Optical properties of lithium niobate and lithium tantalate crystals with impurities and defects

The photoinduced and Raman scattering in lithium niobate and lithium tantalate crystals with impurities and defects have been studied. An exciting laser beam propagated either along the ferroelectric Z axis or perpendicular to it. The conditions for exciting transverse and longitudinal polar optical modes in Raman spectra are established. The regularities of the excitation of Raman spectra in several polarization geometries (X(ZZ)Y, Z(XX, Y Y)Z, Z(XX, Y Y)Z, X(ZX)Y, X(ZX)X and X(ZX)X) have been investigated. Additional (extra) spectral lines are interpreted as a manifestation of a biphonon enhanced by the Fermi resonance and the result of violation of selection rules for pseudoscalar modes of the A ₂ type due to the reduction of the point symmetry group caused by the presence of impurities and defects in real crystals. The conditions for exciting coherent longitudinal and transverse modes in lithium niobate and lithium tantalate single crystals upon stimulated Raman scattering are analyzed. The temperature evolution of the spectra recorded in the X(ZZ)Y geometry near the ferroelectric phase transition point is explained based on the concept of effective soft mode and analysis of the isofrequency opalescence effect. Strong photoluminescence is found in copper-doped lithium niobate crystals.     

Stability of a rotating pinch

The problem of pinch stabilisation is of interest in connection with plasma confinement and has been the subject matter of various investigations in recent years, (Kruskal andSchwarzschild, Taylor, Shafranov). The theoretical investigations in the past have been restricted to static equilibrium configurations. It is of some interest to explore whether an initial motion of plasma tends to make the pinch more, or less stable than when the fluid velocity is zero. Keeping this in mind let us investigate theaxisymmetric stability of an infinitely long cylindrical plasma column of radiusR rotating uniformly with angular velocityΩ about theZ-axis, the fluid being assumed to the incompressible, inviscid, and of infinite electrical conductivity. The plasma carries a uniform axial current of densityj ₀ and a uniform axial magnetic fieldH ₁. The field outside is taken to beH ₂ inZ-direction and a toroidal component which is continuous across the boundary.     

Theoretische Untersuchungen über die Lage des Zwischengitteratoms in Kupfer

The different stable atomic configurations, formation energies and changes in volume of the crystal for an interstitial in copper are calculated with the help of the electronic digital computer Z 22 using a general method developed byTewordt. For the interaction between a pair of ions the Born-Mayer potentialV ₁, given byHuntington, and the Morse potentialV _M, given byGirifalco-Weizer, are employed. Two equilibrium configurations for an interstitial are found. In the stable configuration“A” the interstitial and one next neighboured atom are symmetrically located relative to one of the elementary cube faces along a cubic axis passing through the cube center. In the stable configuration“B” the interstitial and one next neighboured atom are symmetrically located relative to a cube corner along a {111}-axis. The interstitial is found not to reside at the center of an elementary cube. Neglecting electronic contributions to the relaxation of the lattice due to the redistribution of the electrons the calculations showed that the interstitial moved along a cubic axis about 0.4a/2 away from the elementary cube center into a stable configuration“A”. Moreover the crowdion is found to be unstable. It is shown that the crowdion decays into an interstitial lying in a next neighboured configuration“A”. The configuration“B” is separated from surrounding“A” and unstable “body-centered” and “crowdion” configurations by energy barriers. The number of atoms around the mobile interstitial treated as movable discrete particles is about 150 for the configuration“A” and about 50 for the configuration“B”. Using the Born-Mayer potentialV ₁ the changes in volume of the crystal arising from the interstitial are found to be 1.126 atomic volumes for the configuration“A” and 1.432 atomic volumes for the configuration“B”. The contributions to the formation energy of an interstitial arising from the potentialV ₁ turn out to be 3.548 eV for the configuration“A” and 4.098 eV for the configuration“B”. The results of the theoretical calculations are discussed in connection with recent radiation damage experiments performed at low temperatures on copper.     

