Vector correlations in the F + HD reaction

A theoretical study of the orientation of product rotational angular momenta for two chemical reaction channels: F + HD(ν _r = 0, j _r = 0) → HF(ν, j) + D and F + HD(ν _r = 0, j _r = 0) → DF(ν, j) + H at a E _coll = 78.54 meV collision energy was performed. Angular momentum orientation was described on the basis of irreducible tensor operators (state multipoles) expressed through anisotropy transfer coefficients, which contained quantum-mechanical scattering T matrices determined on the basis of exact solutions to quantum scattering equations obtained using the hyperquantization algorithm. The possibility of the existence of substantial orientation of the angular momentum of reaction products j in the direction perpendicular to the scattering plane was demonstrated. The dependences of differential reaction cross sections and state multi-poles on the ν and j quantum numbers were calculated and analyzed. A experimental scheme based on the multiphoton ionization method was suggested. The scheme can be used to detect predicted reaction product angular momentum orientation.     

Dominant decays of scalar leptoquarks and scalar gluons in the minimal four-color symmetry model

Fermionic and weak decays of the scalar leptoquarks S = S ₁ ⁽⁺⁾ , S ₁ ^(?) , and S _m and the scalar gluons F = F ₁ and F ₂ predicted by the minimal model involving four-color symmetry and the Higgs mechanism of quark-and lepton-mass splitting are considered. The widths and the branching ratios are calculated for these decays, and the results are analyzed versus the couplings and masses of decaying particles. It is shown that, at relatively small mass splittings Δm within scalar doublets (Δm < m _W), the fermionic decays S ₁ ⁽⁺⁾ → tl _j ⁺ , S ₁ ^(?) → v _i \(\tilde b\), S _m → t \(\tilde \nu \) _j, F ₁ → t \(\tilde b\), and F ₂ → t \(\tilde t\), which are characterized by few-GeV widths for m _S, m _F < 1 TeV and decay branching ratios close to unity, are dominant, but that, for Δm > m _W, the weak decays S → S′W and F → F’W compete with the above fermionic decays. In the case of m _S < m _t, the processes S ₁ ⁽⁺⁾ → cl _j ⁺ , S ₁ ^(?) → v _i \(\tilde b\), S _m → bl _j ⁺ , and S _m → c \(\tilde \nu \) _j, whose total branching ratios are Br(S ₁ ⁽⁺⁾ → cl ⁺) ≈ Br(S ₁ ^(?) → v \(\tilde b\)) ≈ 1, Br(S _m → bl ⁺) ≈ 0.9, and Br(S _m → c \(\tilde \nu \)) ≈ 0.1, appear to be dominant decays of scalar leptoquarks. Searches for these decays at LHC and the Tevatron are of interest.     

Probabilities of radiative dipole transitions of parahelium in an electric field

Quadratic Stark corrections to the wave functions, matrix elements, and probabilities of transitions between the singlet states ¹ S ₀ and ¹ P ₁ of helium atoms are calculated. The coefficients of the polynomials that depend on the effective principal quantum number of the upper level v _f and that approximate the numerical values of the polarizabilities, the quadratic corrections to the wave functions, and the probabilities of transitions to highly excited Rydberg states with large v _f are determined. The results of calculations testify that the probabilities of all σ transitions n _i ¹ S ₀ → n _f ¹ P ₁ and π transitions to the states with n _f > n _i /2 are decreased with increasing electric field strength, except for the transition 2¹ S ₀ → 2¹ P ₁, whose probability increases both for σ and for π transitions.     

Reciprocal Time Relation of Noncolliding Brownian Motion with Drift

We consider an N-particle system of noncolliding Brownian motion starting from x ₁≤x ₂≤…≤x _N with drift coefficients ν _j , 1≤j≤N satisfying ν ₁≤ν ₂≤…≤ν _N . When all of the initial points are degenerated to be zero, x _j =0, 1≤j≤N, the equivalence is proved between a dilatation with factor 1/t of this drifted process and the noncolliding Brownian motion starting from ν ₁≤ν ₂≤…≤ν _N without drift observed at reciprocal time 1/t, for arbitrary t>0. Using this reciprocal time relation, we study the determinantal property of the noncolliding Brownian motion with drift having finite and infinite numbers of particles.     

