Structure of the intermediate high-pressure phases of ternary lead tellurides

In chambers with diamond anvils, the structure of high-pressure phases of ternary lead tellurides Pb_1?x Sn_xTe (x = 0.29) and Pb_1?x Mn_xTe (x = 0.05) and nonstoichiometric crystals Pb_0.55Te_0.45, Pb_0.45Te_0.55 is analyzed by the synchrotron radiation diffraction method at pressures of P up to 14 GPa. The orthorhombic structure of the intermediate high-pressure phase (space group Pnma) is determined for all the samples above 6 GPa. Models of the phase transition in PbTe from the initial rock salt structure to the orthorhombic phase, which constitutes a distorted variant of NaCl, as well as the properties of this phase, are discussed.     

Two-photon bremsstrahlung processes in atoms: Polarization effects and analytic results for the Coulomb potential

The partial wave analysis of two-photon free-free (bremsstrahlung) electron transition cross sections during scattering by a static potential U(r), as well as by an atom with a nonzero angular momentum, is carried out. The dipole interaction with radiation is taken into account in the second order of perturbation theory for the general case of elliptic polarization of photons. The polarization and angular dependences of the two-photon potential scattering amplitude is presented as a combination of the scalar product of electron momenta and photon polarization vectors and five atomic parameters containing Legendre polynomials of the scattering angle as well as radial matrix elements depending on the initial (E) and final (E′) electron energies. The results are applicable both for spontaneous double bremsstrahlung at nonrelativistic energies and for induced absorption and emission in the field of a light wave. Specific polarization effects (circular and elliptic dichroism) are analyzed for two-photon bremsstrahlung processes associated with the interference of the Hermite and anti-Hermite parts of the amplitude and depending on the sign of photon helicity. The limiting cases of high and low photon frequencies are investigated analytically, and the asymptotic forms of radial matrix elements and amplitudes for the general form of the U(r) potential are determined. Closed analytic expressions are derived for the radial matrix elements of the Coulomb potential in the form of integrals of hypergeometric function, and singularities are singled out in explicit form for E′ → E. The methods of approximate calculation of the radial matrix elements are discussed, and the results of their exact numerical calculation, as well as angular distributions and the cross sections of induced one-and two-photon emission and absorption, are given for the case of the Coulomb potential. The numerical results show that dichroism effects are quite accessible for experimental observations.     

X-Ray Powder Diffraction Studies of Polyhydrates of Cross-Linked Tetraisoamylammonium Polyacrylates

X-ray powder diffraction studies were performed of the polyhydrates, formed at positive temperature in swelled grains of carboxylic cation-exchange resins in the form of tetraisoamylammonium (cross-linked tetraisoamylammonium polyacrylates, differing in the degree of cross-linking: 1, 2 and 3%). It was shown that the polyhydrates exist as the crystalline phase under specific conditions, determined earlier by DTA technique. Diffraction patterns of the samples, recorded at the temperature +3 ± 1 °C, indicate that the polyhydrates crystallize in hexagonal symmetry, the unit cell parameters are close to a=12.25 Å, c=12.72 Å and do not depend significantly upon the degree of cross-linking. The suppositions were made concerning the size of hydrate crystallites, formed in the swelled grains of the studied resins.     

High-pressure clathrate hydrate of acetone

X-ray diffraction study of quenched sample of acetone clathrate hydrate synthesized at 0.8 GPa was carried out. It was shown that the host frameworks of the hydrate comprise uniform cavities which are similar to that of recently characterized structure of high-pressure tetrahydrofurane hydrate. The unique peculiarity of investigated hydrate is decrease in the crystallographic symmetry of the hydrate arising from ordering in guest subsystem.     

Analytic continuation of the sturm expansion of Coulomb Green's functions to the region of the continuous spectrum

Theoretical and Mathematical Physics -     

The stark effect on the hfs of relativistic H-like atoms

The energy shift of relativistic H-like atom is calculated in second order by external field ε, and in the first order by hyperfine-structure interaction. The relativistic corrections to scalar and tensor polarizability are presented.     

Asymptotic behavior of the solutions of the Kadomtsev-Pyatviashvili equation (two-dimensional Korteweg-De Vries equation)

The asymptotic form of the solutions of the Kadomtsev-Pyatviashvili equation for t → ± ∞ is presented. The reverse problem of reconstructing the solution from its asymptotic form is also solved.