Table of contents

We consider here two discrete versions of the modified KdV equation. In one case, some solitary wave solutions, Bäcklund transformations and integrals of motion are known. In the other one, only solitary wave solutions were given, and we supply the corresponding results for this equation. We also derive the integrability of the second equation and give a transformation which links the two models.

Perturbation theory for elliptic pulsons is developed and predicts pulson and eccentricity oscillations. The pulson oscillation period is predicted qualitatively correct.

A modified Kadomtsev–Petviashvili (MKP) equation is proposed. The equation is a weakly two-dimensional generalisation of the Schamel equation. It is shown that one form of this equation arises in the context of the propagation of ion-acoustic waves in a plasma with non-isothermal electrons. The stability of certain plane periodic and solitary travelling wave solutions of the MKP equation to two-dimensional long wavelength perturbations is investigated using the method of Rowlands and Infeld. The results obtained are compared with those for the standard KP equation; some qualitative differences are found.

We investigate a numerical solution of the covariant Bethe–Salpeter equation in the Euclidean space for heavy q meson with gluon ladder in the Landau gauge and scalar confinement. A new approach is presented to solve the non-linear eigenvalue problem with suitable bases and fictitious eigenvalue parameters. We obtain unphysical states when the equation is solved for timelike spectra. We also present how to cover the singularity of a free quark propagator and Schwinger-Dyson equation when extrapolated to the timelike domain in the real plane.

Alpha particle induced reactions on the target element holmium were investigated upto 70 MeV using stacked foil activation technique and Ge(Li) gamma ray spectroscopy methods. Excitation functions for the formation of reaction residues ¹⁶⁸Tm, ¹⁶⁷Tm, ¹⁶⁶Tm and ¹⁶⁵Tm from α-induced reactions on ¹⁶⁵Ho were investigated for the first time in the energy range from 50-70 MeV. The measured cross sections were compared with theoretical calculations considering equilibrium as well as preequilibrium hybrid models of Blann. The high energy tails of the excitation functions show a substantial contribution from preequilibrium emission. A general agreement is observed between the experimental results and theoretical predictions with an initial excition configuration of n₀ = 4(4p 0h).

It is shown that elemental multiplicity distributions, relative abundances of intermediate mass fragments as well as fragment kinetic energy spectra and charged-particle correlations in nucleus-nucleus induced multi-fragmentation reactions can be satisfactorily reproduced by site percolation procedure in the case that the occupation probability is taken explicitly as a function of the geometry of the collision.

The fine-structure splitting in the ground term (4s²4p ²P) of Ga-like ions and magnetic dipole (M₁) and electric quadrupole (E₂) transition rates between the ²P_1/2 and ²P_3/2 levels have been calculated for Ga to U^{61 +} using the multiconfiguration Dirac-Fock (MCDF) method with jj configurations arising from the (n = 4)³ relativistic Coulomb complex. The Breit interaction and the Lamb shift corrections were also included. Our theoretical results are compared with experimental and semiempirical finestructure splittings and theoretical transition rates available in the literature. We find that for highly charged ions, relativistic configurations that include the 4d and 4f orbitals such as 4d²4p, 4f²4p, 4s4d4f etc. (see text) are not needed to obtain accurate results for the fine-structure splitting in agreement with the recent relativistic extension of the Z-expansion theory by Weiss and Kim.

A linear zone plate surface structure was created on the surface of mica crystal and used for obtaining spectrally resolved images of 120 fs laser-produced plasma. A linear Fresnel zone structure was optimized on a wavelength λ = 9.16 Å and has a focal length of f = 5 cm, minimum zone width Δz_n = 300 nm, total length l = 10 cm, total width of zone plate 2r_n = 122.6 μm.

Images of laser-produced plasma in the spectral range 9.12−9.31 Å were obtained. For high Z (Lanthanum) element target the size of the x-ray radiation spot was not more than 20 μm.

The x-ray lines emitted from highly charged ions collisionally excited by longitudinally polarized electrons can be strongly circularly polarized for ions with no nuclear spin. In the present work, we have theoretically investigated the effects of hyperfine interaction on the circular polarization of the 1s2l → 1s² lines of helium-like scandium, for which the nuclear spin is large. The hyperfine splitting of the excited levels and the transition probabilities for the hyperfine-induced E1 decays 2³P₀ → 1¹S₀ and 2³P₂F = 5/2 − 9/2 → 1¹S₀ have been calculated by diagonalizing the complete Hamiltonian including both the spin-orbit interaction and the magneticdipole hyperfine interaction. The collision strengths for transitions to the individual magnetic sublevels of the target ion have been computed in two distorted-wave methods, one semi-relativistic and the other fully relativistic. It is shown that the hyperfine effects result in drastic decreases of the degree of circular polarization for the lines 2³P_{2, 1} → 1¹S₀ (labeled x and y, respectively and 2³S₁ → 1¹S₀ (labeled z). The interference effects between the E1 and M2 transitions for the line x and those between the hyperfine components F = 5/2, 7/2 and 9/2 of the upper level for the line y are considered.