Special features of the structure of the beta-stability line for nuclei

The mass-number (A) dependence Z _β(A) for nuclei lying on the beta-stability line (BSL) is calculated for A and Z values in the ranges of A = 2–258 and Z = 1–100, respectively. The calculated values are compared with experimental data. The deviations ΔZ = Z _expt ? Z _β are analyzed. This analysis of ΔZ reveals that there are three regions of A values in which the A dependence of ΔZ is parabolic. The possible forms of the A dependence of ΔZ are analyzed, and it is shown that the majority of nuclei belong to several parabolas simultaneously.     

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.     

Features of the Emission Spectra of Ni-Like Ions. Application to Calculating the Wavelengths of Self-Photo-Pumped X-Ray Lasers

The energy levels and probabilities of radiative transitions to the ground state of Ni-like ions with Z = 36–51 are calculated. The energies of the upper working level 3d_3/24f_5/2 [J = 1] and the lower working level 3d_3/24d_3/2 [J = 1] of self-photo-pumped X-ray lasers along the sequence of Ni-like ions are studied. It is shown that, at the points of intersection of levels of the same parity, a strong interaction of these levels takes place, which leads to a redistribution of the oscillator strengths of the radiative transitions from these levels. Near the intersection points, the emission spectra change abruptly with variation in the nuclear charge Z.     

Probing of <Emphasis Type="Italic">Z</Emphasis>γγ production sensitivity to anomalous quartic gauge couplings at LHC experiments with √ <Emphasis Type="Italic">s</Emphasis> =13 TeV

Sensitivity to anomalous ZZγγ and Zγγγ couplings in Zγγ production was probed for the ATLAS experiment at Large Hadron Collider. Zγγ process with anomalous couplings simulation in ppcollisions with √ s = 13 TeV was performed using VBFNLO MC generator. The expected limits on the Effective Field Theory parameters f _T0/Λ4, f _T5/Λ4, f _T9/Λ4, f _M2/Λ4, f _M3/Λ4 were extracted for 5 fb^?1 integral luminosity using the distribution on the invariant mass of Zγγ from the combination of charged leptonic decay channels of Z boson (Zγγ → μ⁺μ^?γγ and Zγγ → e⁺e^?γγ).     

New Bounds on the Maximum Ionization of Atoms

We prove that the maximum number N _c of non-relativistic electrons that a nucleus of charge Z can bind is less than 1.22Z + 3Z ^1/3. This improves Lieb’s upper bound N _c  < 2Z + 1 Lieb (Phys Rev A 29:3018–3028, 1984) when Z ≥ 6. Our method also applies to non-relativistic atoms in magnetic field and to pseudo-relativistic atoms. We show that in these cases, under appropriate conditions, \({\limsup_{Z \to \infty}N_c/Z \le 1.22}\).     

The c-axis fluctuation conductivity in layered superconductors in a strong electric field under a magnetic field

The effect of a high electric field on the c-axis fluctuation conductivity in layered superconductors near the superconducting transition is investigated by the time-dependent Ginzburg-Landau equation. The c-axis fluctuation conductivity is calculated in self-consistent Gaussian approximation for an arbitrarily strong electric field and a magnetic field perpendicular to the layers. Our results include all Landau levels and have refined analytical form. The results in linear response are in good agreement with the experimental data in a wide region around T _c in high T _c superconductor. We also show that high electric fields can be effectively used to suppress the c-axis fluctuation conductivity in high-temperature superconductors.     

The 3–3–1 Model with RH Neutrinos and Associated ZH Production at High-Energy ${\bf \textit{e}}^{+}{\bf \textit{e}}^{-}$ Collider

In the context of SU(3) _C ?? SU(3) _L ?? U(1) _X (3–3–1) model with right-handed neutrinos, we study the Higgsstrahlung process e ^?+? e ^???→ZH and calculate the cross section of this process at leading order. Our numerical results showed that the production cross sections for this process can be significantly large as \(M_{Z'}\approx \sqrt{s}\). With reasonable values of the Z′ mass M _Z′, Z′ exchange can generate large corrections to the cross sections of this process, which might be detected in the future high-energy linear e ^?+? e ^??? collider experiments.     

