Laser-induced optical activity in range of Rydberg autoionizing states of xenon

Optical activity of xenon atoms in the vacuum UV range induced by circularly polarized laser light is studied theoretically. The optical activity arises in the vicinity of the autoionizing state 5p ⁵(² P _1/2)8s′$ \left[ {\frac{1} {2}} \right]_1 $ \left[ {\frac{1} {2}} \right]_1 as a result of its coupling via the laser field with the discrete state 5p ⁵(² P _3/2)7p $ \left[ {\frac{1} {2}} \right]_1 $ \left[ {\frac{1} {2}} \right]_1 . Polarization variations of the vacuum UV radiation upon its propagation through the atomic medium are calculated, and the possibility of controlling this polarization is discussed. Manifestations of nonresonant coupling of the discrete state with the broad autoionizing state 5p ⁵(² P _1/2)6d′$ \left[ {\frac{1} {2}} \right]_1 $ \left[ {\frac{1} {2}} \right]_1 induced by the overlap of the Rydberg autoionizing series in xenon are studied.     

Frequency and spatial characteristics of the electrophysical parameters of a living tree trunk

The method of vertical electrical sounding is applied to derive the spatial characteristic of the dc resistivity ρ of a living pine trunk, ρ = L-0.85, and the frequency characteristic of the ac resistance R of the same pine trunk, R = f-0.053. The results are simulated by the methods of fractal geometry, according to which ρ = L ^{−h + 2} and $ R \sim f^{ - \tfrac{3} {h} + 1} $ R \sim f^{ - \tfrac{3} {h} + 1} , where h is the walk dimension of the electric current in the trunk. From comparison between the experimental and theoretical results, it follows that h = 2.85 and fractal dimension D = 1/h = 0.35. Since D = 1, conducting layers form a Cantor set.     

Finite-size scaling and power law relations for dipole-quadrupole interaction on Blume-Emery-Griffiths model

The Blume-Emery-Griffiths model with the dipole-quadrupole interaction ($ \ell = \frac{I} {J} $ \ell = \frac{I} {J} ) has been simulated using a cellular automaton algorithm improved from the Creutz cellular automaton (CCA) on the face centered cubic (fcc) lattice. The finite-size scaling relations and the power laws of the order parameter (M) and the susceptibility (χ) are proposed for the dipole-quadrupole interaction (ℓ). The dipole-quadrupole critical exponent δ_χ has been estimated from the data of the order parameter (M) and the susceptibility (χ). The simulations have been done in the interval $ 0 \leqslant \ell = \frac{I} {J}0 \leqslant 0.01 $ 0 \leqslant \ell = \frac{I} {J}0 \leqslant 0.01 for $ d = \frac{D} {J} = 0,k = \frac{K} {J} = 0 $ d = \frac{D} {J} = 0,k = \frac{K} {J} = 0 and $ h = \frac{H} {J} = 0 $ h = \frac{H} {J} = 0 parameter values on a face centered cubic (fcc) lattice with periodic boundary conditions. The results indicate that the effect of the ℓ parameter is similar to the external magnetic field (h). The critical exponent δ_ℓ are in good agreement with the universal value (δ _h = 5) of the external magnetic field.     

The model-independent analysis indications for spectroscopy of scalar mesons. Proof for the K0* (900)

In a model-independent approach the data on ππ → ππ, K $ \bar K $ \bar K , ηη, ηη′ in the I ^G J ^PC = 0⁺0⁺⁺ channel and on the Kπ scattering in the $ I\left( {J^P } \right) = \frac{1} {2}\left( {0^ + } \right) $ I\left( {J^P } \right) = \frac{1} {2}\left( {0^ + } \right) channel are analyzed jointly for studying the status and QCD nature of the f ₀- and the K*₀-mesons. It is shown that in the 1500-MeV region, there are two states, wide (interpreted as a glueball) and narrow (q $ \bar q $ \bar q ). In the Kπ-scattering data analysis, the proof for the K*₀(900) is given.     

