Statistical properties of Auger amplitudes and rates

The statistical properties of Auger transitions are investigated for the first time. The fairly accurate approximate formula for the number of Auger amplitudes is derived. The symmetry property for this number and its approximation for semicomplementary arrays is determined. The results of calculations of the statistical characteristics (distribution function, initial and central moments, skewness, excess) for the distributions of Auger amplitudes and rates are presented in the case of transitions p⁵d^N→p⁶d^N−2ε, sd^N→s²d^N−2ε, d⁹p^N→d¹⁰p^N−2ε and their dependence on the number of electrons N in the sequences of atoms is investigated. It is shown that statistical properties of Auger spectra mainly depend on the orbital quantum numbers of shells involved in the transitions. For some characteristics the clearly expressed dependence on the even and odd numbers of electrons in outer open shell having integer or half-integer values of spins takes place. The rather large values of skewness and especially excess indicate a significant deviation of distribution of Auger amplitudes from the normal distribution.     

Study of energy-band structures,some thermomechanical properties and chemical bonding for a number of refractory metal carbides by the LMTO-ASA method

The energy-band structures of V, Nb, VC, NbC and WC have been calculated with the use of the linearized method of “muffin-tin” orbitals (LMTO-ASA). The calculated band structures are in good agreement with a previous self-consistent APW calculation. The prominent features of the band structures for WC are a particularly wide 5d W, 2p C band, and also the presence of a separate 5d W band below the Fermi level. The values of the lattice constants, bulk moduli, sound velocities, Debye temperatures and melting temperatures have been calculated and are in reasonable agreement with experiment. It is shown that the high values of the bulk moduli of VC and NbC are explained by the hybridization between s- and p-metal states and 2s C, 2p C states, while the extreme value of the modulus for WC is due mainly to the covalency resulting from 5d W, 2s C and 2p C hybridization.     

Two-way and one-way quantum cryptography protocols

We present two quantum cryptography protocols. The first one generalizes the concept of the two-way deterministic protocol to work with qudits in prime d-dimensional system where d is odd. The second protocol makes use of the tomographically complete set construction for odd d-dimensional systems where d = p₁p₂ to modify the BB84 protocol to work with qudits of such systems. The securities of the two protocols are analyzed according to the intercept and resend attack.     

Structural, electronic and elastic properties of M2SC (M = Ti, Zr, Hf) compounds

Using ab initio calculations, we have studied the structural, electronic and elastic properties of M₂SC, with M = Ti, Zr and Hf. Geometrical optimization of the unit cell are in good agreement with the available experimental data. The band structures show that all three materials are conducting. The analysis of the site and momentum projected densities shows that the bonding is achieved through a hybridization of M-atom d states with S and C-atom p states. The Md-Sp bonds are lower in energy and are stiffer than Md-Cp bonds. The elastic constants are calculated using the static finite strain technique. We derived the bulk and shear moduli, Young's moduli and Poisson's ratio for ideal polycrystalline M₂SC aggregates. We estimated the Debye temperature of M₂SC from the average sound velocity. This is a quantitative theoretical prediction of the elastic properties of Ti₂SC, Zr₂SC, and Hf₂SC compounds, and it still awaits experimental confirmation.     

On the adelic string amplitudes

Some remarkable properties of the adelic string amplitudes for the physical domain of the Mandelstam variables are considered. It is shown that the p-adic four-point functions are always negative. Also, a formula is obtained which expresses the product of moduli of the p-adic amplitudes and the Veneziano amplitude in terms of the zeta functions. This product is absolutely convergent unlike the divergent product of these amplitudes without moduli, recently considered by Freund and Witten. Using the zeta function representation, p-adic interpolation of the Veneziano amplitude is also considered.     

Electric field controlled higher-order diffraction images of paraelectric potassium lithium tantalate niobate

We report some electric field controlled photorefractive higher-order diffraction phenomena of a paraelectric phase potassium lithium tantalate niobate crystal doped with iron. In experiments, a p-polarized semiconductor laser (532 nm) was used to record grating at a small incident angle. Higher-order diffraction images were observed when the signal beam was focused behind and in front of the crystal. Then the higher-order diffraction images were reconstructed by a p-polarized He–Ne laser (632.8 nm) in the direction perpendicular to the surface. The higher-order diffraction images could be controlled by the external electric field. A theory about the higher-order diffraction images of the K and 2K grating is developed. The results show that the even order diffraction images of the K grating and the odd order diffraction of the 2K grating overlap each other. The odd order diffraction images of the K grating are diffracted in unattached direction. The electric field controlled higher-order diffraction image provides a useful method for optical information processing.     

First-principles studies of the electronic and elastic properties of Ti2GeC

We have performed first-principles studies on electronic structure and elastic properties of Ti₂GeC. The calculated band structure shows that this compound is electrical conductor. From the pressure dependence of elastic constants, we find that Ti₂GeC is most stable in the pressure range from 0 to 100 GPa. The strong Ti 3d, Ge 4p and C 2p hybridization may stabilize the structure of Ti₂GeC. By analyzing the ratio between the bulk and shear moduli, we conclude that Ti₂GeC is brittle in nature, and the brittleness of Ti₂GeC originated from the large value of Ti atom occupying the internal parameter z.     

