Table of contents

We have studied the behaviour of a coupled bicritical map, under the influence of a fractal signal. An approximate Renormalization Group equation is set up and analysed to extract the Feigenbaum and non-Feigenbaum type scaling indices. The present system can model the case of a discrete system under an external aperiodic force. The change in the behaviour is similar to the phase transition of a thermodynamic system.

This note deals with diffusion processes for which the transport operators depend on a set of parameters (mobility and diffusion coefficients) subject to random variations determined by a random jump frequency. The model assumes the existence of a complete temporal disorder: a succession of realizations of the random parameters corresponds to a succession of independent random variables selected from the same probability law. The average over the temporal disorder can be computed exactly: the state probability density obeys a linear integral equation which is similar to a continuous time random walk equation or to a system of age-dependent master equations. For time-homogeneous and translationally invariant systems the integral equation can be solved analytically. The behavior of the solution depends on the stochastic properties of the jump rate Ω. If the first two negative moments of Ω, ⟨Ω⁻¹⟩ and ⟨Ω⁻²⟩, exist and are finite then the covariance matrix of the elements of the displacement vector obeys an Einstein like law: ⟨Δx_i(t)Δx_j(t)⟩ ∼ t as t → ∞. If ⟨Ω⁻¹⟩ and ⟨Ω⁻²⟩ are infinite then a supradiffusive behavior ⟨Δx_i(t)Δx_j(t)⟩ ∼ t^a with a ⩾ 1 may occur. A detailed analysis is made in the case if the distribution of jump rates is given by an ultrametric model. An ultrametric structure consisting in branches grouped in levels is generated by means of a stochastic chain process depending on two parameters: the probabilities α and β of a level and branch generation, respectively. The probability distribution ξ(n) of the total number of branches has a long tail ξ(n) ∼ n^{−(H +1)} as n → ∞, where H = ln α/ln (1 − β) is a fractal exponent characteristic for the ultrametric structure. We show that the probability density of the jump rates may be approximated by a power law ∼Ω^H−1 and that a = 2 for 1 > H > 0 and a = 1 for H > 2.

The tagged photon technique has been used to measure the excitation energy spectra resulting from the (γ, p) reaction in ⁶Li and ¹²C at 90 degrees for incident photon energies around 61 and 77 MeV. Strong evidence is found for the quasideuteron absorption mechanism, not only in the high excitation energy regions, but also in bound states. Furthermore, for the ¹²C(γ, p) reaction the photon seems to be absorbed on pn-pairs in both T = 0 and T = 1 states.

Symmetry splittings between e and f components of the rovibronic levels of the Ω = 1 excited electronic states of CuCl have been calculated taking both spin-orbit and Coriolis interactions into account. The model agrees satisfactorily with the experimental data in the case of the D¹Π₁, B³Π₁ and F³Δ₁ states but a strong discrepancy is found in the case of the A³Σ₁⁺ component.

For autoionizing levels converging to the N = 3 threshold of He-like ions with Z = 3–26, energies and widths obtained within the generalized diagonalization approach are compared with the results of S-matrix perturbation theory. The combined data for the expansion coefficients can improve the validity of spectral calculations. Autoionization decay amplitudes and widths are obtained using both unscreened and screened hydrogenic orbitals for the free electron, as well as in the first order in continuum Coulomb coupling. Terms of order 1/Z can be extracted to improve the perturbational data for autoionization amplitudes, involving both screening corrections and the first-order continuum coupling. The relative significance of various atomic interactions in evaluating autoionization decay amplitudes is discussed.

Charge exchange collisions at 105 keV between Ar⁷⁺ ions and lithium atoms have been studied by photon spectroscopy in the 2000-6000 Å wavelength range. A large number of new lines in Ar VII have been identified with the help of ab initio pseudo-relativistic Hartree-Fock calculations taking into account electrostatic interactions between 3snl (n = 6–10), 3 pnl (n = 4–6) and 3dnl (n = 4) configurations. They correspond to transitions 3snl–3sn'l' with n = 7, 8, 9 and Δn = 1 and 2. Lines in Ar VI were also observed and identified as transitions 3s²nl–3s²n'l' and 3s3pnl–3s3pn'l'(n = 6, 7) and Δn = 1.

