Dispersion and attenuation of surface shear acoustic waves with horizontal polarization on the free statistically rough surface of the hexagonal crystal

Expressions for dispersion of the phase velocity and inverse damping depth of surface acoustic waves with shear horizontal polarization are derived in an analytical form within perturbation theory using the modified mean-field method for the Z-cut hexagonal crystal with a free statically rough surface. Both two-and one-dimensionally rough surfaces are considered. The one-dimensionally rough surface is considered as a special case of the two-dimensionally rough surface. It is shown that shear surface waves with horizontal polarization cannot exist on the flat surface of the Z-cut hexagonal crystal. The derived expressions are studied analytically and numerically in the entire frequency range accessible in perturbation theory. The long-wavelength limit (most interesting from the experimental point of view) is considered, where the wavelength is much longer than the roughness correlation radius. The conditions for the existence of SH-polarized waves are determined for both roughness types. It is shown that dispersion and attenuation of SH polarized waves are qualitatively similar in character to those we considered previously for an isotropic medium.     

Dispersion and attenuation of Rayleigh waves at a one-dimensional random roughness of the free surface of a hexagonal crystal

Analytical expressions are derived for dispersion and attenuation of Rayleigh waves propagating along the statistically rough free surface of a hexagonal crystal (Z cut). The roughness under consideration is one-dimensional (the profile function of the roughness depends on one coordinate) and has the form of hollows of a random lattice. The results obtained earlier in the solution of an analogous problem for a two-dimensional roughness are used in the one-dimensional case. The relationships derived for the dispersion and attenuation of Rayleigh waves are treated analytically and numerically over the entire range of frequencies acceptable in the framework of the perturbation theory. It is shown that the dispersion and attenuation of Rayleigh waves are qualitatively similar to those observed in an isotropic medium.     

Rayleigh wave attenuation due to the scattering by two-dimensional irregularities of the walls of an empty borehole

Attenuation of the Rayleigh waves propagating along an irregular surface of an empty borehole is investigated. This problem generalizes the problem on the attenuation of Rayleigh waves by an irregular boundary of a half-space. The technique used to evaluate the attenuation coefficient is based on the perturbation method and the mean field method. As a result, an expression is obtained that relates the partial attenuation coefficients of the surface Rayleigh wave to the scattering by the irregular surface of an empty borehole into the bulk longitudinal and transverse waves (the R → P and R → S processes) and into the surface Rayleigh waves (the R → R processes). The frequency-dependent behavior of the partial attenuation coefficients is analyzed for different correlation functions of irregularities.     

Nonequilibrium energy of Rayleigh waves in half-limited crystals with hot electrons close to the defect surface

Nonequilibrium energies of surface (Rayleigh) lattice oscillations in half-limited crystals with static defects and a two-dimensional layer of hot Fermi and Boltzmann electrons close to the stress free surface were calculated. Substances with electrons heated by an external field retaining their intrinsic temperature for a certain time, T _e ? T, where T is the temperature of the lattice, were considered. As shown earlier, the thermodynamic characteristics of thin films can then be determined by nonequilibrium energy of Rayleigh waves (R-phonons) caused by their interaction with hot electrons. This energy decreases as the widths of the energy spectrum of R-phonons increase. In this work, the earlier calculated spectrum widths are used. These widths are caused by the scattering of R-phonons by electrons and static defects close to the surface (point and extended surface defects, edge dislocations perpendicular to the surface and emerging to it, and random lattice grooves in the lattice plane). In all the calculations, the Keldysh diagram technique transformed for half-limited media was used.     

Effect of the nuclear charge of a fast structural ion on its internal effective stopping in collisions with atoms

The energy losses of fast structural ions in collisions with atoms have been considered in the eikonal approximation. The structural ions are ions consisting of a nucleus and a certain number of electrons bound to it. The effect of nuclear charge Z of the ion on its effective deceleration κ^(p) (energy losses associated with excitation of only intrinsic ion shells) has been analyzed. It is shown that the allowance for the interaction of an atom with the ion nucleus for Z _a Z/v > 1, where Z _a is the charge of the atomic nucleus and v is the velocity of collisions in atomic units, considerably affects the value of κ^(p), which generally necessitates taking into account nonperturbatively the effect of both charges Z _a and Z on κ^(p).     

