Table of contents

Nonstationary solutions of the derivative nonlinear Schrödinger equation are investigated. They are described by a set of the Whitham modulational equations. The Riemann invariants and characteristic velocities for this set are found, and a class of analytical self-similar solutions is presented.

In this paper we consider some of the analytic properties of the generalized Korteweg-de Vries equation u_t + u^pu_x + u_xxx = 0. We study the Lie group symmetries of the equation and show that for p > 2 there is a three parameter group and if p = 1 or 2 the group has four parameters. The Painlevé property is shown to be not satisfied when p > 2. The variational symmetries are also considered and are shown to lead to the only three known conservation laws for general p.

The paper shows how the characteristic time exponent z in slowing down, and the fractal dimension of the order parameter field, are uniquely determined by distinct forms of special thermodynamic functions that describe the interacting systems with some terms of ϕⁿ. It is also shown that for the purpose of obtaining critical exponents, the renormalization group transformation is needed just to perform to the powers of the order parameter and not to their coefficients in thermodynamic functions. This advantage leads to results which are analytically exact.

An analysis of the total photoabsorption cross section for nuclei ranging from ⁴He up to ²³⁸U has been performed in the energy range 0.2-1.0 GeV. Mean total photoabsorption cross sections have been obtained by summing up the contributions from partial photoreactions, and found to follow an A¹-dependence in the 0.2-1.0 GeV range. A review of the available total photoabsorption cross section data is also presented. Comparisons have been made with cross section values calculated by considering both the quasi-deuteron and π-meson photoproduction mechanism of primary nuclear photointeraction.

Configuration interaction calculations have been carried out to obtain rates for electric dipole transitions and lifetimes for the 1s²2s²2p⁶3s² 3p⁶3d⁴4d and 5s⁶D and 4d⁶F levels in Cr II. Up to 40 configurations have been included so correlation effects should be well accounted for. Relativistic interactions are included through the use of the Breit-Pauli hamiltonian to obtain the level wave functions and energies. Strong mixing of the 4d levels occurs and this leads to substantial departures from earlier nonrelativistic calculations that assume LS coupling for these states. Results include the actual compositions of both even and odd parity levels where significant mixing occurs and the rates for all transitions that are allowed to lower levels from these 4d and 5s levels.

The spectrum of antimony was photographed in the 120 Å-270 Å on a 3-m grazing incidence spectrograph at the Moscow laboratory and 10.7 m grazing incidence spectrograph at the NIST laboratory in Washington. A triggered spark source was used in both laboratories to excite the Sb IX spectrum. Seventeen of 19 levels of the 4d⁷ configuration and 132 of 180 levels in the 4d⁶5p configuration of the Sb IX have been established. Two hundred and seventy three lines have been classified as the 4d⁷-4d⁶5p transitions in the 167 Å-202 Å region. Least-squares-fitting calculations were carried out which interpret the spectrum quite adequately.

The spectrum of nine times ionized argon, Ar X, has been studied in the wavelength range 500-800 Å using the beam-foil technique. Twenty-eight new lines of the type 3s-3p and 3p-3d have been identified, and 40 energy levels in the 2p⁴3s, 3p and 3d configurations are established by combining the newly observed transitions with previously known data. The identifications are supported by isoelectronic comparisons of wavenumbers, energy levels and Slater parameters along the isoelectronic sequence.

Experimental lifetimes of quartet levels in the 2p⁵3p² and 2p⁵3s3d core-excited configurations in Na-like S VI and Cl VII have been measured using the beam-foil method. A theoretical study of the different decay modes of the quartet levels, using the superposition-of-configurations method including continuum channels, is also reported. A comparison of the experimental and theoretical total decay rates shows good qualitative agreement, but also that the theoretical predictions underestimate the lifetimes by typically 50%. Larger discrepancies are found for quartet levels predicted to have a significant autoionization rate.

Photon induced fluorescence from O₂ has been studied in various emission regions 1150-6500 Å in the excitation range 14-28eV using the Swedish synchrotron facility MAX in Lund. A rich line structure is observed which is interpreted in terms of autoionization and dissociation of Rydberg levels converging to the a, b, c, and B states in O₂⁺. New features have been observed, for instance, concerning the (c ⁴Σ_u⁻) 3sσ_g Fano resonance which has been viewed in detail in different detection channels including O₂⁺ and O⁺ ions.

The configuration interaction code CIV3 is used to calculate the A-value for the 1909 Å 2s²¹S₀-2s2p³P^o₁ intercombination line in C III. An extensive calculation of valence shell correlation is augmented by the inclusion of core polarization effects both explicitly through further configurations with one or both 1s orbitals replaced by correlation orbitals, and also by the use of model potentials. Our recommended value of 104 ± 4s⁻¹ for the A-value lies somewhat lower than the experimentally determined value of 121 ± 7s⁻¹. We have estimated the expected error in our work by considering the extent of the convergence of our calculation. We also calculated the resonance transition and obtain an oscillator strength in excellent agreement with experiment.

Systematic multiconfiguration Hartree-Fock results in the Breit-Pauli approximation are reported for the 2s²¹S₀ → 2s2p³P₁ intercombination line in C III and the 2s²2p²P-2s2p³⁴P multiplet in C II. Length and velocity forms of the oscillator strengths of related allowed transitions are also reported. The latter are used as a check on accuracy along with term energy separation and spin-orbit splitting. The predicted transition rate of 103 ± 3 s⁻¹ for the intercombination line in C III lies outside the experimental error bars whereas the decay rates for C II are near the lower experimental limits.