We have constructed a simplified setup for the demonstration of laser cooling and trapping of rubidium atoms. An external-cavity diode laser was swept across the F = 3 → F' = 2, 3, 4 resonances of the D₂-line of ⁸⁵Rb at 780 nm to resolve the saturated absorption features. Subsequently, the transition F = 3 → F' = 4 was used to cool rubidium atoms in a roomtemperature vapor cell. A cold cloud of trapped atoms with a diameter of approximately 1 mm was produced. The lifetime of the trap was measured to be 1 second.

Spectra of highly ionized Ni, Ge, Kr, Zr and Mo obtained from the JET tokamak have been studied. In total 20 new lines have been classified as n = 2, Δn = 0 transitions in B-like and F-like ions. Among the identified lines are M1 transitions within the 2s²2p⁵²P ground term of F-like Zr and Mo and within the 2s²2p²P ground term of B-like Mo. Furthermore, for B-like Ni, Kr and Mo, the 2s2p²⁴P_1/2 and ⁴P_5/2 levels, which decay by spin-forbidden transitions, have been found. From the observed wavelengths 20 new energy levels were determined. The experiments have been complemented with multiconfiguration Dirac-Fock (MCDF) calculations and semiempirical analyses of transition energies in the B I and F I isoelectronic sequences.

High resolution spectra of Cu, Mg, Al and V, produced by a hollow cathode with Ar and Ne as carrier gases, have been registered in the infrared region (1800–9000 cm⁻¹) at the National Solar Observatory on Kitt Peak. The spectra reveal the presence of many unidentified lines due to the rare gases. Some of these emission lines have been identified as 2p⁴(³P)nl- 2p⁴(³P)n'l' transitions of Ne II. The observations reported here (367 transitions identified) have allowed us to extend the term system of this ion and to determine 52 new energy levels belonging to the 2p⁴(³P)5d, 2p⁴(³P)6s, 2p⁴(³P)6p, 2p⁴(³P)6d, 2p⁴(³P)6g and 2p⁴(³P)6h configurations.

Calculations of energy levels of 1s²2s²2p⁵nl, 1s²2s2p⁶nl (n = 3–6, l = s, p, d, f) configurations of Ne-like ions with Z = 20-60 have been carried out with use of an MZ program. The energy matrix in this method (1/Z method or Z–expansion) is represented in the form of a Z-expansion, where Z is the nuclear charge. Relativistic effects are taken into account in the framework of the Breit operator. The contributions of radiative and high order relativistic effects are also considered. The results of the calculations are compared with theoretical and experimental data.

By fitting the directly computed dielectronic recombination rate coefficients on the basis of relativistic intermediate-coupling MCDF model by M. H. Chen, we present a set of concise formulas of dielectronic recombination rate coefficients for Li-like ions from C³⁺ to Mo³⁹⁺, which may be used conveniently in the calculations of ionization balance in hot plasmas. The detailed results are tabled.

By fitting the directly computed dielectronic recombination rate coefficients on the basis of the relativistic intermediate-coupling MCDF model by M. H. Chen, we present a set of series formulas of dielectronic recombination rate coefficients for Ne-like ions from Ar⁸⁺ to Xe⁴⁴⁺ with the electron temperature range from 0.2keV to 6.0keV. The reproduced dielectronic recombination rate coefficients are in close agreement with the orginal results of Chen. The errors are generally less than 5%. Our formulas may be used easily to obtain dielectronic recombination rate coefficients in calculations of ionization balance in hot plasmas. The detailed results are tabled and discussed.

Recent electron-impact excitation rates for the C-like ions Ti XVII, Cr XIX and Ni XXIII are used to derive electron density sensitive emission line ratios applicable to the ultraviolet spectra of tokamak plasmas. A comparison of these with ratios measured from the Princeton Large Torus (PLT) tokamak reveals good agreement between theory and observation. These results confirm the validity of the atomic data adopted in the line ratio calculations.