The p/π ratio pT dependence in the RHIC range of baryo-chemical potential

The BRAHMS measurement of proton-to-pion ratios in Au+Au and p+p collisions at $ \sqrt {s_{NN} } $ \sqrt {s_{NN} } = 62.4 GeV and $ \sqrt {s_{NN} } $ \sqrt {s_{NN} } = 200 GeV is presented as a function of transverse momentum and collision centrality within the pseudorapidity range 0 ≤ η ≤ 3. The baryo-chemical potential, μ _B , for the indicated data spans from μ _B ≈ 26 MeV ($ \sqrt {s_{NN} } $ \sqrt {s_{NN} } 200 GeV, η ≈ 0) to μ _B ∼ 260 MeV ($ \sqrt {s_{NN} } $ \sqrt {s_{NN} } = 62.4 GeV, η ≈ 3) [1]. The p/πratio measured for Au+Au system at $ \sqrt {s_{NN} } $ \sqrt {s_{NN} } 62.4 GeV, η ≈ 3 reaches astounding value of 8–10 at p _T > 1.5 GeV/c. For these energy and pseudorapidity interval no centrality dependency of p/π ratio is observed. Moreover, the baryon-to-meson ratio of nucleus-nucleus data are consistent with results obtained for p+p interactions.     

Asymmetries in rare radiative leptonic and semileptonic decays of <Emphasis Type="Italic">B</Emphasis> mesons

The time-dependent and time-independent CP asymmetries $ A_{CP}^{B_q^0 \to f} \left( \tau \right) $ A_{CP}^{B_q^0 \to f} \left( \tau \right) and $ A_{CP}^{B_q^0 \to f} \left( {\hat s} \right) $ A_{CP}^{B_q^0 \to f} \left( {\hat s} \right) for rare semileptonic and radiative leptonic decays of B mesons are calculated by the method of helicity amplitudes. The sensitivity of CP asymmetries to various extensions of the Standard Model that have an operator basis that is identical to the operator basis of the Standard Model is investigated. It is shown that, by combining information about the form of the charge lepton asymmetry A _FB at small values of the square of the invariant dilepton mass and information about the average value of the time-dependent CP asymmetry, one can in principle determine the relative phases of the Wilson coefficients C _7γ , C _9V , and C _10A in the effective Hamiltonian for b → {d, s}ℓ⁺ℓ⁻ transitions.     

Exact solutions of the D-dimensional Schrödinger equation for a ring-shaped pseudoharmonic potential

A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form $ V(r,\theta ) = \tfrac{1} {8}\kappa r_e^2 \left( {\tfrac{r} {{r_e }} - \tfrac{{r_e }} {r}} \right)^2 + \tfrac{{\beta cos^2 \theta }} {{r^2 sin^2 \theta }} A new non-central potential, consisting of a pseudoharmonic potential plus another recently proposed ring-shaped potential, is solved. It has the form . The energy eigenvalues and eigenfunctions of the bound-states for the Schr?dinger equation in D-dimensions for this potential are obtained analytically by using the Nikiforov-Uvarov method. The radial and angular parts of the wave functions are obtained in terms of orthogonal Laguerre and Jacobi polynomials. We also find that the energy of the particle and the wave functions reduce to the energy and the wave functions of the bound-states in three dimensions.      

The band spectrum of SbO: A new doublet system

The band spectrum of SbO was excited in a heavy current discharge from a 2000 volt D. C. generator. A new doublet system of bands occurring in the region λ 2800 toλ 3600 arising from a transition of the type²Δ_r?² Π _r was identified. The lower² Π _r state is found to be common to those of the three band systems reported earlier, which is in all probability the ground state of the SbO molecule. The band heads of the high frequency and low frequency components could be represented by the following quantum formulae:

$$\begin{gathered} ^2 \Delta _{\tfrac{3}{2}} - ^2 \Pi _{\tfrac{1}{2}} : \hfill \\ v = 29754 \cdot 6 + 570 \cdot 6 (v' + \tfrac{1}{2}) - 3 \cdot 52 (v' + \tfrac{1}{2})^2 - 820 \cdot 5 (v'' + \tfrac{1}{2}) + 4 \cdot 62 (v'' + \tfrac{1}{2})^2 \hfill \\ ^2 \Delta _{\tfrac{5}{2}} - ^2 \Pi _{\tfrac{3}{2}} : \hfill \\ v = 28044 \cdot 8 + 568 \cdot 1 (v' + \tfrac{1}{2}) - 3 \cdot 28 (v' + \tfrac{1}{2})^2 - 819 \cdot 2 (v'' + \tfrac{1}{2}) + 4 \cdot 62 (v'' + \tfrac{1}{2})^2 . \hfill \\ \end{gathered} $$     

