Wave Functions and Energy Terms of the SCHR\"Odinger Equation with Two-Center Coulomb Plus Harmonic Oscillator Potential

Schr\"odinger equation for two center Coulomb plus harmonic oscillator potential is solved by the method of ethalon equation at large intercenter separations. Asymptotical expansions for energy term and wave function are obtained in the analytical form.Comment: 4 pages, no figures, LaTeX, submitted to PR

Polarization of Sunyaev-Zeldovich signal due to electron pressure anisotropy in galaxy clusters

We describe polarization of the Sunyaev-Zel'dovich (SZ) effect associated with electron pressure anisotropy likely present in the intracluster medium (ICM). The ICM is an astrophysical example of a weakly collisional plasma where the Larmor frequencies of charged particles greatly exceed their collision frequencies. This permits formation of pressure anisotropies, driven by evolving magnetic fields via adiabatic invariance, or by heat fluxes. SZ polarization arises in the process of Compton scattering of the cosmic microwave background (CMB) photons off the thermal ICM electrons due to the difference in the characteristic thermal velocities of the electrons along two mutually orthogonal directions in the sky plane. The signal scales linearly with the optical depth of the region containing large-scale correlated anisotropy, and with the degree of anisotropy itself. It has the same spectral dependence as the polarization induced by cluster motion with respect to the CMB frame (kinematic SZ effect polarization), but can be distinguished by its spatial pattern. { For the illustrative case of a galaxy cluster with a cold front, where electron transport is mediated by Coulomb collisions, we estimate the CMB polarization degree at the level of 10$^{-8}$ ($\sim 10$ nK). An increase of the effective electron collisionality due to plasma instabilities will reduce the effect. Such polarization, therefore, may be an independent probe of the electron collisionality in the ICM, which is one of the key properties of a high-$\beta$ weakly collisional plasma from the point of view of both astrophysics and plasma theory.Comment: 13 pages, 5 figures, accepted for publication in MNRA

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

Quantum tops as examples of commuting differential operators

We study the quantum analogs of tops on Lie algebras $so(4)$ and $e(3)$ represented by differential operators.Comment: 24 p

Spectra of Doubly Heavy Quark Baryons

Baryons containing two heavy quarks are treated in the Born-Oppenheimer approximation. Schr\"odinger equation for two center Coulomb plus harmonic oscillator potential is solved by the method of ethalon equation at large intercenter separations. Asymptotical expansions for energy term and wave function are obtained in the analytical form. Using those formulas, the energy spectra of doubly heavy baryons with various quark compositions are calculated analytically.Comment: 19 pages, latex2e, published at PRC61(2000)04520

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

Land management cluster zonning’s methods summary

The article focuses on methods of land management cluster zoning analysis. The authors have analyzed a lot of articles and books about zoning and concluded that there was insufficient attention to zoning methods. The article goal is to study different methods of cluster zoning (clustering of the municipal districts of a Russian region) for purposes of land management information support. The authors have defined the concept of “land management cluster zoning”, have analyzed the tree model method, the integrated zoning method and zoning based on the criterion of the efficiency of land management. These methods allow for cluster zoning of municipal districts. These methods have been tested using data from Novgorod Region. Based on the results of the study the authors have concluded that various zoning methods have yielded results close to 80%, but the choice of method should take into account the zoning purposes. For example, the tree model method is the most suitable one in the case of zoning based on indicators that have identical impact on land management. The method of integrated zoning is the most appropriate for application in the case of indications having different impact on land management. Zoning based on the criterion of land management efficiency separates municipal districts by one indicator. But this indicator is the key one.Статья посвящена вопросам анализа методов проведения кластерного зонирования территория региона для целей управления земельными ресурсами. Авторы проанализировали имеющийся массив литературных источников по теме и сделали вывод о незначительном внимании, которое уделяется непосредственно методам зонирования. Целью статьи является исследование различных методов кластерного зонирования региона (кластеризации административных образований, входящих в субъект Федерации) для целей информационного обеспечения процесса стратегического управления земельными и природными ресурсами региона. Для достижения указанной цели было дано определение кластерного зонирования для целей управления земельными ресурсами, проанализированы методы древовидной модели, зонирования с помощью интегрального показателя и зонирования по показателю эффективности, позволяющие разделить провести кластерное зонирование муниципальных образований региона. С помощью указанных методов проведено зонирование территории Новгородской области. По результатам исследования сделаны выводы, что различные методы зонирования в 80 % дали схожие между собой результаты, но различия в основе каждого из трех рассматриваемых методов позволяют выработать рекомендации по их применению, исходя из целей зонирования. Например, метод древовидной модели наиболее целесообразно применять при наличии комплекса показателей, оказывающих одинаковое влияние на управление земельными ресурсами. Метод комплексного зонирования разумнее всего применять в случаях, когда значимость факторов, влияющих на систему управления земельными ресурсами, сильно различается. Метод зонирования по критерию экономической эффективности разделяет муниципальные образования по одному, но ключевому для системы управления земельными ресурсами показателю. Широкие возможности открываются для использования результатов кластерного зонирования в системе стратегического планирования использования земельных ресурсов на региональных и муниципальных уровнях, т. к. в результате применения кластерного зонирования образуются группы муниципальных образований, однородных по показателям, влияющим на использование земельных ресурсов, или однородных по качеству управления ими

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

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

Sonoprocessing of materials (Special issue)

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