O. Yu. Khetselius

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 {dxi } ) 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.

GENERALIZED MULTICONFIGURATION MODEL OF DECAY OF MULTIPOLE GIANT RESONANCES APPLIED TO ANALYSIS OF REACTION (μ - n) ON THE NUCLEUS 40Ca

It is presented the generalized multiconfiguration model to decay of the multipole giant resonances (MGR), which is based on the shell models (with limited basis) and microscopic model of pre-equilibrium decay with statistical account for complex configurations 2p2h, 3p3h etc. The model is applied to analysis of reaction (μ-n) on the nucleus 40Ca.

Relativistic Quantum Chemistry and Spectroscopy of Exotic Atomic Systems with Accounting for Strong Interaction Effects

We present the fundamentals of a consistent relativistic theory of spectra of the exotic pionic atomic systems on the basis of the Klein-Gordon-Fock equation approach and relativistic many-body perturbation theory (electron subsystem). The key feature of the theory is simultaneous accounting for the electromagnetic and strong pion-nuclear interactions by means of using the generalized radiation and strong pion-nuclear optical potentials. The nuclear and radiative corrections are 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, which generalizes the Mohr procedure and radiation model potential method by Flambaum-Ginges. There are presented data of calculation of the energy and spectral parameters for pionic atoms of the 93Nb, 173Yb, 181Ta, 197Au, with accounting for the radiation (vacuum polarization), nuclear (finite size of a nucleus) and the strong pion-nuclear interaction corrections. The measured values of the Berkley, CERN and Virginia laboratories and alternative data based on other versions of the Klein-Gordon-Fock theories with taking into account for a finite size of the nucleus in the model uniformly charged sphere and the standard Uehling-Serber radiation correction are listed too.

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.

Electrodynamical and Quantum Chemical Modelling of Electrochemical and Catalytic Processes on Metals and Semiconductors: A Review

The advanced quantum-mechanical and electrodynamical approaches in the electron theory of catalysis have been generalized to determine quantitatively the catalytic activity for metals, binary metallic alloys and semiconductor materials. The solutions of some model tasks associated with stabilization of ionic states of atomic hydrogen and molecular oxygen in effective electron gas are given. Within the approach the quantitative correlation between the electron structure parameters of the materials and their catalytic activity is found on example of simple model reactions.

Modelling dynamics of atmosphere ventilation and industrial city’s air pollution analysis: New approach

We present a new effective approach to analysis and modelling the natural air ventilation in an atmosphere of the industrial city, which is based on the Arakawa-Schubert and Glushkov models, modified to calculate the current involvement of the ensemble of clouds, and advanced mathematical methods of modelling an unsteady turbulence in the urban area. For the first time the methods of a plane complex field and spectral expansion algorithms are applied to calculate the air circulation for the cloud layer arrays, penetrating into the territory of the industrial city. We have also taken into account for the mechanisms of transformation of the cloud system advection over the territory of the urban area. The results of test computing the air ventilation characteristics are presented for the Odessa city. All above cited methods and models together with the standard monitoring and management systems can be considered as a basis for comprehensive Green City construction technology.