Electron gas induced in SrTiO<Subscript>3</Subscript>

This mini-review is dedicated to the 85th birthday of Prof. L.V. Keldysh, from whom we have learned so much. In this paper, we study the potential and electron density depth profiles in surface accumulation layers in crystals with a large and nonlinear dielectric response such as SrTiO₃ (STO) in the cases of planar, spherical, and cylindrical geometries. The electron gas can be created by applying an induction D₀ to the STO surface. We describe the lattice dielectric response of STO using the Landau–Ginzburg free energy expansion and employ the Thomas–Fermi (TF) approximation for the electron gas. For the planar geometry, we arrive at the electron density profile n(x) ∝ (x + d)^–12/7, where d ∝ D₀^–12/7. We extend our results to overlapping electron gases in GTO/STO/GTO heterojunctions and electron gases created by spill-out from NSTO (heavily n-type doped STO) layers into STO. Generalization of our approach to a spherical donor cluster creating a big TF atom with electrons in STO brings us to the problem of supercharged nuclei. It is known that for an atom with a nuclear charge Ze where Z > 170, electrons collapse onto the nucleus, resulting in a net charge Zn < Z. Here, instead of relativistic physics, the collapse is caused by the nonlinear dielectric response. Electrons collapse into the charged spherical donor cluster with radius R when its total charge number Z exceeds the critical value Z_c ≈ R/a, where a is the lattice constant. The net charge eZ_n grows with Z until Z exceeds Z* ≈ (R/a)^9/7. After this point, the charge number of the compact core Z_n remains ≈ Z*, with the rest Z* electrons forming a sparse TF atom with it. We extend our studies of collapse to the case of long cylindrical clusters as well.     

Sound attenuation in a random waveguide when using a radiating system with different patterns of directivity

Using numerical simulations of sound propagation on Russia’s shallow Arctic shelf, low frequency sound attenuation is analyzed for acoustic sources with different patterns of directivity, i.e., vertical discrete radiating arrays of different length. It is shown that sound attenuation depends largely on the parameters of patterns of directivity and the intensity of surface waves even at short ranges r from a source (r < 250H, where H is the waveguide depth).     

Use of sturmian expansions in calculations of the hyperfine structure of atomic spectra

A procedure for calculating hyperfine structure (HFS) parameters using the basis of Sturmian functions is developed. The procedure is used to calculate the HFS parameter a _4d ⁵ of the 4d ⁵ levels of the niobium atom. The contributions of the continuous spectrum and higher orders of the perturbation theory are quantitatively estimated by comparing the numerical values of the parameter a _4d ¹⁰ obtained in the framework of the perturbation theory with the results of direct calculations by the configuration interaction method. Comparison of the results of relativistic and nonrelativistic calculations allows the contribution of relativistic effects to HFS parameters to be found.     

Crystallization and melting of spin-polarized<Superscript>3</Superscript>He

The melting and growth of³He crystals, spin-polarized by an external magnetic field, are different in nature depending on whether the temperature is higher or lower than the characteristic ordering temperatures in the crystal (the Neel temperatureT _N ) and in the liquid (the superfluid transition temperatureT _c ). In the high-temperature region (T≥T _N ,T _c ) the liquid which appears upon melting has a high nonequilibrium spin density. In the low-temperature region (T?T _N ,T _c ) the melting and growth are accompanied by spin supercurrents both in the liquid and in the crystal in addition to mass supercurrents in the liquid. The crystallization waves at the liquid-solid interface should exist in the low-temperature region. With increasing magnetic field the waves change in nature, because the spin currents begin to play a dominant role. The wave spectrum becomes linear with a velocity inversely proportional to the magnetic field. The attenuation of the waves at low enough temperatures is mainly due to the interaction of the moving crystal-liquid interface with thermal spin waves in the crystal. The waves could be weakly damped at temperatures below a few hundreds microkelvins.     

