2,145 research outputs found
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 ( 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- 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 and
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. 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 zonningβs 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 βland management cluster zoningβ, 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.Π‘ΡΠ°ΡΡΡ ΠΏΠΎΡΠ²ΡΡΠ΅Π½Π° Π²ΠΎΠΏΡΠΎΡΠ°ΠΌ Π°Π½Π°Π»ΠΈΠ·Π° ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½ΠΈΡ ΠΊΠ»Π°ΡΡΠ΅ΡΠ½ΠΎΠ³ΠΎ Π·ΠΎΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ΅ΡΡΠΈΡΠΎΡΠΈΡ ΡΠ΅Π³ΠΈΠΎΠ½Π° Π΄Π»Ρ ΡΠ΅Π»Π΅ΠΉ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ Π·Π΅ΠΌΠ΅Π»ΡΠ½ΡΠΌΠΈ ΡΠ΅ΡΡΡΡΠ°ΠΌΠΈ. ΠΠ²ΡΠΎΡΡ ΠΏΡΠΎΠ°Π½Π°Π»ΠΈΠ·ΠΈΡΠΎΠ²Π°Π»ΠΈ ΠΈΠΌΠ΅ΡΡΠΈΠΉΡΡ ΠΌΠ°ΡΡΠΈΠ² Π»ΠΈΡΠ΅ΡΠ°ΡΡΡΠ½ΡΡ
ΠΈΡΡΠΎΡΠ½ΠΈΠΊΠΎΠ² ΠΏΠΎ ΡΠ΅ΠΌΠ΅ ΠΈ ΡΠ΄Π΅Π»Π°Π»ΠΈ Π²ΡΠ²ΠΎΠ΄ ΠΎ Π½Π΅Π·Π½Π°ΡΠΈΡΠ΅Π»ΡΠ½ΠΎΠΌ Π²Π½ΠΈΠΌΠ°Π½ΠΈΠΈ, ΠΊΠΎΡΠΎΡΠΎΠ΅ ΡΠ΄Π΅Π»ΡΠ΅ΡΡΡ Π½Π΅ΠΏΠΎΡΡΠ΅Π΄ΡΡΠ²Π΅Π½Π½ΠΎ ΠΌΠ΅ΡΠΎΠ΄Π°ΠΌ Π·ΠΎΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ. Π¦Π΅Π»ΡΡ ΡΡΠ°ΡΡΠΈ ΡΠ²Π»ΡΠ΅ΡΡΡ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠ΅ ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ
ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΠΊΠ»Π°ΡΡΠ΅ΡΠ½ΠΎΠ³ΠΎ Π·ΠΎΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ΅Π³ΠΈΠΎΠ½Π° (ΠΊΠ»Π°ΡΡΠ΅ΡΠΈΠ·Π°ΡΠΈΠΈ Π°Π΄ΠΌΠΈΠ½ΠΈΡΡΡΠ°ΡΠΈΠ²Π½ΡΡ
ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΠΉ, Π²Ρ
ΠΎΠ΄ΡΡΠΈΡ
Π² ΡΡΠ±ΡΠ΅ΠΊΡ Π€Π΅Π΄Π΅ΡΠ°ΡΠΈΠΈ) Π΄Π»Ρ ΡΠ΅Π»Π΅ΠΉ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΎΠ½Π½ΠΎΠ³ΠΎ ΠΎΠ±Π΅ΡΠΏΠ΅ΡΠ΅Π½ΠΈΡ ΠΏΡΠΎΡΠ΅ΡΡΠ° ΡΡΡΠ°ΡΠ΅Π³ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ Π·Π΅ΠΌΠ΅Π»ΡΠ½ΡΠΌΠΈ ΠΈ ΠΏΡΠΈΡΠΎΠ΄Π½ΡΠΌΠΈ ΡΠ΅ΡΡΡΡΠ°ΠΌΠΈ ΡΠ΅Π³ΠΈΠΎΠ½Π°. ΠΠ»Ρ Π΄ΠΎΡΡΠΈΠΆΠ΅Π½ΠΈΡ ΡΠΊΠ°Π·Π°Π½Π½ΠΎΠΉ ΡΠ΅Π»ΠΈ Π±ΡΠ»ΠΎ Π΄Π°Π½ΠΎ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ ΠΊΠ»Π°ΡΡΠ΅ΡΠ½ΠΎΠ³ΠΎ Π·ΠΎΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π΄Π»Ρ ΡΠ΅Π»Π΅ΠΉ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ Π·Π΅ΠΌΠ΅Π»ΡΠ½ΡΠΌΠΈ ΡΠ΅ΡΡΡΡΠ°ΠΌΠΈ, ΠΏΡΠΎΠ°Π½Π°Π»ΠΈΠ·ΠΈΡΠΎΠ²Π°Π½Ρ ΠΌΠ΅ΡΠΎΠ΄Ρ Π΄ΡΠ΅Π²ΠΎΠ²ΠΈΠ΄Π½ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ, Π·ΠΎΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΠΈΠ½ΡΠ΅Π³ΡΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Ρ ΠΈ Π·ΠΎΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΠΎ ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Ρ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ, ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡΠΈΠ΅ ΡΠ°Π·Π΄Π΅Π»ΠΈΡΡ ΠΏΡΠΎΠ²Π΅ΡΡΠΈ ΠΊΠ»Π°ΡΡΠ΅ΡΠ½ΠΎΠ΅ Π·ΠΎΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΌΡΠ½ΠΈΡΠΈΠΏΠ°Π»ΡΠ½ΡΡ
ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΠΉ ΡΠ΅Π³ΠΈΠΎΠ½Π°. Π‘ ΠΏΠΎΠΌΠΎΡΡΡ ΡΠΊΠ°Π·Π°Π½Π½ΡΡ
ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½ΠΎ Π·ΠΎΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΡΠ΅ΡΡΠΈΡΠΎΡΠΈΠΈ ΠΠΎΠ²Π³ΠΎΡΠΎΠ΄ΡΠΊΠΎΠΉ ΠΎΠ±Π»Π°ΡΡΠΈ. ΠΠΎ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ°ΠΌ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΡΠ΄Π΅Π»Π°Π½Ρ Π²ΡΠ²ΠΎΠ΄Ρ, ΡΡΠΎ ΡΠ°Π·Π»ΠΈΡΠ½ΡΠ΅ ΠΌΠ΅ΡΠΎΠ΄Ρ Π·ΠΎΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π² 80 % Π΄Π°Π»ΠΈ ΡΡ
ΠΎΠΆΠΈΠ΅ ΠΌΠ΅ΠΆΠ΄Ρ ΡΠΎΠ±ΠΎΠΉ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ, Π½ΠΎ ΡΠ°Π·Π»ΠΈΡΠΈΡ Π² ΠΎΡΠ½ΠΎΠ²Π΅ ΠΊΠ°ΠΆΠ΄ΠΎΠ³ΠΎ ΠΈΠ· ΡΡΠ΅Ρ
ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΠΌΡΡ
ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ² ΠΏΠΎΠ·Π²ΠΎΠ»ΡΡΡ Π²ΡΡΠ°Π±ΠΎΡΠ°ΡΡ ΡΠ΅ΠΊΠΎΠΌΠ΅Π½Π΄Π°ΡΠΈΠΈ ΠΏΠΎ ΠΈΡ
ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΡ, ΠΈΡΡ
ΠΎΠ΄Ρ ΠΈΠ· ΡΠ΅Π»Π΅ΠΉ Π·ΠΎΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ. ΠΠ°ΠΏΡΠΈΠΌΠ΅Ρ, ΠΌΠ΅ΡΠΎΠ΄ Π΄ΡΠ΅Π²ΠΎΠ²ΠΈΠ΄Π½ΠΎΠΉ ΠΌΠΎΠ΄Π΅Π»ΠΈ Π½Π°ΠΈΠ±ΠΎΠ»Π΅Π΅ ΡΠ΅Π»Π΅ΡΠΎΠΎΠ±ΡΠ°Π·Π½ΠΎ ΠΏΡΠΈΠΌΠ΅Π½ΡΡΡ ΠΏΡΠΈ Π½Π°Π»ΠΈΡΠΈΠΈ ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠ° ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Π΅ΠΉ, ΠΎΠΊΠ°Π·ΡΠ²Π°ΡΡΠΈΡ