Description of composite systems in the spectral integration technique: The gauge invariance and analyticity constraints for the radiative decay amplitudes

The constraints following from gauge invariance and analyticity are considered for the amplitudes of radiative transitions of composite systems, when composite systems are treated in terms of spectral integrals. We discuss gauge-invariant amplitudes for the transitions S → γS and V → γS, with scalar S and vector V mesons being two-particle composite systems of scalar (or pseudoscalar) constituents, and we demonstrate the mechanism of cancellation of false kinematical singularities. Furthermore, we explain how to generalize this consideration for quark-antiquark systems, in particular, for the reaction φ(1020) → γf₀(980). Here, we also consider in more detail the quark-model nonrelativistic approach for this reaction.     

Theoretical Analysis of the Fluorescence Spectra of 7-Azaindole and Its Tautomer

The electronic—vibrational fluorescence spectra of the first, S₀ → ¹L_b, and second, S₀ → ¹L_a, electronic transitions of 7-azaindole and its tautomer for an isolated state have been calculated. Specific features of structural changes in 7-azaindole and its tautomer upon electronic excitation are determined. Vibrational spectra are assigned for the ground state, and the vibrational structure of fluorescence spectra is interpreted. It is shown that the intensity redistribution between the 6a and 6b oscillations, which is observed in the fluorescence spectrum of the S₀ → ¹L_b transition in 7-azaindole, can be explained as a result of intensity borrowing (according to the Herzberg—Teller mechanism) from the ¹L_a state.     

Self-similar magnetic structures and magnetic flux “Giant” creep

The penetration of a magnetic flux into a type-II high-T _c superconductor occupying the half-space x > 0 is considered. At the superconductor surface, the magnetic field amplitude increases in accordance with the law b(0, t) = b ₀(1 + t)^m (in dimensionless coordinates), where m > 0. The velocity of penetration of vortices is determined in the regime of thermally activated magnetic flux flow: v = v ₀exp?ub;?(U _0/T )(1-b?b/?x)?ub;, where U ₀ is the effective pinning energy and T is the thermal energy of excited vortex filaments (or their bundles). magnetic flux “Giant” creep (for which U ₀/T? 1) is considered. The model Navier-Stokes equation is derived with nonlinear “viscosity” v ∝ U ₀/T and convection velocity v _f ∝ (1 ? U ₀/T). It is shown that motion of vortices is of the diffusion type for j → 0 (j is the current density). For finite current densities 0 < j < j _c, magnetic flux convection takes place, leading to an increase in the amplitude and depth of penetration of the magnetic field into the superconductor. It is shown that the solution to the model equation is finite at each instant (i.e., the magnetic flux penetrates to a finite depth). The penetration depth x _eff ^A (t) ∝ (1 + t)^{(1 + m/2)/2} of the magnetic field in the superconductor and the velocity of the wavefront, which increases linearly in exponent m, exponentially in temperature T, and decreases upon an increase in the effective pinning barrier, are determined. A distinguishing feature of the solutions is their self-similarity; i.e., dissipative magnetic structures emerging in the case of giant creep are invariant to transformations b(x, t) = β^m b(t/β, x/β^{(1 + m/2)/2}), where β > 0.     

Time constants of radiative transitions from the 5<Emphasis Type="Italic">d</Emphasis>[3/2]<Subscript>1</Subscript> level of a xenon atom

Integral yields of spontaneous emission at wavelengths of 1.73, 2.03, and 2.65 μm have been measured upon excitation of pure xenon by a pulsed electron beam. These yields have been analyzed and experimental data have been obtained on time constants of radiative transitions 5d[3/2]₁ → 6p[5/2]₂, 5d[3/2]₁ → 6p[3/2]₁, and 5d[3/2]₁ → 6p[1/2]₀ of XeI, which appeared to be equal to (2300 ± 400) × 10^?9, (300 ± 40) × 10^?9, and (1300 ± 200) × 10^?9 s, respectively. It is shown that the experimental data are in a qualitative agreement with the results of computational and theoretical investigations. The results of averaging the experimental and calculated data are proposed for use as recommended values of the corresponding constants.     