<Emphasis Type="Italic">Z</Emphasis><Superscript>0</Superscript>-boson decays in a strong electromagnetic field

The probability of Z ⁰-boson decay to a pair of charged fermions in a strong electromagnetic field, Z ⁰ → \(\bar f\) f, is calculated. On the basis of a method that employs exact solutions to relativistic wave equations for charged particles, an analytic expression for the partial decay width Γ(?) = Γ(Z ⁰ → \(\bar f\) f) is obtained at an arbitrary value of the parameter ? = \(eM_Z^{ - 3} \sqrt { - (F_{\mu \nu } q^\nu )^2 } \), which characterizes the external-field strength. The total Z ⁰-boson decay width in an intense electromagnetic field, Γ _Z (?), is calculated by summing these results over all known generations of charged leptons and quarks. It is found that, in the region of relatively weak fields (? < 0.06), the field-induced corrections to the standard Z ⁰-boson decay width in a vacuum do not exceed 2%. As ? increases, the total decay width Γ _Z (?) develops oscillations against the background of its gradual decrease to the absolute-minimum point. At ?_min = 0.445, the total Z ⁰-boson decay width reaches the minimum value of Γ _Z (?_min) = 2.164 GeV, which is smaller than the Z ⁰-boson decay width in a vacuum by more than 10%. In the region of superstrong fields (? > 1), Γ _Z (?) grows monotonically with increasing external-field strength. In the region ? > 5, the t-quark-production process Z ⁰ → \(\bar t\) t, which is forbidden in the absence of an external field, begins contributing significantly to the total decay width of the Z ⁰ boson.     

Cross sections of electron capture by Boron ions in gaseous media

We study the cross sections σ_{i, i?1}, σ_{i, i?2}, and σ _{i, i?3} of capture of one, two, and three electrons by boron ions with charges i=1?5 and velocities V=(1.83?5.50)V₀ in gaseous media with atomic numbers Z_t varying from 1 to 54. The oscillatory form of the Z_t dependence of electron capture cross section by boron ions, which has been established for lighter ions, is confirmed.     

Ternary generalization of Pauli’s principle and the <Emphasis Type="Italic">Z</Emphasis><Subscript>6</Subscript>-graded algebras

We show how the discrete symmetries Z ₂ and Z ₃ combined with the superposition principle result in the SL(2,C) symmetry of quantum states. The role of Pauli’s exclusion principle in the derivation of the SL(2,C) symmetry is put forward as the source of the macroscopically observed Lorentz symmetry; then it is generalized for the case of the Z ₃ grading replacing the usual Z ₂ grading, leading to ternary commutation relations. We discuss the cubic and ternary generalizations of Grassmann algebra. Invariant cubic forms on such algebras are introduced, and it is shown how the SL(2,C) group arises naturally in the case of two generators only, as the symmetry group preserving these forms. The wave equation generalizing the Dirac operator to the Z ₃-graded case is introduced, whose diagonalization leads to a sixthorder equation. The solutions of this equation cannot propagate because their exponents always contain non-oscillating real damping factor. We show how certain cubic products can propagate nevertheless. The model suggests the origin of the color SU(3) symmetry.     

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).     