Two-loop self-energy correction in a strong Coulomb nuclear field

The two-loop self-energy correction to the ground-state energy levels of hydrogen-like ions with nuclear charges Z≥10 is calculated without the Zα expansion, where α is the fine-structure constant. The data obtained are compared with the results of analytical calculations within the Zα expansion; significant disagreement with the analytical results of order α²(Zα)⁶ has been found. Extrapolation is used to obtain the most accurate value for the two-loop self-energy correction for the 1s state in hydrogen.     

Double <Emphasis Type="Italic">K</Emphasis>-shell ionization of atoms by a single photon

We investigate the double K-shell ionization of heliumlike ions by a single photon. A fast convergence of QED perturbation theory with respect to the parameter 1/Z is demonstrated in the entire nonrelativistic domain for moderate nuclear charge numbers Z≥2. The ratio of double-to-single photoionization cross sections is calculated for light heliumlike ions, taking into account the leading orders of 1/Z and αZ expansions. A comparison of our results with the available experimental data for a number of neutral atoms is presented.     

Soliton dynamics in a spin nematic

One-dimensional localized waves, which can be considered as soliton elementary excitations, exist in a magnet with a unit spin and comparable bilinear and biquadratic spin-spin interactions, with which the state of spin nematic is realized. These excitations are characterized by a certain momentum P and a certain energy E. The structure of these solitons has been found, and the E = E(P) dependence, which plays the role of the dispersion law of these soliton elementary excitations, has been constructed. The energy of a soliton with a certain momentum is shown to be lower than that of the quasiparticles of a linear theory. At small momenta, these E = E(P) dependences of the soliton and quasiparticles coincide asymptotically. The dependence of the soliton energy on the soliton momentum is a periodic function with a period P ₀ = π?/a, whose value does not depend on exchange integrals and depends only on a single crystal parameter, namely, the interatomic distance a. These soliton excitations have common features with the so-called Lieb states, which are well known in many condensed matter models.     

Transformation of Bessel Beams in <Emphasis Type="Italic">C</Emphasis>-Cuts of Uniaxial Crystals by Varying the Emission Source Wavelength

We investigate experimentally the transformation of zero-order Bessel beams to a second-order Bessel eam in a c-cut of a CaCO₃ crystal. We show that the output-beam shape can be controlled by varying the emission-source wavelength and using a diffractive axicon. Beams were converted nearly totally at a wavelength change of Δλ = 1.5 nm and an initial wavelength λ = 637.5 nm of a CaCO₃ crystal, 15 mm in length, and a diffractive axicon with a period of 2 μm. We estimate the required wavelength variation Δλ = 1.7 nm, which is consistent with the experimental results.     

Obliquely Propagating Electron Acoustic Shock Waves in Magnetized Plasma

Obliquely propagating electron acoustic shock waves in plasma with stationary ions, cold and superthermal hot electrons are investigated in magnetized plasma. Employing reductive perturbation method, Korteweg-de Vries-Burgers equation (KdVB) is derived in the small amplitude approximation limit. The analytical and numerical calculations of the KdVB equation show the variation of shock waves structure (amplitude, velocity, and width) with different plasma parameters. Particle density (α), superthermal parameter (κ), electron temperature ratio (??), kinetic viscosity (η₀), obliqueness (k_z), and strength of magnetic field (ω_c) significantly modify the properties of the shock waves structures. The present investigation is useful to understand dissipative structures observed in space or laboratory plasma where multielectrons population with superthermal electrons are prevalent.     

Delbrück-Streuung von 17 MeV-Photonen

Differential cross sections have been measured for the small angle scattering ofγ-rays by iron, silver, tantalum, lead and uranium with 17 MeV photons from Li⁷ (p, γ) Be⁸ at mean four momentum transfersq of 0·5mc and 1·3mc and with 7 MeV photons from F¹⁹(p, αγ)O¹⁶ at mean four momentum transfer of 0·5mc. Under these experimental conditions only Compton, Rayleigh and possibly Delbrück scattering are of importance. Extrapolation of known theoretical results to higher energies shows, that Rayleigh and Compton scattering from bound electrons should depend only onq for small angles, smallq and fixedZ. Using this it follows, that at 17 MeV andq≈0·5mc an additional scattering process must be present, which increases with growingZ and which is negligible in the measurements at 17 MeV withq≈1·3mc and at 7 MeV withq≈0·5mc. These results are in qualitative agreement with the approximate theory for Delbrück scattering ofBethe andRohrlich, however experimental cross sections at 17 MeV andq≈0·5mc are about a factor of 1·6 lower than those predicted by this theory. This discrepancy is not unexpected, since exact calculations of Delbrück scattering amplitude fromKessler andZernik at 2·62 MeV and 6·14 MeV show even greater deviations in the same sense.     

