V. V. Buyadzhi

Relativistic Quantum Chemistry: An Advanced Approach to the Construction of the Green Function of the Dirac Equation with Complex Energy and Mean-Field Nuclear Potential

We present an advanced approach to construction of the electron Green’s function of the Dirac equation with a non-singular central nuclear potential and complex energy. The Fermi-model and relativistic mean-field (RMF) nuclear potentials are used. The radial Green’s function is represented as a combination of two fundamental solutions of the Dirac equation. The approach proposed includes a procedure of generating the relativistic electron functions with performance of the gauge invariance principle. In order to reach the gauge invariance principle performance we use earlier developed QED perturbation theory approach. In the fourth order of the QED perturbation theory (PT) there are diagrams, whose contribution into imaginary part of radiation width Im δE for the multi-electron system accounts for multi-body correlation effects. A minimization of the functional Im δE leads to integral-differential Dirac-Kohn-Sham-like density functional equations. Further check for the gauge principle performance is realized by means of the Ward identities. In the numerical procedure we use the effective Ivanova-Ivanov’s algorithm, within which a determination of the Dirac equation fundamental solutions is reduced to solving the single system of the differential equations. This system includes the differential equations for the nuclear potential and equations for calculating the integrals of \( {\iint {dr_{1} dr_{2} } } \) type in the Mohr’s formula for definition of the self-energy shift to atomic levels energies. Such a approach allows to compensate a main source of the errors, connected with numerical integration \( \int {d\xi } \) and summation on χ in the Mohr’s expressions during calculating the self-energy radiative correction to the atomic levels energies. As illustration, data on the nuclear finite size effect and self-energy Lamb shift contributions to the energy of 2s-2p1/2 transition for the Li-like ions of argon, iron, krypton and uranium are presented and compared with available theoretical and experimental results.

Spectroscopy of Rydberg atoms in a Black-body radiation field: Relativistic theory of excitation and ionization

The combined relativistic energy approach and many-body perturbation theory with zeroth model potential approximation are used for computing Blackbody radiation ionization characteristics of the Rydberg atoms, in particular, the sodium in states with n=17,18,40-70. The calculated ionization rate values are compared with available theoretical and experimental data.

Relativistic Many-Body Perturbation Theory Calculations of the Hyperfine Structure and Oscillator Strength Parameters for Some Heavy Element Atoms and Ions

The formalism of the relativistic many-body perturbation theory with an optimized zeroth approximation is applied to computing the energies and hyperfine structure constants for some heavy Li-like multicharged ions and alkali (caesium) atoms. The exchange-correlation, nuclear and radiative corrections are correctly and effectively taken into account. The modified Uehling-Serber approximation is used to take into account for the Lamb shift polarization part. In order to take into account the contribution of the Lamb shift self-energy part we have used the generalized non-perturbative procedure, developed by Ivanov-Ivanova et al. The energies and oscillator strengths of radiation transition in spectra of some Li-like ions (Z = 20 – 70) and Cs are computed on the basis of the combined relativistic energy approach (S-matrix formalism) and relativistic many-body perturbation theory. The data on oscillator strengths of radiative transitions from the ground state to the low-excited and Rydberg states 2s1/2 – np1/2,3/2, np1/2,3/2-nd3/2,5/2 (n = 2 – 12) in the Li-like ions are presented. Some results are obtained at first. It is performed an analysis of the computed oscillator strength values with available theoretical and experimental results.

An effective chaos-geometric computational approach to analysis and prediction of evolutionary dynamics of the environmental systems: Atmospheric pollution dynamics

The present paper concerns the results of computational studying dynamics of the atmospheric pollutants (dioxide of nitrogen, sulphur etc) concentrations in an atmosphere of the industrial cities (Odessa) by using the dynamical systems and chaos theory methods. A chaotic behaviour in the nitrogen dioxide and sulphurous anhydride concentration time series at several sites of the Odessa city is numerically investigated. As usually, to reconstruct the corresponding attractor, the time delay and embedding dimension are needed. The former is determined by the methods of autocorrelation function and average mutual information, and the latter is calculated by means of a correlation dimension method and algorithm of false nearest neighbours. Further, the Lyapunovs exponents spectrum, Kaplan-Yorke dimension and Kolmogorov entropy are computed. It has been found an existence of a low-D chaos in the time series of the atmospheric pollutants concentrations.

Nonlinear dynamics of laser systems with elements of a chaos: Advanced computational code

A general, uniform chaos-geometric computational approach to analysis, modelling and prediction of the non-linear dynamics of quantum and laser systems (laser and quantum generators system etc) with elements of the deterministic chaos is briefly presented. The approach is based on using the advanced generalized techniques such as the wavelet analysis, multi-fractal formalism, mutual information approach, correlation integral analysis, false nearest neighbour algorithm, the Lyapunovs exponents analysis, and surrogate data method, prediction models etc There are firstly presented the numerical data on the topological and dynamical invariants (in particular, the correlation, embedding, Kaplan-York dimensions, the Lyapunovs exponents, Kolmogorovs entropy and other parameters) for laser system (the semiconductor GaAs/GaAlAs laser with a retarded feedback) dynamics in a chaotic and hyperchaotic regimes.