Deconvolution of partial pair correlation functions of an n component system using n diffraction experiments

A proof of the relation g_iig_jj = g_ijg_ji is given. This relation gives an additional $\text{n(n ? 1)}\text{2}$ equation for use in deconvoluting partial pair correlation functions from experimental diffraction data. Formulae for g₁₁, g₁₂, g₂₂ for a binary alloy system are explicitly derived.     

Gammaübergangswahrscheinlichkeit und Quasiteilchenapproximation

The transition probability of the isometricM4-transitions 1g _9/2-2p _1/2, 1h _11/2-2d _3/2 and 1i _13/2-2f _5/2 in near magic nuclei is calculated on the basis of the theory of finite Fermi systems. It is shown, that the constantg ₀ for the spin-spin interaction of quasiparticles, depends strongly on the special kind of representation for the single particle states. Using oscillator functions the valueg ₀=3.3 has to be taken, in order to get hindrance factors, which are approximately equal to one, whereas in the case of square well functions the constantg ₀=1.4 is necessary, in order to get agreement with the experimental transition probabilities.     

Phase Behavior of Bow-Shaped Hard Particles in Two Dimensions

The phase behavior of a two-dimensional hard-particle model is studied via Monte Carlo simulations using the grand canonical, the isobaric and the canonical ensembles. This model consists of a three-segmented line whose geometry resembles a bow shape. The model reduces to some limiting cases: hard needles and bent-core particles. Manipulating the molecular parameters, a variety of molecular shapes were generated. As a result, several liquid crystalline structures like nematic and tetratic were obtained. Additionally, there are some other regions where the molecules form curvilinear paths. As the density increases, the formation of clusters of two or more particles is observed, producing assemblies with different shapes depending on the particular values of the molecular parameters. One interesting example is when the clusters have chiral features despite the particles are achiral. The two-dimensional tetratic, nematic and polar order parameters as well as the orientational correlation functions g ₂(r ^?) and g ₄(r ^?) and the distribution functions g _∥ and g _⊥ were calculated to describe the resulting mesophases. Besides this, the Gibbs ensemble was used to investigate some cases where indications of first-order phase transitions appeared. The mesophases diagrams are also reported.     

Electronic g factors eleven atomic states of Zr

The g_j for eleven low-lying levels of Zr I have been measured with the atomic-beam magnetic resonance method. The agreement between the experimental g_J values and theoretical predictions deduced from intermediate coupling wave functions is better than 0.1%.     

EXAFS and cumulant expansion studies of an amorphous Se90P10 alloy produced by mechanical alloying

We investigated the local atomic order of an amorphous Se₉₀P₁₀ alloy produced by Mechanical Alloying through EXAFS measurements on Se K edge at five temperatures followed by a cumulant expansion analysis. We obtained a lot of structural information such as average coordination numbers and interatomic distances, structural and thermal disorder, asymmetry of the pair distribution functions g_ij(r), anharmonicity of the interatomic potential, thermal expansion and Einstein and Debye temperatures for the Se-Se and Se-P pairs. We also reconstructed the g_ij(r) functions for the Se-Se and Se-P pairs at the temperatures investigated.     

Two and three pion-cut contributions to nucleon-nucleon scattering

Examining information from NN forward scattering in terms of discrepancy functions, we show that the 2π cut contributions as calculated via dispersion methods from πN scattering are in perfect agreement with NN scattering. Furthermore, we demonstrate the need for 3π cut contributions which are quantitatively well described by a nucleon exchange model. Finally, in addition to the 2π and 3π cut contributions, we determine the coupling constants of the ω and A₁ to be: g_Vω²/4π = 8.1 ± 1.5, g_Tω/g_Vω = 0.14 ± 0.20 and g_A1²/4π = 7.3 ± 3.0. The coupling of the η turns out to be zero.     

The general class of the vacuum spherically symmetric equations of the general relativity theory

The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g ₀₀ and g ₂₂ is obtained. The properties of the found solutions are analyzed.     

Renormalization problem in nonrenormalizable massless Φ4 theory

Nonrenormalizable massless Φ⁴ theory is made finite by regularization via higher derivatives in the kinetic part of the Lagrangean. The theory is shown to remain finite in the infinite cutoff limit if certain integrals over functions of one variable, with computable Taylor expansion at the origin, are finite. The values of these integrals are the only unknowns in the double series in powers ofg andg ^2/ε obtained for the Green's functions in massless (Φ⁴)_4+ε with generic ε. For ε=1 and ε=2, these series reduce to double series in powers ofg and lng. The problems of extension to (Φ⁴)_4+ε with mass, of causality and unitarity, of the relation to the BPHZ formalism, and of the indeterminacy of the result are discussed.     

