On integration of the Kowalevski gyrostat and the Clebsch problems

For the Kowalevski gyrostat change of variables similar to that of the Kowalevski top is done. We establish one to one correspondence between the Kowalevski gyrostat and the Clebsch system and demonstrate that Kowalevski variables for the gyrostat practically coincide with elliptic coordinates on sphere for the Clebsch case. Equivalence of considered integrable systems allows to construct two Lax matrices for the gyrostat using known rational and elliptic Lax matrices for the Clebsch model. Associated with these matrices solutions of the Clebsch system and, therefore, of the Kowalevski gyrostat problem are discussed. The Kotter solution of the Clebsch system in modern notation is presented in detail.Comment: LaTeX, 24 page

Operator method in solving non-linear equations of the Hartree-Fock type

The operator method is used to construct the solutions of the problem of the polaron in the strong coupling limit and of the helium atom on the basis of the Hartree-Fock equation. $E_0=-0.1085128052\alpha^2$ is obtained for the polaron ground-state energy. Energies for 2s- and 3s-states are also calculated. The other excited states are briefly discussed.Comment: 7 page

Relativistic dynamical polarizability of hydrogen-like atoms

Using the operator representation of the Dirac Coulomb Green function the analytical method in perturbation theory is employed in obtaining solutions of the Dirac equation for a hydrogen-like atom in a time-dependent electric field. The relativistic dynamical polarizability of hydrogen-like atoms is calculated and analysed.Comment: 15 pages, 3 figures (not included, but hard copies are available upon request

Structural Peculiarities of A3B5 Nanocrystals Created in Si by Ion-Beam Synthesis

We reported the structure peculiarities of nanocrystals formed in Si by means of high-fluence implantation at 25 and 500 °С followed by rapid thermal annealing (RTA). The structure of implanted samples has been investigated by means of transmission electron microscopy (TEM). The crystalline nature of the precipitates is proved by the Moiré fringe patterns presence in the TEM images. The Moiré fringe distance (Moiré period) is equal of 1.8 nm for small precipitates. This experimental value coincides with the calculated one for crystalline InAs. It is noted a Moiré period increasing in the case of large precipitates. We suppose that this feature is a result of surplus As or In atoms embedded in precipitates. One can see an interesting effect – “glowng” of nanocrystal/Si interfaces at the dark-field images of implanted and annealed samples. We ascribe this effect to a presence of misfit dislocation networks at the InAs/Si interfaces generated as a result of strain relaxation in highly mismatched InAs/Si system. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/3543

Mechanisms of arsenic clustering in silicon

A model of arsenic clustering in silicon is proposed and analyzed. The main feature of the proposed model is the assumption that negatively charged arsenic complexes play a dominant role in the clustering process. To confirm this assumption, electron density and concentration of impurity atoms incorporated into the clusters are calculated as functions of the total arsenic concentration. A number of the negatively charged clusters incorporating a point defect and one or more arsenic atoms are investigated. It is shown that for the doubly negatively charged clusters or for clusters incorporating more than one arsenic atom the electron density reaches a maximum value and then monotonically and slowly decreases as total arsenic concentration increases. In the case of doubly negatively charged cluster incorporating two arsenic atoms, the calculated electron density agrees well with the experimental data. Agreement with the experiment confirms the conclusion that two arsenic atoms participate in the cluster formation. Among all present models, the proposed model of clustering by formation of doubly negatively charged cluster incorporating two arsenic atoms gives the best fit to the experimental data and can be used in simulation of high concentration arsenic diffusion.Comment: 13 pages, 4 figures. Revised and shortened version of the paper has been published in Phys. Rev. B, Vol.74 (3), art. no. 035205 (2006

Change in structural properties of thin crystals of Si under electron irradiation

The action of electron irradiation on the structural properties of silicon was studied

A new method for calculation of crystal susceptibilities for X-ray diffraction at arbitrary wavelength

A novel method for the calculation of the X-ray susceptibility of a crystal in a wide range of radiation wavelengths is described. An analytical interpolation of one-electron wave functions is built to approximate the solution to Hartree± Fock equations for all atoms and ions of the periodic system of elements with high accuracy. These functions allow the calculation of the atomic form factors in the entire range of a transmitted momentum as well as the description of their anisotropy taking into account external and intracrystalline ®elds. Also, an analytical approximation for the force matrix of an arbitrary crystal is obtained and the microscopic calculation of the Debye±Waller factor for crystals with a complicated unit cell is presented

Glass capillary X-ray lens: fabrication technique and ray tracing calculations

A new method for producing a compound refractive X-ray lens is described. The lens is designed as glass capillary "lled by a set of concave individual lenses. The method is appropriate for the preparation of 10}1000 spherical lenses in a glass capillary with a diameter of 0.1}1 mm. Lens aberrations are considered and simple formulas for spot size are derived. Ray-tracing simulations on the focusing experiments using 18 keV X-rays are reported. ( 2000 Elsevier Science B.V. All rights reserved

Development of technology and investigation of structure and properties of composites on the basis of shungit and polymer resins

The technology for manufacturing of composites based on polymer (epoxy) resins and shungites was developed by using of the electron irradiation and experienced samples with different percentages of the components a) 90 and 10 %, b) 70 and 30 %, c) 50 and 50 %, were manufactured respectively. It was carried out the series of experimental studies of the structure and properties of the obtained materials, including the atomic force microscope images were obtained and Raman spectra of these composites were measured and their analysis was per-formed