Multicomponent <Emphasis Type="Italic">n</Emphasis>-(Bi,Sb)<Subscript>2</Subscript>(Te,Se,S)<Subscript>3</Subscript> solid solutions with different atomic substitutions in the Bi and Te sublattices

The thermoelectric properties of n-Bi_{2 ? x} Sb _x Te_{3 ? y ? z} Se _y S _z solid solutions are studied in the temperature range 300–550 K. It is shown that an increase in the parameter β determining the figure-of-merit Z of the material is observed in compositions with the optimally related effective mass of the density of states m/m ₀, the carrier mobility μ₀, and the lattice thermal conductivity κ _L . Within the temperature range 300–350 K, the parameter β and the figure-of-merit Z are found to increase in solid solutions with substitutions in both bismuth telluride sublattices Bi → Sb and Te → Se, S (x = 0.16, y = z = 0.12) for optimum electron concentrations. An increase in the electron concentration and substitutions of atoms only in the tellurium sublattice bring about an increase in the β parameter and the value of Z at higher temperatures. Within the range 350–450 K, the parameters β and Z are observed to increase in a solid solution with a low content of substituted atoms in the tellurium sublattice Te → Se, S for y = z = 0.09 and, at higher temperatures up to 550 K, in compositions with tellurium substituted by selenium only, with increasing content of substituted atoms.     

Optical and x-ray diffraction studies of the symmetry of distorted phases of the (NH<Subscript>4</Subscript>)<Subscript>3</Subscript>ZrF<Subscript>7</Subscript> crystal

(NH₄)₃ZrF₇ single crystals were grown, and polarization-optical and x-ray diffraction studies were performed on powders and crystalline plates of various cuts over a wide temperature range. Phase transitions are revealed at temperatures T _1↑ = 280 K, T _2↑ = 279.6 K, T _3↑ = 260–265 K, and T _4↑ = 238 K on heating and at T _1↓ = 280 K, T _2↓ = 269–270 K, T _3↓ = 246 K, and T _4↓ = 235 K on cooling. The sequence of changes in symmetry is established to be as follows: O _h ⁵ (Z = 4) ? D _2h ²⁵ (Z = 2) ? C _2h ³ (Z = 2) ? C _i ¹ (Z = 108) ? monoclinic²(Z = 216).     

Variation in the energy spectra of primary cosmic rays for 2007–2015, according to data from the URAGAN muon hodoscope

Simulations of how secondary components of cosmic rays are generated and pass through the atmosphere are performed using the CORSIKA software package. The relationship between the vertical projection of the local anisotropy vector A _Z and the index of primary particle spectrum γ is calculated. The time series of A _Z for 2007–2015 are obtained using data from the URAGAN muon hodoscope. Matrix data corrected for barometric and temperature effects are used to estimate A _Z . Using the A _Z time series, the average annual daily variations Δγ are estimated. Annual and daily variations in the slope of the energy spectrum of primary protons are observed.     

Screened self-energy correction to the 2<Emphasis Type="Italic">p</Emphasis><Subscript>3/2</Subscript>-2<Emphasis Type="Italic">s</Emphasis> transition energy in Li-like ions

We present an ab initio calculation of the screened self-energy correction for 1s² 2p_3/2 and 1s² 2s states of Li-like ions with nuclear charge numbers in the range Z = 12?100. The evaluation is carried out to all orders in the nuclear strength parameter Zα. This investigation concludes our calculations of all two-electron QED corrections for the 2p_3/2-2s transition energy in Li-like ions and thus considerably improves theoretical predictions for this transition for high-Z ions.     

Die Coulomb-Energien leichter Atomkerne

A compilation of the known data on Coulomb energy differences of isobaric doublets and isobaric triplets is given. Plots of the Coulomb energy differences versus¯Z/A ^1/3 with¯Z=(Z ₁+Z ₂)/2 show an analogous shell structure behaviour for the three series with 2¯Z=A?1,A andA+1 (T=1, 1/2 and 1), i.e. discontinuities at the closed shells atA=4, 16 and 40 and the closed subshell atA=32 and oscillations mainly being due to Coulomb proton-proton pairing energy. A positive energy shift of the lowest states withT=1 of all self-conjugate nuclei withA=4n+2 seems to be indicated by the experimental data. A semi-empirical formula is given that describes the data.