Table of contents

We discuss the decimation as a useful alternative for solving the Schrödinger problem. We find that the eigenvalue it gives matches perfectly the wave-function equations with periodic boundary conditions for localized and critical states. We illustrate the precision of the method with the binary alloy problem. We also perform a standard multifractal analysis on the eigenstates of the Anderson model and of the binary alloy and find that both are multifractal, at calculable lengths (up to 2¹⁶). The controversy started in the past, receives our point of view for calculable lengths. However, the finite size analysis we perform, due to memory limitations cannot be pushed to draw conclusions for the thermodynamic limit.

Rapidity and multiplicity correlations of particle production in high energy hadronic collisions are studied. A simple model including short range correlations in rapidity due to clustering and long range correlations due to energy conservation is able to describe the two-body correlation functions well in hadron-nucleon collisions around lab energies of 250 GeV. In this model factorial moments are calculated and compared to data. The strong rise of the factorial moments in rapidity intervals by size δy ~ 1 can be explained by long and short range correlation alone whereas the factorial moments approach a constant value at very small δy due to lack of correlations also in agreement with experiment. There is therefore no need for introducing intermittency in the particle production in hadronic collisions at these energies.

The high-spin structure of ⁹¹Tc has been studied by means of γ-spectroscopy. ⁹¹Tc was produced by use of the ⁵⁸Ni(⁴⁰Ca,α3p)⁹¹Tc reaction at beam energies of 180 and 187 MeV. The NORDBALL detector system including charged particle and neutron selection was used. A large number of positive as well as negative parity states with excitation energies up to 12 MeV and spin values up to (47/2, 49/2) has been established. The level scheme has been compared with shell model calculations using both ⁸⁸Sr and ¹⁰⁰Sn as cores. Some first information of the level scheme of ⁹⁰Tc is also given.

We examine the use of the momentum distribution of recoiling nucleons to study the stopping power law of nuclear matter for incident nucleons with high energies. The dependence of the momentum distribution on the stopping power index is studied in detail for both leading nucleons and recoiling nucleons in p + d reactions. There are two regions where the momentum distribution of the recoiling nucleons is sensitive to the stopping power law. This sensitivity can be used to study the stopping power law experimentally.

We have calculated energies and transition rates for the 2s²2p³⁴S° ground state and a number of excited states in the isoelectronic sequence of atomic nitrogen using the multiconfiguration optimized potential model (MCOPM). The excited states include the 2s²2p²3s⁴P, 2s2p⁴⁴P, 2s²2p²3p⁴D°, 2s²2p²3p⁴P°, 2s²2p²3p⁴S°, 2s²2p²3d⁴F, 2s²2p²3d⁴D and 2s²2p²3d⁴P terms. The oscillator strengths for transitions among these terms have been calculated in both length and velocity gauge. Particular emphasis has been put on an accurate description near level crossings. Comparison with other theoretical and experimental results are made. However, the experimental data are rather sparse, and verification of many of the calculated trends against experiment is therefore not yet possible.

Recently calculated electron impact excitation rates for transitions in helium-like CI XVI are used to derive the electron temperature sensitive emission line ratio G = [(x + y + z)/w] and the electron density sensitive ratio R = [z/(x + y)] where w, x, y and z are the resonance 1s²¹S₀-1s2p¹P₁, intercombination 1s²¹S₀-1s2p³P_2,1 and forbidden 1s²¹S₀-1s2s³S₁ transitions, respectively. These calculations, which differ from those of previous authors, are compared with experimental R and G ratios obtained from X-ray spectra from the JET (Joint European Torus) plasma, for which the electron temperature and density have been measured by independent methods. The R ratio is approximately in its low density limit (R_o) for this device and is therefore not electron density sensitive. However it does function as an electron temperature diagnostic as does the G ratio. A comparison is also made with the previously reported results from the Alcator-C tokamak, where the experimental results lie in the electron density sensitive region. The current results show good agreement between theory and observation, with discrepancies of typically 7% in R_o and 10% in G for JET, implying that the theoretical results may be applied to the analysis of remote plasma sources in order to derive values for these parameters, where no independent measurements exist. A departure from coronal equilibrium due to diffusion effects is taken into account for the JET plasma conditions, and the resulting non-coronal ionization balance is found to produce changes to the theoretical ratios at temperatures exceeding T_m.

