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

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

On integrable system on S2S^2 with the second integral quartic in the momenta

We consider integrable system on the sphere $S^2$ with an additional integral of fourth order in the momenta. At the special values of parameters this system coincides with the Kowalevski-Goryachev-Chaplygin system.Comment: LaTeX, 6 page

Total spectrum of photon emission by an ultra-relativistic positron channeling in a periodically bent crystal

We present the results of numerical calculations of the channelling and undulator radiation generated by an ultra-relativistic positron channelling along a crystal plane, which is periodically bent. The bending might be due either to the propagation of a transverse acoustic wave through the crystal, or due to the static strain as it occurs in superlattices. The periodically bent crystal serves as an undulator. We investigate the dependence of the intensities of both the ordinary channelling and the undulator radiations on the parameters of the periodically bent channel with simultaneous account for the dechannelling effect of the positrons. We demonstrate that there is a range of parameters in which the undulator radiation dominates over the channelling one and the characteristic frequencies of both types of radiation are well separated. This result is important, because the undulator radiation can be used to create a tunable source of X-ray and gamma-radiation.Comment: published in J. Phys. G: Nucl. Part. Phys. 26 (2000) L87-L95, http://www.iop.org ; 12 pages, 4 figures, LaTe

Система стратегического планирования: глобальные тенденции, внешние шоки и разработка подходов адаптации к ним

An effective modern strategic planning system should be based on two basic concepts: resilience (resistance or stability against any shocks) and long-term sustainability (with special emphasis on long-term). It is the ability to adapt to modern realities that determines the relevance and effectiveness of the implementation of strategic planning documents. According to various estimates, a full frontal national strategy can “fade” completely within 4–5 years. For a regional or sectoral strategy, according to our estimates, this happens in 2-3 years, for urban - in one. In this regard, it is necessary to determine the factors contributing to the “fading” (forgetting) of strategic documents, and to identify the main approaches, which can be implemented to extend their relevance. The study is dedicated to the analysis of the applicability of existing economic concepts to ensure the solution of the modern problem of socio-economic development: improving the quality of life, ensuring the stability and viability (resilience) of the economic system without increasing economic growth and investment activity (like GDP growth and increase in investments raised) as well as to putting forward recommendations for updating methodological approaches to the development of strategic documents with the aim of creating an adaptive and up-to-date strategic planning system. It was revealed that the strategic planning documents being developed in Russia are static and not capable of responding to changes in the socio-economic, political, cultural situation, while the country’s socio-economic development strategy should be a response tool of state authorities to external challenges, a flexible tool that allows reconfiguring the public administration system to respond to these challenges. It was found that there are two groups of factors responsible for the “fading” of strategic documents: direct - arising from the end of the official validity period of the strategies or due to their cancellation by the authority responsible for the development and implementation of these documents, and indirect – arising from socio-economic transformations taking place in the field of strategic planning and influencing the achievement of the respective documents. According to the results of the analysis of the news background of 10 strategies at regional and municipal level, it was revealed that the “fading period” differs both between regions and municipalities, and between individual cities and regions, depending on the local institutional environment, activity level of the civil society, attitude to the strategy (“formal implementation of the rules” against an effectively working document), etc. Changes were also proposed to Law 172-FZ regarding revision of the existing principles of goal-setting, as well as special testing procedures to ensure the resilience and stainability of the documents

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

Quantal Two-Centre Coulomb Problem treated by means of the Phase-Integral Method I. General Theory

The present paper concerns the derivation of phase-integral quantization conditions for the two-centre Coulomb problem under the assumption that the two Coulomb centres are fixed. With this restriction we treat the general two-centre Coulomb problem according to the phase-integral method, in which one uses an {\it a priori} unspecified {\it base function}. We consider base functions containing three unspecified parameters $C, \tilde C$ and $\Lambda$. When the absolute value of the magnetic quantum number $m$ is not too small, it is most appropriate to choose $\Lambda=|m|\ne 0$. When, on the other hand, $|m|$ is sufficiently small, it is most appropriate to choose $\Lambda = 0$. Arbitrary-order phase-integral quantization conditions are obtained for these choices of $\Lambda$. The parameters $C$ and $\tilde C$ are determined from the requirement that the results of the first and the third order of the phase-integral approximation coincide, which makes the first-order approximation as good as possible. In order to make the paper to some extent self-contained, a short review of the phase-integral method is given in the Appendix.Comment: 23 pages, RevTeX, 4 EPS figures, submitted to J. Math. Phy

The pd→3HΛK+pd\to ^3H_\Lambda K^+ reaction cross section

The one- and two-step mechanisms of the $pd\to ^3H_\Lambda K^+$ reaction in the range of incident proton kinetic energy 1.13-3.0 GeV have been investigated. A remarkable peculiarity of the two-step mechanism which incorporates subprocesses $pp\to d\pi ^+$ and $\pi^+n\to K^+\Lambda$ is the so called velocity matching providing the presence of all intermediate particles nearly to the on-mass-shell. The differential cross section has been calculated using a realistic model for the hypertritium $^3H_\Lambda$ wave function. The maximum value of the cross section is estimated as $\sim$1nb/sr. The contribution of the one-step mechanism with the elementary process $pN\to NK\Lambda$ into the cross section has been found to be two - three orders of magnitude smaller in comparison with the two-step mechanism.Comment: 10 pages, Latex, 3 Postscript figure

The problems of utilizing graphite of stopped graphite-uranium reactors

A list of radioactive nuclides, the activity of which forms the main part of total activity of graphite stack and graphite elements of the construction of stopped industrial graphite-uranium reactors has been defined. The analysis of activity part contributed by these nuclides at different moments of time after stopping reactor was carried out. A set of construction graphite elements, in which there is a possibility of self-sustaining release of the energy stored (Wigner's energy) was determined. It was stated that the most value of the Wigner's energy is achieved in graphite constructions operated in low-temperature region or at high values of flux densities of damaging neutrons and concurrent gamma radiation