Electronic structure of the F-center in CaO and MgO

The energy levels and wave functions of the F-center in CaO and MgO have been calculated as function of the A_1g and E_g displacements of the nearest neighbor ions of the oxygen vacancy. In CaO, the calculated level scheme partially supports the interpretation of published experimental data on the luminescence bands but there are significant discrepancies. The localization of the wave function of the ³T_1u state is rapidly varying function of the A_1g lattice distortion. The present calculations give a Jahn-Teller splitting of this state of between 0.15 and 0.2 eV.     

On the largeN c limit of theSU(N c ) colour quark-gluon partition function

Using Shifman-Vainshtein-Zakharov sum rules applied to three-point Green functions we obtain mass differences betweenSU _F (3) isomultiplets for the 1/2⁺ baryons. We also give some results for theg _A /g _V ratio.     

Low temperature asymptotic behaviours of the correlation functions in the one-dimensional fermi gas

The g-model of the one-dimensional (1-D) Fermi gas including the same site interaction g₄ is investigated in the self-consistent harmonic approximation (SCHA) for the Bosonized Hamiltonian. The asymptotic form of the gap of the spin-density excitation is determined at low temperatures. It is found that the phase transition is of first order and the transition exists if g₁₆ < 0 but does not if g₁₆ > 0. The correlation functions for the order parameters of the charge-density wave (CDW) and singlet-superconductor (SS) are evaluated at low temperatures.     

Structural study of nanoporous carbon produced from polycrystalline carbide materials: Small-angle x-ray scattering

An x-ray small-angle scattering study is reported of the structure of nanoporous carbon prepared by chlorinating carbide compounds having different crystal structures (SiC, TiC, Mo₂C). The measurements were carried out both in reflection and transmission. The angular dependences of the scattering intensity obtained are treated as a result of scattering from nanoparticles of different size. By unfolding the experimental curves into components corresponding to particles with different gyration radii R _g, scatterer distribution functions in gyration radius m(R _g) were found. It is shown that, irrespective of the type of the starting carbide, particles with R _g～5 Å make up the largest fraction in porous carbon. Samples prepared from different carbides differ in the degree of nanoparticle uniformity in size. The most uniform in size are nanoparticles in the samples prepared from SiC, in which the average value R _g ^av <6 Å. Nanoparticles in the porous carbon produced from Mo₂C are about twice larger.     

Non-spherical magnetic moment in MnAlGe

The magnetic structure factors of MnAlGe (space groupP4/nmm) measured with polarised neutrons have been expressed in terms of the magnetic moment of the Mn atom (site symmetry tetrahedral with tetragonal distortion), the Bessel transforms 〈j _n〉 of the Mn radial functions and the fractional occupancies of the moment density in the various crystal field orbitals. The measured structure factors were least-squares fitted with the theoretical expression involving 〈j _n〉 appropriate to the Mn⁰, Mn⁺ and Mn²⁺ atoms. The best fit was got using Mn⁰ transforms, yielding 1·45µ _B as the Mn magnetic moment. The fractional occupancies of the moment density in the crystal field orbitalsA _1g,B _1g E _g andB _2g were obtained. This analysis shows the magnetic moment to be highly non-spherical with a large fractional occupancy (38%) in theA _1g orbital directed along the tetragonal axis while the fractional occupancies ofB _1g andB _2g are found to be 31% and 30% respectively. The fractional occupancy of the moment in theE _g orbital directed towards the Ge and Al atoms is very low (1%). The spatially averaged moment density of Mn in MnAlGe is more diffuse than that of Mn I and Mn II in isostructural Mn₂Sb.     

The derivative nonlinear Schrödinger equation on the half-line

We analyze the derivative nonlinear Schrödinger equation on the half-line using the Fokas method. Assuming that the solution q(x,t) exists, we show that it can be represented in terms of the solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter ζ. The jump matrix has explicit x,t dependence and is given in terms of the spectral functions a(ζ), b(ζ) (obtained from the initial data q₀(x)=q(x,0)) as well as A(ζ), B(ζ) (obtained from the boundary values g₀(t)=q(0,t) and g₁(t)=q_x(0,t)). The spectral functions are not independent, but related by a compatibility condition, the so-called global relation. Given initial and boundary values {q₀(x),g₀(t),g₁(t)} such that there exist spectral functions satisfying the global relation, we show that the function q(x,t) defined by the above Riemann-Hilbert problem exists globally and solves the derivative nonlinear Schrödinger equation with the prescribed initial and boundary values.     