In order to test the reliability of the Configuration Interaction (CI) method to predict the atomic parameters viz oscillator strengths of complex ions, we measured the profiles of forth (40) strong 6s-6p transitions of Xe III emitted by a pulsed capillary discharge. After deconvoluting the experimental shapes, Stark widths and relative oscillator strengths were obtained. When Least Square Fitted parameters were used in addition to extensive CI (CI + LSF), the agreement between theory and experiment for the gf's is within a factor two for the whole of the lines. Concerning the widths, the semiempirical approach provides values also within a factor two when the Gaunt factor is taken to be g(x) ~ 0.30.

The dielectronic recombination rate coefficients to the excited states for n = 2–6 are calculated including 1s²2l2l'nl'' (n = 2–6, l'' ⩽ (n − 1)). The values for the excited states higher than n = 6 are extrapolated and the total dielectronic recombination rate coefficients are derived. The rate coefficients to the excited states are fitted to an analytical formula and the fit parameters are given. The effective recombination rate coefficient for different electron densities are also derived.

The atomic quantities for bound-bound transitions such as the oscillator strengths, the line strengths, and the Einstein A-coefficients are obtained for a large number of dipole allowed (ΔS = 0) transitions for the astrophysically important ion S II. The oscillator strengths in LS coupling are obtained in an ab initio manner in the close coupling approximation using R-matrix method. The quantities for the fine structure transitions are obtained through an algebraic transformation of the LS values. The spectroscopic energies of the fine structure levels are used instead of the calculated energies to improve the accuracy of these values. Present calculations employs a 17-state eigenfunction expansion of the S III core states. Results are presented for 1466 fine structure dipole allowed transitions in S II corresponding to 350 transitions in LS coupling. This work reports the first extensive tabulation of S II radiative transitions including fine structure. Comparison is made with the available experimental and theoretical data and good agreement is found with the observed values and other accurate theoretical works.

The potential of a test particle in the presence of electron-acoustic waves in a uniform unmagnetized plasma has been obtained. Besides the well known Debye-Hückel potential, an oscillatory wake potential behind a test particle is found. The relevance of our investigation to macroparticles in plasmas with two distinct groups of electrons has been discussed.

A one-dimensional periodic potential is described such that the spectral distribution curve of an electron moving through the potential has an exact unique gap. Above the gap the curve is strictly continuous.

Polyvinylchloride (PVC) films containing different amounts of NiCl₂ have been prepared using a casting method. The UV/VIS (200-800 nm) and IR (200-4000 cm⁻¹) spectra and dc electric conductivity have been investigated. One optical absorption edge was found for pure PVC, while the addition of NiCl₂ led to the appearance of a second edge at lower photon energy. The change of the calculated values of the optical energy gaps with increasing NiCl₂ content has been interpreted in terms of the structural modifications of the PVC matrix. The spectral analysis indicated that the Ni⁺² ions are present in its octahedral symmetrical forms. The infrared analysis revealed that there is a change of the NiCl₂ chliation mode beyond 0.25 filling level. The electric conduction was attributed to an intrachain one dimensional interpolaron hopping mechanism. The calculated hopping distance was R₀ ⩾ five monomer unit lengths. R₀ depends linearly on both temperature and filling level.

The problem of characterization of electronic states in disordered systems is readdressed. For this task, we present our ensemble-averaged calculations of both density of states and dc-conductivity for linear chains containing up to 3500 sites and modeling the Anderson Hamiltonian with on-site energies randomly chosen from a box distribution of width W. The analysis of the spatial behaviour of eigenfunctions when increasing the disorder shows an increase of the curdling of the wavefunction amplitude, which reflects a stronger localization. The dc-conductivity results show that, for low disorder W/V < 2, the states at the midband seem to have localization length λ at least as large as the system sizes considered here. For larger disorder, the system exhibits "almost an Anderson transition" between localized and quasi-extended states, which are localized with very large λ. Our dc-conductivity results suggest a critical fractal dimension d^*_c = 0.70 ± 0.09 to discriminate between the exponentially and the power-law localized states. The relatively large error bar Δd^*_c may reflect the nature of a continuous transition between the two regimes.

The quantum coherent motion of excitons (quasiparticles) in a chain with alternating site energies (model A) or intersite interactions (model B) is studied analytically. Exact solutions for the mean polarizations and the mean-square displacements for both systems are obtained explicitly, from which an inherent symmetry between the two models is revealed. It is found that the effects of the site-energy mismatch and the hopping disturbance to the diffusing behavior of the moving quasiparticles are almost identical. Similarities and differences for the two models are manifested in these analyses.