Luminescence properties of europium(III) compounds with quinaldic acid and nitrogen-containing ligands

Luminescent mixed-ligand Eu(III) complexes with quinaldic acid and nitrogen-containing dimeric ligands are synthesized. The thermal and spectral-luminescent properties of the obtained mixedligand Eu(III) complexes are studied. It is shown that a water molecule and a neutral ligand are detached during thermolysis in two stages with endothermic effects. It is found that the quinaldinate ion is coordinated to a europium(III) ion in a bidentate fashion. The Stark structure of the 5D₀–7F _j (j = 0, 1, 2) transitions in the low-temperature luminescence spectra of europium(III) complexes is analyzed.     

Determination of quark-antiquark component of the photon wave function for <Emphasis Type="Italic">u,d, s</Emphasis> quarks

Based on the data for the transitions π⁰, η, η′ → γγ*(Q²) and reactions of the e⁺e^? annihilations e⁺e^? → ρ⁰, ω, ? and e⁺e^? → hadrons at 1<E _e+e? <3.7 GeV, we determine the light-quark components of the photon wave function \(\gamma * (Q^2 ) \to q\bar q(q = u,d,s)\) for the region 0 ? Q² ? 1 (GeV/c)².     

Morphological transformations of diblock copolymers in binary solvents: A simulation study

Morphological transformations of amphiphilic AB diblock copolymers in mixtures of a common solvent (S1) and a selective solvent (S2) for the B block are studied using the simulated annealing method. We focus on the morphological transformation depending on the fraction of the selective solvent C _S2, the concentration of the polymer C _p , and the polymer–solvent interactions ε _ij (i = A, B; j = S1, S2). Morphology diagrams are constructed as functions of C _p , C _S2, and/or ε _AS2. The copolymer morphological sequence from dissolved → sphere → rod → ring/cage → vesicle is obtained upon increasing C _S2 at a fixed C _p . This morphology sequence is consistent with previous experimental observations. It is found that the selectivity of the selective solvent affects the self-assembled microstructure significantly. In particular, when the interaction ε _BS2 is negative, aggregates of stacked lamellae dominate the diagram. The mechanisms of aggregate transformation and the formation of stacked lamellar aggregates are discussed by analyzing variations of the average contact numbers of the A or B monomers with monomers and with molecules of the two types of solvent, as well as the mean square end-to-end distances of chains. It is found that the basic morphological sequence of spheres to rods to vesicles and the stacked lamellar aggregates result from competition between the interfacial energy and the chain conformational entropy. Analysis of the vesicle structure reveals that the vesicle size increases with increasing C _p or with decreasing C _S2, but remains almost unchanged with variations in ε _AS2.     

Density functional study of $$\hbox {AgScO}_2$$: Electronic and optical properties

Dielectric relaxation studies of binary (jk) polar mixtures of tetrahydrofuran with N-methyl acetamide, N,N-dimethyl acetamide, N-methyl formamide and N,N-dimethyl formamide dissolved in benzene(i) for different weight fractions (w _{j k} ’s) of the polar solutes and mole fractions (x _j ’s) of tetrahydrofuran at 25 ^°C are attempted by measuring the conductivity of the solution under 9.90 GHz electric field using Debye theory. The estimated relaxation time (τ _{j k} ’s) and dipole moment (μ _{j k} ’s) agree well with the reported values signifying the validity of the proposed methods. Structural and associational aspects are predicted from the plot of τ _{j k} and μ _{j k} against x _j of tetrahydrofuran to arrive at solute–solute (dimer) molecular association upto x _j =0.3 of tetrahydrofuran and thereafter solute–solvent (monomer) molecular association upto x _j =1.0 for all systems except tetrahydrofuran + N,N-dimethyl acetamide.     