Ionization-Excitation of helium-like ions by high-energy electrons

The differential and total cross sections are calculated for the ionization of helium-like ions that is accompanied by the excitation of residual ions to ns states owing to an electron impact. Nonrelativistic perturbation theory in electron–electron interaction with Coulomb functions used for a zero-order approximation underlies these calculations. The expressions obtained in this way have a universal character. They are applicable at moderate values of the target charge number Z and high energies of incident electrons. A comparison with total cross sections calculated for the helium atom within various theoretical approaches is performed.     

Ab initio calculations of Born charges in ferroelectrics with a perovskite structure

A method has been proposed for calculating Born effective charges in compounds with a cubic perovskite structure. The method is based on the first-principles calculation of individual contributions from the short-range interaction and the intercell dipole-dipole interaction to the Born tensor Z _ii (s) for crystalline dielectrics. It has been shown that the contribution from the short-range interaction Z _ii ^sr (s) to the Born tensor components can be derived from ab initio calculations performed for polyatomic clusters. The results of the calculations of the short-range interactions Z _ii ^sr (s) for the cubic phases of the BaTiO₃, SrTiO₃, CaTiO₃, PbTiO₃, BaZrO₃, PbZrO₃, KNbO₃, and KTaO₃ compounds with the use of the electronic structure calculations within the Hartree-Fock approximation and the density functional theory are presented. For the BaTiO₃, SrTiO₃, CaTiO₃, PbTiO₃, KNbO₃, and KTaO₃ compounds, the components of the complete Born tensor have been also calculated. The obtained values of Z _ii (s) are in good agreement with the results of the calculations in terms of the linear response theory and the Berry phase approach.     

Characteristics of surface acoustic waves in (11$$\bar 2$$ 0)ZnO film/ R-sapphire substrate structures

(11\(\bar 2\)0)ZnO film/R-sapphire substrate structure is promising for high frequency acoustic wave devices. The propagation characteristics of SAWs, including the Rayleigh waves along [0001] direction and Love waves along [1ī00] direction, are investigated by using 3 dimensional finite element method (3D-FEM). The phase velocity (v _p), electromechanical coupling coefficient (k ²), temperature coefficient of frequency (TCF) and reflection coefficient (r) of Rayleigh wave and Love wave devices are theoretically analyzed. Furthermore, the influences of ZnO films with different crystal orientation on SAW properties are also investigated. The results show that the 1st Rayleigh wave has an exceedingly large k ² of 4.95% in (90°, 90°, 0°) (11\(\bar 2\)0)ZnO film/R-sapphire substrate associated with a phase velocity of 5300 m/s; and the 0th Love wave in (0°, 90°, 0°) (11\(\bar 2\)0)ZnO film/R-sapphire substrate has a maximum k ² of 3.86% associated with a phase velocity of 3400 m/s. And (11\(\bar 2\)0)ZnO film/R-sapphire substrate structures can be used to design temperature-compensated and wide-band SAW devices. All of the results indicate that the performances of SAW devices can be optimized by suitably selecting ZnO films with different thickness and crystal orientations deposited on R-sapphire substrates.     

Relativistic theory of the electric quadrupole moment of a hydrogen-like atom in the <Emphasis Type="Italic">s</Emphasis>1/2 and <Emphasis Type="Italic">p</Emphasis>1/2 states

Relativistic analytical expressions are derived for the electric quadrupole moment induced by the hyperfine interaction of the electron with the nucleus of a hydrogen-like atom in the ns_1/2 and np_1/2 states. The magnetic dipole and electric quadrupole hyperfine interactions are taken into account. The calculations are performed using the generalized virial relationships for the Dirac equation in a central field. The dependences of the electric quadrupole moment on the nuclear charge Z and the principal quantum number n are analyzed. The induced quadrupole moments are compared with the nuclear quadrupole moments.