Melting curve and Grüneisen coefficient for aluminum

The Lindeman law and a model for the volume dependence of the Grüneisen coefficient generalizing previous current theories are used to calculate the melting curve of aluminum at high pressure. In this model, the Grüneisen coefficient depends on a parameter p specific for the investigated material. Agreement between the calculated melting curve and experimental results involves a negative value of p for aluminum. This result confirms previous determinations of p from shock-wave data and also from the pressure dependance of the elastic moduli determined by ultrasonic measurements.     

Photoabsorption cross sections for chlorinated methanes and ethanes between 46 and 100 Å

Photoabsorption cross sections for the methanes CCl₄, CCl₃F, CCl₂F₂, CClF₃, CF₄, CHClF₂, CHCl₂F and the ethanes C₂F₆, C₂ClF₅, C₂Cl₂F₄ were measured between 46 and 100 Å. In particular, the 0.2 Å resolution provides some insight into the Cl 2p absorption process. It is noted that the molecular cross section for all 8 Cl-containing gases display an L edge “discontinuity” of 3.55±0.15 Mb per Cl atom. The experimental molecular cross sections are compared with sums of atomic cross sections at 100 Å using both theoretical and empirical atomic values. The sums of theoretical atomic cross sections describe every experimental molecular value to better than 10%. The sums of empirical atomic cross sections describe molecular values to within 2%.     

Flavour symmetry breaking in antiquark distributions

We show that knowledge of the valence quark distribution of a proton at one value of q², enables one to calculate a contribution to the difference between the distribution of anti-up quarks $\text{(}\text{u}{}_{\mathrm{<mtext>p</mtext>}}\text{)}$ and anti-down quarks $\text{(}\text{d}{}_{\mathrm{<mtext>p</mtext>}}\text{)}$ in the sea of the proton at higher values of q². This difference can be expressed as a linear combination of the structure functions F₁, for νp → νX and e^?p → e^?p (for which one knows the q² behaviour of the moments) and for $\text{ν}\text{p}\text{→ μ}{}^{\mathrm{?}}\text{X}\text{and}\text{ν}\text{p}\text{→ μ}{}^{\mathrm{+}}\text{X}$ (for which one knows the q² behaviour of the odd moments). The calculable contribution involves a non-trivial continuation of the even (odd) moments of the neutral (charged) current structure functions to odd (even) moments. We calculate this contribution and although we find that its sign is negative we point out that this cannot be interpreted as a consequences of the Pauli exclusion principle. We discuss the constraints our results impose on antiquark distributions.     

Hydrostatic pressure derivatives of the single crystal elastic moduli of Gd,Dy and Er

The hydrostatic pressure derivatives of the single crystal elastic moduli of Gd, Dy and Er have been measured at 298°K, to pressures near 5 Kbar. The very small pressure derivatives of the adiabatic bulk moduli indicate that a small ion core model should be appropriate for interpreting the data. The long-range electrostatic contributions to the shear moduli have a dominant influence on the pressure derivatives of the shear moduli of Er, whereas the Gd and Dy data evidently reflect band structure contributions. The values of the longitudinal stiffnesses correspond remarkably well with the Bohm-Staver model for velocity of waves in an ion plasma dispersed in a sea of electrons, where the ionic interaction is perely Coulombic. This model is extended to provide an interpretation of the volume derivatives of the longitudinal moduli in terms of the volume derivative of the density of electron states at the Fermi energy.The Grüneisen parameters calculated from averages of the acoustic model gammas are in relatively poor agreement with those determined from thermal expansion data. An explanation based on the changes in c/a ratio with volume change is tested quantitatively and found to be reasonably successful. The values of dK_T/dP, where K_T is the isothermal bulk modulus, are applied to the Murnaghan equation of state and give excelent agreement with Bridgman's direct compression data for Dy and Er to 40 Kbar. For Gd, Bridgman's data indicate either that (dK_T/dP)_p=0 should be considerably larger than deduced from the adiabatic dK_s/dP measurements or that a phase change occurs near 20 Kbar. The occurrence of a phase change in Er at ～90 Kbar is definitely indicated when comparing the Murnaghan equation with X-ray diffraction data.     

Effective quadrupole operators for the second half of the 2p-1f shell

The one body matrix elements of the effective quadrupole operator in the 2p _3/2, 1f _5/2 2p _1/2 configurations have been calculated taking into account the renormalization effects due to excitations from the closed 1f _7/2 shell. First and second order perturbations of the residual interaction as well as an infinite series involving one particle-one hole core excitations are considered. The results are used to calculate quadrupole moments of odd mass nuclei together withBE 2 values between low-lying states. Agreements with experimental results, whereever known, are seen to be generally greatly improved.     