Chemical Shift of the <Emphasis Type="Italic">K</Emphasis><Subscript>α1</Subscript> and <Emphasis Type="Italic">K</Emphasis><Subscript>α2</Subscript> Lines of the X-ray Emission Spectrum of Yb(II)/Yb(III) Fluorides: a Quantum-Chemical Investigation

Chemical shifts of the K_α1 and K_α2 lines (the 2p_3/2 → 1s_1/2 and 2p_1/2 → 1s_1/2 transitions, respectively) of the X-ray emission spectrum of the Yb atom in fluorides have been calculated by ab initio modeling the electronic structure. The valence transition Yb(II) → Yb(III) has been analyzed by examples of YbF₂, YbF₃, and Yb₂F₄ molecules and YbF₂⁺ cation. The relativistic pseudopotential and basis sets corresponding to it have been constructed for the ytterbium atom. They were used in calculations by the two-component noncollinear version of the density functional theory (DFT) with the PBE0 exchange-correlation functional. Results for the three-coordinated Yb(II) in the FYbF₂YbF dimer demonstrated a very weak dependence of the chemical shift on the coordination number of the Yb atom and on the molecular association of ytterbium difluoride. Chemical shifts of the X-ray emission spectrum for the ytterbium compound are related mainly to the change in the occupation of the 4 f shell.     

Limit of Fluctuations of Solutions of Wigner Equation

We consider fluctuations of the solution W _ε (t, x, k) of the Wigner equation which describes energy evolution of a solution of the Schrödinger equation with a random white noise in time potential. The expectation of W _ε (t, x, k) converges as ε → 0 to \({\bar{W}(t,x,k)}\) which satisfies the radiative transport equation. We prove that when the initial data is singular in the x variable, that is, W _ε (0, x, k) = δ(x)f(k) and \({f\in {\mathcal{S}}(\mathbb{R}^d)}\), then the laws of the rescaled fluctuation \({Z_\varepsilon(t):=\varepsilon^{-1/2}[W_\varepsilon(t,x,k)-\bar{W}(t,x,k)]}\) converge, as ε → 0+, to the solution of the same radiative transport equation but with a random initial data. This complements the result of [6], where the limit of the covariance function has been considered.     

Precision measurements of optical excitation functions for the mercury atom

We describe a computer-based facility for studying the excitation of atoms by ultramonochromatic electrons and give optical excitation functions for the 12 mercury spectral lines that originate from the n ¹ S ₀, n ¹ P ₁, n ¹ D ₂, n ³ S ₁, n ³ P _j , and n ³ D _j levels. We detected about 100 features in the energy dependences measured from the excitation threshold to 15.5 eV. The previously found positions of the features on the energy scale are in good agreement with our results. Most of the resonant features are shown to be mainly attributable to the decay of short-lived states of the negative mercury ion. We detected a postcollision interaction effect in the optical excitation functions of the lines that originate from the n ¹ S ₀ levels at energies of about 11 eV.     

A Liouville-type Theorem for Schrödinger Operators

In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a symmetric critical operator P ₁, such that a nonzero subsolution of a symmetric nonnegative operator P ₀ is a ground state. Particularly, if P _j : = ?Δ + V _j , for j = 0,1, are two nonnegative Schrödinger operators defined on \(\Omega\subseteq \mathbb{R}^d\) such that P ₁ is critical in Ω with a ground state φ, the function \(\psi\nleq 0\) is a subsolution of the equation P ₀ u = 0 in Ω and satisfies \(\psi_+\leq C\varphi\) in Ω, then P ₀ is critical in Ω and \(\psi\) is its ground state. In particular, \(\psi\) is (up to a multiplicative constant) the unique positive supersolution of the equation P ₀ u = 0 in Ω. Similar results hold for general symmetric operators, and also on Riemannian manifolds.     

