1,396 research outputs found
Quantal Two-Centre Coulomb Problem treated by means of the Phase-Integral Method II. Quantization Conditions in the Symmetric Case Expressed in Terms of Complete Elliptic Integrals. Numerical Illustration
The contour integrals, occurring in the arbitrary-order phase-integral
quantization conditions given in a previous paper, are in the first- and
third-order approximations expressed in terms of complete elliptic integrals in
the case that the charges of the Coulomb centres are equal. The evaluation of
the integrals is facilitated by the knowledge of quasiclassical dynamics. The
resulting quantization conditions involving complete elliptic integrals are
solved numerically to obtain the energy eigenvalues and the separation
constants of the and states of the hydrogen molecule ion
for various values of the internuclear distance. The accuracy of the formulas
obtained is illustrated by comparison with available numerically exact results.Comment: 19 pages, RevTeX 4, 4 EPS figures, submitted to J. Math. Phy
Reply to comment ``On the test of the modified BCS at finite temperature''
This is our formal Reply to revised version (v2) of arXiv: nucl-th/0510004v2.Comment: accepted in Physical Review
Quantum Size Effect in Conductivity of Multilayer Metal Films
Conductivity of quantized multilayer metal films is analyzed with an emphasis
on scattering by rough interlayer interfaces. Three different types of quantum
size effect (QSE) in conductivity are predicted. Two of these QSE are similar
to those in films with scattering by rough walls. The third type of QSE is
unique and is observed only for certain positions of the interface. The
corresponding peaks in conductivity are very narrow and high with a finite
cutoff which is due only to some other scattering mechanism or the smearing of
the interface. There are two classes of these geometric resonances. Some of the
resonance positions of the interface are universal and do not depend on the
strength of the interface potential while the others are sensitive to this
potential. This geometric QSE gradually disappears with an increase in the
width of the interlayer potential barrier.Comment: 12 pages, 10 figures, RevTeX4, to be published in Phys. Rev B (April
2003
Test of modified BCS model at finite temperature
A recently suggested modified BCS (MBCS) model has been studied at finite
temperature. We show that this approach does not allow the existence of the
normal (non-superfluid) phase at any finite temperature. Other MBCS predictions
such as a negative pairing gap, pairing induced by heating in closed-shell
nuclei, and ``superfluid -- super-superfluid'' phase transition are discussed
also. The MBCS model is tested by comparing with exact solutions for the picket
fence model. Here, severe violation of the internal symmetry of the problem is
detected. The MBCS equations are found to be inconsistent. The limit of the
MBCS applicability has been determined to be far below the ``superfluid --
normal'' phase transition of the conventional FT-BCS, where the model performs
worse than the FT-BCS.Comment: 8 pages, 9 figures, to appear in PR
Theoretical and methodological grounds for the modernization of the tax administration system
The article stands for the theoretical underpinning of economic grounds of tax system and its building on the basis of social- and business-oriented socioeconomic features.
Authors proved the need for tax process management that represent the features of government-society-taxpayer relations with taxpayer’s leading role as macroeconomic tool for economic regulation process as well as providing the sustainable and balanced economic growth and innovative modernization of Russian economy.peer-reviewe
Self-consistent approach for the quantum confined Stark effect in shallow quantum wells
A computationally efficient, self-consistent complex scaling approach to
calculating characteristics of excitons in an external electric field in
quantum wells is introduced. The method allows one to extract the resonance
position as well as the field-induced broadening for the exciton resonance. For
the case of strong confinement the trial function is represented in factorized
form. The corresponding coupled self-consistent equations, which include the
effective complex potentials, are obtained. The method is applied to the
shallow quantum well. It is shown that in this case the real part of the
effective exciton potential is insensitive to changes of external electric
field up to the ionization threshold, while the imaginary part has
non-analytical field dependence and small for moderate electric fields. This
allows one to express the exciton quasi-energy at some field through the
renormalized expression for the zero-field bound state.Comment: 13 pages, RevTeX4, 6 figure
Inelastic neutrino scattering off hot nuclei in supernova environments
We study inelastic neutrino scattering off hot nuclei for temperatures
relevant under supernova conditions. The method we use is based on the
quasiparticle random phase approximation extended to finite temperatures within
the thermo field dynamics (TQRPA). The method allows a transparent treatment of
upward and downward transitions in hot nuclei, avoiding the application of
Brink's hypothesis. For the sample nuclei Fe and Ge we perform a
detailed analysis of thermal effects on the strength distributions of allowed
Gamow-Teller (GT) transitions which dominate the scattering process at low
neutrino energies. For Fe and Ge the finite temperature
cross-sections are calculated by taking into account the contribution of
allowed and forbidden transitions. The observed enhancement of the
cross-section at low neutrino energies is explained by considering thermal
effects on the GT strength. For Fe we compare the calculated
cross-sections to those obtained earlier from a hybrid approach that combines
large-scale shell-model and RPA calculations.Comment: 12 pages, 9 figure
Can We Apply Statistical Laws to Small Systems? the Cerium Atom
It is shown that statistical mechanics is applicable to quantum systems with
finite numbers of particles, such as complex atoms, atomic clusters, etc.,
where the residual two-body interaction is sufficiently strong. This
interaction mixes the unperturbed shell-model basis states and produces
``chaotic'' many-body eigenstates. As a result, an interaction-induced
equilibrium emerges in the system, and temperature can be introduced. However,
the interaction between the particles and their finite number can lead to
prominent deviations of the equilibrium occupation numbers distribution from
the Fermi-Dirac shape. For example, this takes place in the cerium atom with
four valence electrons, which was used to compare the theory with realistic
numerical calculations.Comment: 4 pages, Latex, two figures in eps-forma
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