Pre-exponential factor of the hopping conductivity in disordered carbon films

The conductivity of carbon films grown by polymethylphenylsiloxane vapor decomposition in stimulated dc discharge plasma was studied. It is found that the Mott hopping conductivity $ \sigma \left( T \right) = \sigma _0 \left( T \right)\exp \left\{ { - \frac{{T_0 }} {T}^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} } \right\} $ \sigma \left( T \right) = \sigma _0 \left( T \right)\exp \left\{ { - \frac{{T_0 }} {T}^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} } \right\} is characteristic of the samples under study in the temperature range of 80–400 K in the electric field E to 5 · 10⁴ V/cm. An analysis of the pre-exponential factor σ ₀(T) = σ ₀₀(T ₀)T ^α allowed the conclusion that the hopping transport is most adequately described in the model with the exponential energy dependence of the density of localized states for which α = −1/2 and the universal relation ln σ ₀₀ −T ₀^1/4 0 is valid, which is satisfied in the range where the parameter σ ₀₀ varies by eight orders of magnitude.     

Level crossings in complex two-dimensional potentials

Two-dimensional $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric quantum-mechanical systems with the complex cubic potential V ₁₂ = x ² + y ² + igxy ² and the complex Hénon-Heiles potential V _HH = x ² +y ² +ig(xy ² −x ³/3) are investigated. Using numerical and perturbative methods, energy spectra are obtained to high levels. Although both potentials respect the $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} symmetry, the complex energy eigenvalues appear when level crossing happens between same parity eigenstates.     

Directed flow of identified particles from Au+Au collisions at RHIC

We present the measurement of directed flow (v ₁) for the identified particles, namely, Λ, $ \bar \Lambda $ \bar \Lambda and K _s ⁰, as a function of rapidity and centrality in Au+Au collisions at $ \sqrt {s_{NN} } $ \sqrt {s_{NN} } = 200 GeV and 62.4 GeV. The measurement is based on the run IV data obtained by the STAR experiment at RHIC. In order to enhance event plane resolution, we use tracks reconstructed from the Forward Time Projection Chambers (FTPCs), together with the sideward deflection of spectator neutrons measured by the STAR’s Shower Maximum Detector at Zero Degree Calorimeters (ZDC-SMDs). We find that for 200 GeV, proton and antiproton v ₁ is less than 1%, the K _s ⁰ Λ, $ \bar \Lambda $ \bar \Lambda v ₁ is less than 2%; for 62 GeV, proton v ₁ is less than 1% and antiproton is less than 2%, v ₁ for K _s ⁰, Λ, $ \bar \Lambda $ \bar \Lambda is less than 2% in Au+Au collisions at 200 GeV.     

Spontaneous breakdown of $$ \mathcal{P}\mathcal{T} $$ symmetry in the complex Coulomb potential

The $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} symmetry of the Coulomb potential and its solutions are studied along trajectories satisfying the $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} symmetry requirement. It is shown that with appropriate normalization constant the general solutions can be chosen $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric if the L parameter that corresponds to angular momentum in the Hermitian case is real. $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} symmetry is spontaneously broken, however, for complex L values of the form L = −1/2 + iλ. In this case the potential remains $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric, while the two independent solutions are transformed to each other by the $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} operation and at the same time, the two series of discrete energy eigenvalues turn into each other’s complex conjugate.     

Wakimoto realization of drinfeld current for the elliptic quantum algebra Uq,p( $$ \widehat{sl_3 } $$ )

We study a free field realization of the elliptic quantum algebra U_q,p($ \widehat{sl_3 } $ \widehat{sl_3 } ) for arbitrary level k. We give the free field realization of elliptic analog of Drinfeld current associated with U_q,p($ \widehat{sl_3 } $ \widehat{sl_3 } ) for arbitrary level k. In the limit p → 0, q → 1 our realization reproduces Wakimoto realization for the affine Lie algebra $ \widehat{sl_3 } $ \widehat{sl_3 } .     