The Zeeman effect of six transitions between levels of the 5s²5p6s and 5s²5p6p electron configurations of Sb II was studied. The experimental studies were performed on isotope 121 for two directions of observation, i.e. longitudinal (σ) and transverse (π), using a silver-coated Fabry-Perot etalon and a two-grating-spectrograph. The performed studies allowed us to redetermine the magnetic dipole (A) nd the electric quadrupole (B) hfs splitting constants and find the Lande g_J factors of the levels belonging to the 5s²5p6s and 5s²5p6p electronic configurations. The g_J values are compared with theoretical results. An analysis of the obtained g_J values implies, that the effect of configuration mixing is not significant.

Radiative lifetimes and relative intensities of a number of the NO⁺ A¹Π-X¹Σ⁺ emission bands have been measured using the High Frequency Deflection technique. The experimentally determined transition moment and the oscillator strengths are in good agreement with the recent ab initio calculations, but deviate substantially from earlier experimental results.

The angular and energy distribution of the electrons ejected in collisions between fast heavy charged particles and atoms has been studied in the simple Born approximation using the semiclassical approximation for atoms. As a result of this approach an analytical solution of the problem is obtained. Comparisons are made with reported experimental results.

Results of experiments on low pressure broadening and shift of 17 spectral lines of argon involving intermediate Rydberg states are interpreted in the framework of the impact theory. Using a treatment due to Kaulakys it is shown that in pure argon and in the Ar-He mixture the experimental data are in satisfactory agreement with those calculated on the basis of the Fermi pseudopotential and polarization interaction. On the other hand, for the Ar-Ne mixture the theoretical broadening and shift values computed from this treatment are in poor agreement with experiment. The role of Maxwellian averaging as well as the scattering length in the analysis of the broadening cross-sections are also discussed.

The energy levels, wavelengths, oscillator strengths, Auger rates and level-to-level dielectronic recombination rate coefficients describing dielectronic recombination into excited levels of Ne-like titanium from F-like low-lying states are calculated. Our calculations are based on Dr. R. D. Cowan's semi-relativistic superposition-of-configuration Hartree-Fock (HFR) code, where the relativistic mass-velocity and Darwin corrections are included in the Hamiltonian, and the distorted-wave model is used for the calculation of free electron wavefunctions. In order to set the recombination rate coefficients on a level by level basis, in a manner compatible with detailed level population kinetics modelling of highly-stripped ions in plasma, the dielectronic recombination rate coefficients as a function of free electron temperatures are given in an analytical form, which is not only very convenient in practice, but also hopefully accurate compared with the exactly calculated numerical results.

We present detailed experimental studies of regular and chaotic motion in a periodically perturbed neon glow discharge. Due to the simultaneous presence of two competing fundamental oscillatory modes intrinsic to our discharge system and their nonlinear interaction with the external periodic forcing two- and three-frequency quasiperiodic and mode locked states as well as low-dimensional chaos can be observed. In our experiment, chaos is distinguished from quasiperiodicity by evaluation of the temporal decay of the envelope of the time series autocorrelation function and careful estimation of the correlation dimension of the corresponding attractor.

In this paper, a nonlinear analytical solution for a cold plasma-bunched beam system based on the Hamiltonian formalism where α = n_b/n_o and β_ϕ = v_ϕ/c have been taken as parameters matching between zero and unity is given. The oscillation limiting energies, frequencies and transformer ratios have been carried out in general for both the one-dimensional and the case where a small transverse component of motion is included. The plasma wakefield accelerator has been treated as a special case.

The propagation of a relativistically strong electromagnetic pulse in an underdense homogeneous plasma is considered with the focus on the possible existence of stationary structure of a pulse front. The analytical stationary shock-like solutions are obtained and analyzed. These solutions correspond to the conversion of the pulse electromagnetic energy to an electron plasma wave in the narrow region of the considered stationary front. Our theoretical analysis is supported by the PIC simulations, which demonstrate the formation and existence of the shock-like structure of the pulse leading front and extremely fast pulse depletion.

We formulate a model equation for nonlinear modulated waves valid near the marginal state of instability. This equation we henceforth call the Extended Derivative Nonlinear Schrödinger equation (EDNLS). EDLNS has the same form as the Derivative Nonlinear Schrödinger equation (DNLS) except for a quintic nonlinear term which in special cases might be zero. EDNLS has three conservation laws which correspond to the first three of the conservation laws of the DNLS equation. We find the following criterion for modulational instability, k₀ > –2a₀²σ. (Here k₀, a₀ and σ are the normalized background wavenumber and amplitude and the coefficient for the quintic term in the EDNLS equation.) In addition we classify the solitary and cnoidal waves for the EDNLS equation and study the nonlinear behavior of the modulational instability.

Results of theoretical investigations on the interaction of electron beams and clusters of longitudinal HF fields in a plasma are presented. A general expression to describe the energy exchange in this interaction is derived. This expression takes into account the static fields due to a plasma inhomogeneity and external forces. The problem is considered by two examples: electron beams - clusters of Langmuir oscillations interaction near electrodes and electron beam - Langmuir soliton interaction. The stationary Langmuir soliton may be pumped by the electron beam due to the presence of the electrostatic field in the cavern. The sign of the interaction depends on the space profile of the HF field.

Two radiophysics diagnostic methods (interferogram measurements and field radial decay method) are used for determining the plasma behaviour in microwave discharges sustained by surface wave propagation. The interferogram technique which is slightly modified and simplified is used as a reference method for verifying the applicability of the method of the field radial decay. Comparison with theoretical results for the axial density gradient is given and discussed.

The effects of Hall currents and finite electrical conductivity on the gravitational instability of an infinite homogeneous rotating fluid have been studied. The fluid is assumed to be permeated by an oblique magnetic field. The dispersion relation has been obtained. It is found that Jean's criterion remains unchanged in the presence of Hall currents at finite conductivity. Numerical calculations have been performed to obtain the dependence of the growth rate of the gravitationally unstable mode on the various physical parameters involved. The Hall currents, finite conductivity have destabilizing influence while the coriolis force has a stabilizing influence on the unstable mode of wave propagation of the gravitationally unstable.

The nonlinear propagation of Alfvén waves in a hot electron-positron plasma of a pulsar magnetosphere is investigated. Spiky intense Alfvén solitons are found to exist at ultrarelativistic (T ≫ Mc²) temperatures. Landau damping and three dimensional modulation perturbations of these solitons are discussed.

The evolution of resonant waves due to the nonlinear interaction associated with the plasma-maser effect is considered, and the nonlinear growth rate obtained. It is shown that the latter contains a "polarization" (only for the resonant waves) as well as a "direct third-order" contribution. In particular, the effect of the plasma-maser mechanism on the beam instability caused by Landau growth is investigated. It is shown that this effect can significantly modify the behavior of the instability. The conditions for the dominance of the plasma-maser effect nonlinearity over that of the usual quasilinear mechanism are given.

A nonlinear description of Drift and Rossby waves turbulence in a dissipative media with a driven force is built, using a statistic based on a three-modes interaction model. The statistical dynamics of the system is investigated on the basis of the existence of a most physically important triad (MPI triad). Then, the neglected modes are modeled as a white-noise contribution leading to a Langevin equation. A probability density function is obtained for the associated Fokker-Planck equation of the turbulent field. The spectrum cascades and the most physically important triad (MPI triad) are analyzed.

Renormalized statistical theory of low-frequency hydrodynamic fluctuations in magnetized plasmas is applied for the general case of electromagnetic fluctuations. Stationary spectra of electromagnetic field thermal fluctuations are derived with regard to nonlinear interaction between potential and magnetic field excitations. The well known results of potential theories are recovered only in the limit of cold electrons or for plasmas with very low pressure. Substantial broadening of the convective cell potential spectrum and suppression of convective cell diffusion due to magnetic field fluctuations in the plasma of small but finite pressure are predicted.

A quasiparticle concept is developed systematically, from first principles, within the context of microscopic description of magnetized plasma. It is argued that the zeroth velocity-gyroangle harmonic of the microscopic particle distribution function under the gyrokinetic change of variables can be taken as a microscopic quasi-particle density in a reduced phase space. The nature of quasiparticles is discussed and equations of their motion are derived within both exact and reduced microscopic descriptions. The reduced one employs explicitly the separation of interesting time scales.

The two-fluid equations governing the nonlinear evolution and saturation of drift wave-like turbulence and transport in tokamaks under quasi-neutral conditions in periodic cylinder geometry are investigated. Using experiment as guide and employing appropriate orderings, two non-adiabaticity parameters, Υ_es and Υ_em are derived as functions of the reduced frequency ωa/v_thi and wave number ρ_ik_r characteristic of the turbulent fluctuation spectrum. These parameters correspond respectively to the electrostatic limit and the general electromagnetic case. It is shown that they must be O(1) if significant particle and ion energy transport are to be expected from the turbulence. In other words, they are measures of the departure from neo-classical particle and ion energy transport due to the turbulence. These analytic results are complementary to, and serve as guidelines for, any future direct numerical simulations of the set of seven nonlinear partial differential equations which must be solved with suitable sources of particles, momentum and energy to determine the turbulence evolution and resultant saturated power spectra of density, pressure, electrostatic potential and magnetic field. The nonadiabaticity parameters discussed suggest possible qualitative explanations of the isotope effect and reduction of anomalous transport noted in H-mode tokamak discharges.