Luminescence properties of compounds of europium(III) with quinaldic acid and phosphor-containing neutral ligands

Luminescent complex mixed-ligand compounds of europium(III) with quinaldic acid and phosphor- containing neutral ligands have been obtained. Their composition and structure have been determined. The thermal and spectral-luminescent properties of the obtained complex mixed-ligand compounds of europium( III) have been studied. It is shown that, during thermolysis, a water molecule and neutral ligand are detached in two stages with endothermic effects. It is established that quinaldinate ion is coordinated to europium(III) ion in a bidentate fashion. The Stark structure of the ⁵D₀–⁷F_j (j = 0, 1, 2) transitions in low-temperature luminescence spectra of complex compounds of europium(III) has been analyzed.     

Collision frequency shift of hyperfine transitions in atomic hydrogen at a low temperature

The experimental results on the collision frequency shift of ESR in diluted two-and three-dimensional atomic hydrogen at ultralow temperature have been analyzed. The apparent contradiction between experiment and theory is resolved by taking into account the relation between the symmetry of the state of two atoms and their total electron spin S. For example, transitions between symmetric and antisymmetric states of a pair of atoms induced by a symmetric perturbation are forbidden. If symmetric and antisymmetric states are, respectively, pure electronic triplets (S= 1) and singlets (S = 0), this results in the cancellation of the singlet-triplet transitions. Thus, the collision frequency shift of b → c and b → a transitions vanishes in a completely electron and nuclear spin-polarized gas (hyperfine state b). The comparison is performed with experiments in ultracold alkali vapors.     

Structure,ionic conduction,and phase transformations in lithium titanate Li<Subscript>4</Subscript>Ti<Subscript>5</Subscript>O<Subscript>12</Subscript>

The spinel structure of lithium titanate Li₄Ti₅O₁₂ is refined by the Rietveld full-profile analysis with the use of x-ray and neutron powder diffraction data. The distribution and coordinates of atoms are determined. The Li₄Ti₅O₁₂ compound is studied at high temperatures by differential scanning calorimetry and Raman spectroscopy. The electrical conductivity is measured in the high-temperature range. It is shown that the Li₄Ti₅O₁₂ compound with a spinel structure undergoes two successive order-disorder phase transitions due to different distributions of lithium atoms and cation vacancies (□, V) in a defect structure of the NaCl type: (Li)_8a[Li_0.33Ti_1.67]_16dO₄ → [Li□]_16c[Li_1.33Ti_1.67]_16dO₄ → [Li_1.33□_0.67]_16c[Ti_1.67□_0.33]_16dO₄. The low-temperature diffusion of lithium predominantly occurs either through the mechanism ... → Li(8a) → V(16c) → V(8a) → ... in the spinel phase or through the mechanism ... → Li(16c) → V(8a) → V(16c) → ... in an intermediate phase. In the high-temperature phase, the lithium cations also migrate over 48f vacancies: ... Li(16c) → V(8a, 48f) → V(16c) → ....     

Lightest scalar resonances and the dynamics of the γγ → ππ reactions

The high-statistics Belle data on the γγ → π⁺π^? and γγ → π⁰π⁰ reactions have been jointly analyzed. The main dynamical mechanisms of these reactions for energies below 1.5 GeV have been revealed. It has been shown that the direct coupling constants of the σ(600) and f ₀(980) resonances with a γγ pair are small and that the σ(600) → γγ and f ₀(980) → γγ decays are four-quark transitions due primarily to π⁺π^? and K ⁺ K ^?-loop mechanisms, respectively. The role of the chiral shielding of the σ(600) resonance is emphasized. The widths of the f ₀(980) → γγ and σ(600) → γγ decays averaged over the resonance mass distributions, as well as the width of the f ₂(1270) → γγ decay, are estimated as \(\langle \Gamma _{f_0 \to \gamma \gamma } \rangle _{\pi \pi } \approx 0.19 keV, \langle \Gamma _{\sigma \to \gamma \gamma } \rangle _{\pi \pi } \approx 0.45 keV\), and \(\Gamma _{f_2 \to \gamma \gamma } (m_{f_2 }^2 ) \approx 3.8 keV\).