Influence of the Axial-Vector Coupling Constant and the Energy Distribution Function on <Emphasis Type="Italic">β</Emphasis>-Decay Rates Within the Gross Theory of Beta Decay

We evaluate the β-decay rates within the gross theory of beta decay (GTBD) and compare the results for different values of the axial-vector coupling constant, g_A =?0.76, g_A =?0.88, g_A =?1, g_A =?1.13, and g_A =?1.26, and also different energy distribution functions like Gaussian, exponential, Lorentzian, and modified Lorentzian ones. We use new sets of parameters as well as updated experimental mass defects and also an improved approximation for the Fermi function. We compare our calculated results for a set of 94 nuclei of interest in pre-supernova phase, with experimental data in terrestrial conditions and also with other theoretical models like the QRPA, the shell model (SM), and different versions of the GTBD. We show that best results are obtained with g_A =?1 using Gaussian and Lorentzian distributions, being the rates for the 74 and 80% of our sample, respectively, of the same order of magnitude that of experimental data. Finally, we show that the present results within the GTBD are better than those within the QRPA model and also older versions of the GTBD for the isotopes of cobalt and iron families, and comparable with SM for some elements.     

Type-III and IV interacting Weyl points

3+1-dimensional Weyl fermions in interacting systems are described by effective quasi-relativistic Green’s functions parametrized by a 16-element matrix e _α ^μ in an expansion around the Weyl point. The matrix e _α ^μ can be naturally identified as an effective tetrad field for the fermions. The correspondence between the tetrad field and an effective quasi-relativistic metric g_μν governing the Weyl fermions allows for the possibility to simulate different classes of metric fields emerging in general relativity in interacting Weyl semimetals. According to this correspondence, there can be four types of Weyl fermions, depending on the signs of the components g ⁰⁰ and g ₀₀ of the effective metric. In addition to the conventional type-I fermions with a tilted Weyl cone and type-II fermions with an overtilted Weyl cone for g ⁰⁰ > 0 and, respectively, g ₀₀ > 0 or g ₀₀ < 0, we find additional “type-III” and “type-IV” Weyl fermions with instabilities (complex frequencies) for g ⁰⁰ < 0 and g ₀₀ > 0 or g ₀₀ < 0, respectively. While the type-I and type-II Weyl points allow us to simulate the black hole event horizon at an interface where g ⁰⁰ changes sign, the type-III Weyl point leads to effective spacetimes with closed timelike curves.     

Global structure of the superstring partition function and resolution of the supermoduli measure ambiguity

We investigate the global structure of the fermionic string partition function on the supermoduli space M_g^sup. In particular we show how the recently discovered moduli total-derivative ambiguity is due to a non-trivial cocycle on M_g^sup, present if an atlas of coordinates of M_g^sup can be found, whose transition functions contain even, nilpotent components. We find a correction to the usual Berezin measure on M_g^sup, given by the so-called Rothstein volume form, that eliminates the above boundary ambiguities of the supermoduli measure at any genus. We discuss also the so-called theorem of holomorphic factorization in this particular case and its relation to the physical requirement of modular invariance.     

Formation of the distribution function of the aerosol-particle radii for the hydrolysis products of uranium hexafluoride in industrial premises

We consider UO₂F₂ and HF aerosol particles that formed in the air of industrial premises at a factory of the nuclear industry. The distribution function g ₁ of the aerosol-particle radii at a given space-time point is analyzed. Some of the lognormal distribution functions that are related to a gas-dispersed environment of the working premise are considered. The deviation of g ₁ from lognormal distribution functions is estimated. The related problems of calculating the average transmission coefficients of atoms of toxic substances (uranium or fluorine) in the human body during inhalation are discussed.     

Observation of the vortex-glass transition in YBa2Cu3O7 by phase-resolved current-voltage measurements

Abstract. We report on investigations of the current-dependent ac impedance Z at 17 Hz of a YBa₂Cu₃O₇ thinfilm microbridge in magnetic fields from 1 to 8 T. A phasesensitive lock-in technique was applied and supplemented by a pulsed method for high current densities. Above the vortex-glass transition temperature T _g a constant Z(j) is observed with low current densities j, and a power-law behavior at high currents. Below T _g, the curvature of the Re Z vs. j curve is negative in a log-log plot. The Re Z(j) isotherms can be collapsed onto two universal scaling functions according to the predictions of the vortex-glass model. Close to and below T _g, a phase lag between current and voltage appears, which saturates to finite values at low j and to zero at high j. The phase lag within the constant-Z(j) region remains below the critical value, predicted theoretically by Dorsey, if T > T _g and approaches 90° at T < T _g indicating the freezing of the vortices into the dissipation-free vortex-glass state.