again to determine the magnetic fields ratio from Frenet curvature and torsion of the vortex lines. Recently, Schekochihin et al (2001 Phys. Rev. E 65 016305) obtained a similar relation between the ratios of magnetic field components by using a detailed analysis of the statistics of curvature. However, in their work no reference is made to torsion or helical vortex filaments.

Spatial distribution of electromagnetic wave fields within the local Alfven resonance (AR) region is studied under the conditions when this distribution is governed just by a helical inhomogeneity of the confining magnetic field rather than electron inertia or finite ion Larmor radius. It is shown that accounting for the helical inhomogeneity of the steady magnetic field can remove the infinite discontinuity of the wave fields that takes place in the case of straight magnetic field rather than other weak effects. Radio frequency (RF) power absorption within the local AR region is compared with the case when AR structure is governed by other weak phenomena.

The availability of small solid-state lasers, efficient CCD detectors and compact optics has permitted the development of portable Raman spectrometers, which are of great interest for some applications, like cultural heritage or geochemistry. Some of them are 'home made' designs built by combining different elements that are commercially available. In the design phase of these instruments it is of great help to use computer tools, like ray-tracing, that permit the calculation of the spectrometer's performances, and the selection and optimization of the most suitable design. In this paper, we present a ray-tracing study of a laboratory dispersive Raman spectrometer performed with a freely available software package. We calculate the instrumental functions, resolving power, resolutions, aberrations, etc and benchmark some of the results with experimental values. We demonstrate the suitability of these codes for modelling Raman dispersive spectrometers, and their utility, not only in the design phase, but also during the operation of the spectrometer in order to check if it works close to the theoretical performance.

General fluid dispersion relations for the Jeans instability in a complex plasma have been derived in two cases. (i) Electrons, positive ions and negative ions are all Boltzmann distributed and dust grains are cold and inertial. (ii) Electrons are Boltzmann distributed, positive ions and negative ions are inertial and dust grains are streaming. In both cases grain charge fluctuations are considered. Both the dispersion relations show that presence of negative ions reduces the threshold of the Jeans instability in the complex plasma system. The streaming motion of dust grains is responsible for the development of an unstable mode which is not purely growing.

We obtain two useful recurrence relations between diagonal matrix elements for the Klein–Gordon equation with a Coulomb potential. Some explicit expressions of diagonal matrix elements of r^k(6 ⩾ k ⩾ −6) are presented. The general calculation formulae for off-diagonal matrix elements ⟨n'₁l'₁|r^k|n'₂l'₂⟩ are derived analytically. An important five-term recurrence relation among off-diagonal matrix elements, the analogue to what is known as Blanchard's rule in the non-relativistic Schrödinger equation case, is obtained explicitly.

The role of Professor Dr Gerhard Soff (deceased on 10 December 2004) in the creation and development of the theory of quantum electrodynamics (QED) of strongly bound electrons in quasi-molecules, highly charged ions and atoms is highlighted. The most important achievements by Professor Soff in this area of research are revisited and commented. Emphasis is placed on a summary of the results of his long-term research activity devoted to bound state QED.