ΠΎΠ΄ΠΈΠ½Π°ΠΊΠΎΠ²ΠΎΠ΅ Π²Π»ΠΈΡΠ½ΠΈΠ΅ Π½Π° ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠ΅ Π·Π΅ΠΌΠ΅Π»ΡΠ½ΡΠΌΠΈ ΡΠ΅ΡΡΡΡΠ°ΠΌΠΈ. ΠΠ΅ΡΠΎΠ΄ ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠ½ΠΎΠ³ΠΎ Π·ΠΎΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ°Π·ΡΠΌΠ½Π΅Π΅ Π²ΡΠ΅Π³ΠΎ ΠΏΡΠΈΠΌΠ΅Π½ΡΡΡ Π² ΡΠ»ΡΡΠ°ΡΡ
, ΠΊΠΎΠ³Π΄Π° Π·Π½Π°ΡΠΈΠΌΠΎΡΡΡ ΡΠ°ΠΊΡΠΎΡΠΎΠ², Π²Π»ΠΈΡΡΡΠΈΡ
Π½Π° ΡΠΈΡΡΠ΅ΠΌΡ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ Π·Π΅ΠΌΠ΅Π»ΡΠ½ΡΠΌΠΈ ΡΠ΅ΡΡΡΡΠ°ΠΌΠΈ, ΡΠΈΠ»ΡΠ½ΠΎ ΡΠ°Π·Π»ΠΈΡΠ°Π΅ΡΡΡ. ΠΠ΅ΡΠΎΠ΄ Π·ΠΎΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΠΎ ΠΊΡΠΈΡΠ΅ΡΠΈΡ ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ ΡΠ°Π·Π΄Π΅Π»ΡΠ΅Ρ ΠΌΡΠ½ΠΈΡΠΈΠΏΠ°Π»ΡΠ½ΡΠ΅ ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΡ ΠΏΠΎ ΠΎΠ΄Π½ΠΎΠΌΡ, Π½ΠΎ ΠΊΠ»ΡΡΠ΅Π²ΠΎΠΌΡ Π΄Π»Ρ ΡΠΈΡΡΠ΅ΠΌΡ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ Π·Π΅ΠΌΠ΅Π»ΡΠ½ΡΠΌΠΈ ΡΠ΅ΡΡΡΡΠ°ΠΌΠΈ ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Ρ. Π¨ΠΈΡΠΎΠΊΠΈΠ΅ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠΈ ΠΎΡΠΊΡΡΠ²Π°ΡΡΡΡ Π΄Π»Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠΎΠ² ΠΊΠ»Π°ΡΡΠ΅ΡΠ½ΠΎΠ³ΠΎ Π·ΠΎΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π² ΡΠΈΡΡΠ΅ΠΌΠ΅ ΡΡΡΠ°ΡΠ΅Π³ΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΠΏΠ»Π°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ Π·Π΅ΠΌΠ΅Π»ΡΠ½ΡΡ
ΡΠ΅ΡΡΡΡΠΎΠ² Π½Π° ΡΠ΅Π³ΠΈΠΎΠ½Π°Π»ΡΠ½ΡΡ
ΠΈ ΠΌΡΠ½ΠΈΡΠΈΠΏΠ°Π»ΡΠ½ΡΡ
ΡΡΠΎΠ²Π½ΡΡ
, Ρ. ΠΊ. Π² ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΡ ΠΊΠ»Π°ΡΡΠ΅ΡΠ½ΠΎΠ³ΠΎ Π·ΠΎΠ½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΎΠ±ΡΠ°Π·ΡΡΡΡΡ Π³ΡΡΠΏΠΏΡ ΠΌΡΠ½ΠΈΡΠΈΠΏΠ°Π»ΡΠ½ΡΡ
ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈΠΉ, ΠΎΠ΄Π½ΠΎΡΠΎΠ΄Π½ΡΡ
ΠΏΠΎ ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»ΡΠΌ, Π²Π»ΠΈΡΡΡΠΈΠΌ Π½Π° ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ Π·Π΅ΠΌΠ΅Π»ΡΠ½ΡΡ
ΡΠ΅ΡΡΡΡΠΎΠ², ΠΈΠ»ΠΈ ΠΎΠ΄Π½ΠΎΡΠΎΠ΄Π½ΡΡ
ΠΏΠΎ ΠΊΠ°ΡΠ΅ΡΡΠ²Ρ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ ΠΈΠΌΠΈ
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
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