Nonlinear double layers are investigated in dusty plasmas. The dust dynamics is modelled by a highly negatively charged and massive fluid in the presence of two isothermal proton populations. For electrostatic double layers one either integrates the cold dust equations exactly, to get a description in terms of a Sagdeev potential, or one uses a reductive perturbation analysis leading to modified Korteweg–de Vries equations. It is then shown that when the exact Sagdeev potential yields weak double layers, they can be quite different from what one would obtain via more approximate methods, and vice versa. This casts serious doubts upon the adequacy of modified Korteweg–de Vries equations for the description of weak double layers in more complicated cases where no exact analytical results are available. Such findings are relevant for different kinds of astrophysical and heliospheric plasmas, as well as for ordinary ion-acoustic double layers.

An analysis is made of the central expansion form of solution for a nonlinear reaction-diffusion equation in order to determine the break-point (knee) in the profile of a bounded fusion plasma. A suggestion is made of using the break-point as a check-point for numerical studies or as a tool for diagnostic purposes.

We study the motion of the Klein-Gordon kink in presence of two particular types of lattice defects. The first type consists of two potential walls of impurities, one of which is oscillating. It is shown that the motion of kink in the presence of these impurities reveals a chaotic behavior. The second type of defects considered consists of discrete potential and dissipative installed microinhomogeneities. We find that such lattice defects give rise to an oscillatory motion for the kink.

The confined electron gas in modulation doped quantum wells is studied by means of a self-consistent calculation using the Hedin-Lundqvist density functional for exchange and correlation. The need for a reliable knowledge of the position of the Fermi level is critically discussed. Comparison is made with experimental data on total and - where available - partial subband population and the role of the different parameters characterizing each sample is discussed and demonstrated with suitable calculations and experimental evidence.

The calculations of the electronic structure and X-ray spectra of the MO₆⁸⁻ (M = Ti, V, Cr, Mn) clusters, which were used as models for respective solid state dioxides, have been performed by the X_α-DV method. The one-electron model for resonant emission (reemission) was used. The calculations show, that X-ray resonant emission significantly affects the shape of the ML_2,3 and MM_2,3 emission spectra. The theoretical XESs, XASs and valence XPSs are compared with the experimental ones. Some contradictions arising from the assumed reemission origin of high-energy structure of the ML_2,3 XES are discussed.

Calculations of the electronic structure and X-ray spectra of the MO₆¹⁰⁻ (M = Ti, V, Mn, Fe, Co, Ni) clusters, modeling the respective solid-state monoxides, have been performed by the X_α-DV method. The main purpose of the present work was to investigate an influence of the resonant emission processes on the X-ray emission spectra of the monoxides. It has been shown, that resonant emission can appreciably affect the shape of the ML_2,3- and, to an even greater degree, the MM_2,3-X-ray emission spectra of the l.h.s. transition 3d-metal monoxides.

We study the motional narrowing of a spin-½ particle diffusing in a solid with random magnetic fields at sites. The crystal environment is modeled in a simple way interpolating between zero temperature and high temperatures. A two-site problem is solved exactly and the findings are in accordance with expectation. In the N-site problem the low temperature spin relaxation is found to be in striking contrast to the classical theory of motional narrowing. The relation to μSR experiments is discussed.

Development of the modulational instability is analyzed in an effectively inhomogeneous one-wave or two-wave fiber in the situation when the instability sets in at some critical point and grows down the fiber. In the one-wave case, it is assumed that the dispersion coefficient, being a linear function of the spatial coordinate, changes its sign at the critical point. In the two-wave case, the fiber itself is homogeneous, while an effective inhomogeneity is produced by energy transfer between the two waves via the stimulated Raman scattering. In addition, it is assumed that the pump-wave belongs to the normal-dispersion region, while the Stokes wave lies in the region of the anomalous dispersion; the instability sets in when the ratio of powers of the two waves passes through a certain critical value. In both cases, the frequency of the disturbance which is expected to play a dominant role at the nonlinear stage is found, provided that the initial disturbances are white-nose-like. In particular, it is demonstrated that, in the two-wave case, the solitons produced by the modulational instability from cw can be especially short.

In this paper we investigate anharmonic lattices that support the formation and propagation of Toda solitons along their chains. The main objective is to examine the influence of Toda solitons on the Mössbauer effect. We find that the presence of Toda solitons may, under suitable conditions, significantly affect the probability of Mössbauer emission of gamma photons.