86 research outputs found
Analytic approximation for eigenvalues of a class of symmetric Hamiltonians
An analytical approximation for the eigenvalues of symmetric
Hamiltonian ,
is developed via simple basis sets of harmonic-oscillator wave
functions with variable frequencies and equilibrium positions. We demonstrate
that our approximation provides high accuracy for any given energy level for
all values of .Comment: 8 pages, 3 figure
Self-consistent approach to x-ray reflection from rough surfaces
A self-consistent analytical approach for specular x-ray reflection from interfaces with transition layers I. D.
Feranchuk et al., Phys. Rev. B 67, 235417 2003 based on the distorted-wave Born approximation DWBA
is used for the description of coherent and incoherent x-ray scattering from rough surfaces and interfaces. This
approach takes into account the transformation of the modeling transition layer profile at the interface, which
is caused by roughness correlations. The reflection coefficients for each DWBA order are directly calculated without phenomenological assumptions on their exponential decay at large scattering angles. Various regions of scattering angles are discussed, which show qualitatively different dependence of the reflection coefficient on the scattering angle. The experimental data are analyzed using the method developed
Radical increase of the parametric X-ray intensity under condition of extremely asymmetric diffraction
Parametric X-ray radiation (PXR) from relativistic electrons moving in a
crystal along the crystal-vacuum interface is considered. In this geometry the
emission of photons is happening in the regime of extremely asymmetric
diffraction (EAD). In the EAD case the whole crystal length contributes to the
formation of X-ray radiation opposed to Laue and Bragg geometries, where the
emission intensity is defined by the X-ray absorption length. We demonstrate
that this phenomenon should be described within the dynamical theory of
diffraction and predict a radical increase of the PXR intensity. In particular,
under realistic electron-beam parameters, an increase of two orders of
magnitude in PXR-EAD intensity can be obtained in comparison with conventional
experimental geometries of PXR. In addition we discuss in details the
experimental feasibility of the detection of PXR-EAD.Comment: 9 pages, 5 figure
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
Operator Method for Nonperturbative Calculation of the Thermodynamic Values in Quantum Statistics. Diatomic Molecular Gas
Operator method and cumulant expansion are used for nonperturbative
calculation of the partition function and the free energy in quantum
statistics. It is shown for Boltzmann diatomic molecular gas with some model
intermolecular potentials that the zeroth order approximation of the proposed
method interpolates the thermodynamic values with rather good accuracy in the
entire range of both the Hamiltonian parameters and temperature. The systematic
procedure for calculation of the corrections to the zeroth order approximation
is also considered.Comment: 22 pages, 7 Postscript figures, accepted for publication in Journal
of Physics
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