The problem of the Rayleigh-Taylor instability of the stratified layer of incompressible viscous infinitely conducting partially ionized plasma has been investigated. Effects of Hall currents have been taken into account. It is assumed that the plasma is permeated by a uniform two-dimensional horizontal magnetic field. Making use of the variational principle which is shown to characterize the problem, proper solutions have been obtained for a semi-infinite plasma in which the density varies exponentially along the vertical. The dispersion relation has been derivd and solved numerically. We find that collisions with neutrals and viscosity have a stabilizing influence while Hall currents have a destabilizing influence on the growth rate of the unstable mode of disturbance.

The instability in a stratified layer of a self-gravitating infinitely conducting incompressible inviscid partially ionized plasma has been studied in the presence of effects of Hall currents, for a plasma permeated by a uniform two dimensional horizontal magnetic field, the proper solution has been obtained through the use of a variational principle which is shown to characterize the problem for a plasma in which the density is stratified exponentially along the vertical, the dispersion relation has been derived. Numerical calculations of the growth rate of the unstable modes of propagation have been performed from the dispersion relation for different values of the physical effects. It is found that the Hall currents have a destabilizing effect while the neutral gas frictional effects have a stabilizing influence on the instability of a conducting plasma.

The instability of a finite amplitude longitudinal plasma wave with trapped particles is discussed. Distinct instability regimes are examined within the framework of the simplest model wherein all trapped particles are assumed to be concentrated at the bottom of the potential energy troughs of a sinusoidal wave. The dispersion relation describing the instability is solved in combination with the nonlinear dispersion law of the primary wave. The self-consistent approach allows one to establish the conditions of validity of the model considered and to find, for practical purposes, convenient expressions for growth rates in all limiting cases. In accordance with the analysis carried out the ratio of trapped particle energy flux to wave energy flux is of great importance in the classification of sideband instability regimes.

The radio frequency absorption near the lower hybrid resonance of an inhomogeneous plasma has been studied using Langmuir and magnetic probes and also a Faraday cup. The plasma was confined in the mirror linear device LISA, excited by a 28 MHz RF source. It has been shown that the absorption rate and the resonance region in space depends on the resonant volume created by the external magnetic field. Due to the collisional damping, the quality factor of the machine is comparable to a low-Q cavity resonator.

The effect of an axial energy spread on the linear gain in backward wave oscillators is considered. The electron beam is assumed to be monoenergetic with a momentum spread. The results obtained show that for a Gaussian distribution in the beam axial momentum, the gain of a backward wave oscillator falls off rapidly when the momentum spread is of the order of 2.0% for a given set of parameters corresponding to backward wave oscillator experiments.

The nonlinear self-interaction of surface magnetoplasmons (SM) propagating across an external magnetic field at an n-type semiconductor-metal interface is considered. The studied nonlinearity is due to the nonparabolicity of the free carriers spectrum. The self-interaction of the SM is shown to be different in semiconductors with normal and inverse band structures. The results of the SM field envelope evolution are given. The action of the studied nonlinearity is shown to be most significant in narrow-gap semiconductor materials.

A simple model is introduced to describe the electronic structure of donor/conjugated-bridge/acceptor molecules. We apply a two-band model for the conjugated-bridge segment; these two (valence and conduction) bands are coupled with the frontier orbitals of the end groups (the donor and the acceptor, respectively). The ground state then consists of a hybridization of the valence band and the donor orbital. The excited state leading to charge transfer is expressed by a partially filled acceptor orbital hybridized with the conduction band. The partial density of states (PDOS) of the end groups is calculated by the Green's function method. The PDOS is determined by three factors: the unperturbed energy of the end groups, the unperturbed DOS of the bridge bands, and the coupling constants between the bridge bands and the end groups. Based on the results we obtain, a simple description of the intramolecular adiabatic charge transfer and the nonlinear optical response.