Beam-laser and beam-foil measurements of the lifetimes of the 5p²P^o levels in Cd II are used to obtain the f-value of the 5s²S-5p²P^o multiplet. The beam-laser results give an f-value of 0.745 ± 0.012 while the beam-foil results incorporating cascade correction give 0.708 ± 0.045, the large uncertainty coming mainly from a 6% uncertainty in the post-foil ion velocity. The results are discussed in light of the experimental and theoretical data available for the lower-Z ions of the Ag I isoelectronic sequence.

The spectrum of barium was photographed in the 300 Å-1240 Å wavelength region on a 3-m normal incidence spectrograph at the Antigonish laboratory. The source used was a triggered spark. All five levels of the ground configuration 5s²5p³ and 42 of 44 levels of the 5s5p⁴ + 5s²5p²5d + 5s²5p²6s configurations of Ba VI have been established. One hundred and twenty-seven lines have been classified. The parametric least-squaresfitted calculations involving configuration interaction amongst even parity configurations were carried out to interpret the observed spectrum satisfactorily.

The growth rate spectrum of the ideal pressure-driven localized modes in a general screw pinch configuration is obtained in an explicit analytical from under the condition of the Suydam criterion violation. The suppression effect of the magnetic shear near the singular surface is exponential and depends strongly upon the relative values of two small parameters: μ = m/[(kr_s)² + m²] and ε = (P' - P'_s), where m(k) is a poloidal (axial) wavenumber and P'_s is the Suydam marginally stable pressure gradient. The result is applied to partially relaxed states of reversed field pinch.

An expression for two-gas gas-puff Z-θ pinch compression is derived and the dynamic behavior of the implosion is investigated. It is observed that the compression and the azimuthal magnetic field strengths are critically dependent on the target to driver mass density ratio and on the driver gas shell thickness.

It is shown that the oscillatory magnetic electron drift mode in an unmagnetized plasma is unstable if the wavevector is not strictly perpendicular to the external density and temperature gradients. A purely growing density gradient driven instability also has a small real frequency in this case.

New exact analytical solutions describing the non-stationary propagation of non-sine electromagnetic waves in plasma are obtained by direct solution of Maxwell equations without the traditional Fourier transformations. Unlike the usual travelling monochromatic waves the fields discussed are distinguished by unequal periods of electric and magnetic oscillations, fast oscillative diffusion of the envelope and collisionless damping of peak amplitudes due to strong plasma dispersion. The transformation of these non-sine fields to the trains of quasimonochromatic waves in the depth of plasma is considered for both isotropic and magnetized plasmas.

We consider intermediate frequency electrostatic drift modes in the UMIST magnetic quadrupole, with one and two full wavelengths along a closed magnetic field line. The dispersion curves and the shape of the longitudinal eigenfunctions are calculated. The effect of variations of various parameters is also studied. In particular, we conclude that whereas resonant non-linear interactions between the drift modes are possible for some parameter values, the interaction may be strongly non-resonant for other parameter values.

Cast thin films of the composites PVA-CrCl₃ were prepared. The absorption spectra, X-ray diffraction, hardness number and dielectric constant were measured before and after irradiation by neutrons in the fluence range of 3.4 × 10⁵ to 1.68 × 10⁸ n/cm². The Racah constant was calculated to be 600 cm^-1 which is about 65% of the free ion value. A pronounced band characterizing the carbonyl group has developed at 220 nm by irradiation. The degree of crystallinity is enhanced with the increase of neutron fluence. The position of the glass transition and α-relaxation temperatures were dependent on neutron fluence and doping content.

Ion diffusion across material interfaces is considered in the framework of the one-dimensional lattice-gas model of hopping diffusion, which is generalized to include the space-charge effects near the solid-solid interface, by solving the coupled diffusion and Poisson equations with appropriate boundary conditions. Overvoltage measurements on InSe, and dielectric loss measurements on the ternary glass B₂O₃–0.5Li₂0–0.15Li₂SO₄ are used to determine the field-free hopping rates in the two materials. The influence of the Coulomb correlations on the ion diffusion is demonstrated and numerical illustrative examples are presented for different values of the model parameters. An important application of these results is the simulation of charge transfer across the interface glass-intercalate in a thin-film battery.

A formulation is presented to find the electronic states of a D⁻ centre in a many-valley semiconductor. Parameterizing the intervalley scattering terms and using a model potential in the central cell region the D⁻ binding energies in Si and Ge doped with group V elements are calculated variationally, including electron correlation. The binding energy obtained for Si : P and Ge : Sb are in good agreement with experimental results. D⁻ formed by As donors appears to require a more detailed consideration for the central cell potential.

The Hurwitz criteria are used for a stability analysis of the steady state excitonic optical bistability curves in a semiconductor pumped by an external laser resonant with the exciton level. Besides the middle branch of the bistability curves which is unstable in the sense of the linear stability theory, we have found other domains of instability in the upper and lower branches of the steady state curves. Numerical results show that a possible route to chaos in the photon-exciton system is period-doubling self-oscillation process. The influence of the presence of free carriers that coexist with the excitons is also discussed.