3nj coefficients of u q(2) and multiple basic hypergeometric series

Triple-sum formulas for 9j coefficients and multiple-sum expressions [with five or four separate sums of the _p+1 F _p(1) or _p+1 φ _p type, p=2, 3, 4] for the 12j coefficients of both kinds (with or without braiding) of the SU(2) group and the quantum algebra u _q(2) are derived, eliminating sums over the j type parameters [q generalizations of the very well poised (Dougall’s type) hypergeometric ₄ F ₃(?1), ₅ F ₄(1), and ₆ F ₅(?1) series] from their expansions in terms of q-6j coefficients. The rearrangements of the derived formulas for generic and stretched q-9j coefficients (related to the q versions of some Kampé de Fériet series) are discussed, as well as the different versions of stretched and doubly stretched q-12j coefficients.     

The Hilbert series of the one instanton moduli space

The moduli space of k G-instantons on \( {\mathbb{R}^4} \) for a classical gauge group G is known to be given by the Higgs branch of a supersymmetric gauge theory that lives on Dp branes probing D(p + 4) branes in Type II theories. For p = 3, these (3 + 1) dimensional gauge theories have \( \mathcal{N} = 2 \) supersymmetry and can be represented by quiver diagrams. The F and D term equations coincide with the ADHM construction. The Hilbert series of the moduli spaces of one instanton for classical gauge groups is easy to compute and turns out to take a particularly simple form which is previously unknown. This allows for a G invariant character expansion and hence easily generalisable for exceptional gauge groups, where an ADHM construction is not known. The conjectures for exceptional groups are further checked using some new techniques like sewing relations in Hilbert Series. This is applied to Argyres-Seiberg dualities.     

Study of elastic properties of CeO2 by statistical moment method

The purpose of the present paper is to investigate the temperature and pressure dependences of the elastic properties of cerium dioxide using the statistical moment method (SMM). The equation of states of bulk CeO₂ is derived from the Helmholtz free energy, and the pressure dependences of the elastic moduli like the bulk modulus, B_T, shear modulus, G, Young’s modulus, E, and elastic constants (C11, C12, and C44) are presented taking into account the anharmonicity effects of the thermal lattice vibrations. In the present study, the influence of temperature and pressure on the elastic moduli and elastic constants of CeO₂ has also been studied, using three different interatomic potentials. We compare the results of the present calculations with those of the previous theoretical calculations as well as with the available experiments.     

Raman spectra of TiO2-II,TiO2-III,SnO2, and GeO2 at high pressure

Raman spectra of the orthorhombic (II) and high pressure (III) phases of titanium dioxide at pressures to 372 kbar and effects of temperature and hydrostatic pressure on Raman spectra of the tetagonal cassiterite-like phases of TiO₂, GeO₂ and SnO₂ are described. At room temperature, the TiO₂ II–III transition is sluggish, and metastable coexistence was observed from 200 to 300 kbar. The Raman spectra of TiO₂-III imply that its primitive cell contains at least four formula units; however, the structure could not be established from the Raman spectra and available powder X-ray diffraction patterns.The temperature and pressure dependences of the spectrum of the tetragonal MO₂ phases together with bulk moduli and thermal expansion data were used to evaluate the pure-volume and pure-temperature contributions to the isobaric temperature dependence of the Raman frequencies. Large anharmonicities in TiO₂ are attributed to hybridization of the oxygen p states with the d states of the Ti ion. GeO₂, where p-electron bonding is involved, is much less Enharmonic.     

Statistics of disordered chains

The statistical weights of the stationary states in various ensembles of isotopically disordered harmonic chains are compared. It is proven that the ensemble defined by boundary conditions at both ends of the chain is constructed with correct statistical weights as follows: One matches at sitei the stationary states of the ensemble defined by the boundary condition at one end and frequencyω with those of the ensemble defined by the boundary condition at the other end andω. Finally one integrates overω and sums over all sitesi. This confirms and substantiates the conjecture on the exponential localization of the eigenstates in one dimension. The matching procedure yields an equation for the density of states.     

Hyperfine structure and nuclear magnetic moments of some neutron-deficient thallium isotopes

Using the atomic-beam magnetic resonance method, hyperfine structure (h.f.s.) measurements have been performed in the²P_1/2 electronic ground state of the neutron-deficient thallium isotopes^193–202Tl. In the doubly odd isotopes, the magnetic dipole hyperfine interaction constantsa were determined, while in the odd-A isotopes, direct measurements of the nuclearg-factors,g _I , were made. The electronicg-factor was measured in¹⁹⁸Tl. The magnetic dipole moments of the doubly odd isotopes have been evaluated by a direct comparison with known values in the stable isotope²⁰³Tl. The moments of the odd-A isotopes are in agreement with pervious measurements by optical spectroscopy. A discussion of the magnetic dipole moments in terms of different nuclear models is included. The moments of the 2^? nuclear ground states of the doubly odd isotopes may be interpreted as arising from a combination of the configurations 2^? (πs_1/2 vf_5/2) and 2^? (πs_1/2 vp_3/2).