The band spectrum of PO: Two new doublet systems in the ultraviolet

The band spectrum of PO was excited in a high frequency discharge from a 1/2 kW oscillator working at a frequency of 30 to 40 Mc/sec. A new doublet system of bands degraded to red designated asC′?X ² Π _r occuring in the region λ 2200–λ 2900 was observed and analyzed. The following vibrational quantum formula was derived for the inner heads (R ₁ andQ ₂)

$$\begin{gathered} v = ^{43854 \cdot 5} + 825 \cdot 8(\upsilon ' + \tfrac{1}{2}) - 6 \cdot 44(\upsilon ' + \tfrac{1}{2})^2 \hfill \\ ^{43631 \cdot 4} - 1232 \cdot 6(\upsilon '' + \tfrac{1}{2}) - 6 \cdot 48(\upsilon '' + \tfrac{1}{2})^2 . \hfill \\ \end{gathered}$$     

Maximal possible accretion rates for slim disks

It was proved in the previous work that there must be a maximal possible accretion rate $ \dot M_{max} $ \dot M_{max} for a slim disk. Here we discuss how the value of $ \dot M_{max} $ \dot M_{max} depends on the two fundamental parameters of the disk, namely the mass of the central black hole M and the viscosity parameter α. It is shown that $ \dot M_{max} $ \dot M_{max} increases with decreasing α, but is almost independent of M if $ \dot M_{max} $ \dot M_{max} is measured by the Eddington accretion rate $ \dot M_{Edd} $ \dot M_{Edd} , which is in turn proportional to M.     

Theoretical studies on intervalley splittings in Si/SiO<Subscript>2</Subscript> quantum dot structures

Using the coupled cluster method we investigatespin-s J ₁-J′ ₂ Heisenberg antiferromagnets (HAFs) on an infinite, anisotropic, two-dimensional triangular lattice for the two cases where the spin quantum number s = 1 and s = $\frac{3} {2}$\frac{3} {2}. With respect to an underlying square-lattice geometry the model has antiferromagnetic (J ₁ > 0) bonds between nearest neighbours and competing (J′ ₂ > 0) bonds between next-nearest neighbours across only one of the diagonals of each square plaquette, the same diagonal in each square. In a topologically equivalent triangular-lattice geometry, the model has two types of nearest-neighbour bonds: namely the J′ ₂ ≡ κJ ₁ bonds along parallel chains and the J ₁ bonds producing an interchain coupling. The model thus interpolates between an isotropic HAF on the square lattice at one limit (κ = 0) and a set of decoupled chains at the other limit (κ → ∞), with the isotropic HAF on the triangular lattice in between at κ = 1. For both the spin-1 model and the spin-$\frac{3} {2}$\frac{3} {2} model we find a second-order type of quantum phase transition at κ _c = 0.615 ± 0.010 and κ _c = 0.575 ± 0.005 respectively, between a Néel antiferromagnetic state and a helically ordered state. In both cases the ground-state energy E and its first derivative dE/dκ are continuous at κ = κ _c , while the order parameter for the transition (viz., the average ground-state on-site magnetization) does not go to zero there on either side of the transition. The phase transition at κ = κ _c between the Néel antiferromagnetic phase and the helical phase for both the s = 1 and s = $\frac{3} {2}$\frac{3} {2} cases is analogous to that also observed in our previous work for the s = $\frac{1} {2}$\frac{1} {2} case at a value κ _c = 0.80 ± 0.01. However, for the higher spin values the transition appears to be of continuous (second-order) type, exactly as in the classical case, whereas for the s = $\frac{1} {2}$\frac{1} {2} case it appears to be weakly first-order in nature (although a second-order transition could not be ruled out entirely).     

Influence of salts of 1,1,2,2-tetrachloroethane on the acidity function of the solutions of methanesulfonic acid

The influence of salts CH₃SO₃Na and/or CH₃SO₃Bu₄N on the acidity function H ₀ of methanesulfonic acid (MSA) and its solutions in water, N,N-dimethylformamide (DMF) in mixtures of methanesulfonic acid-N,N-dimethylformamide MSA-DMF ≤ 1 and ethyl acetate (EA) in a mixture of methanesulfonic acid-ethyl acetate MSA/EA (1: 1) and 1,1,2,2-tetrachloroethane (TCE) on H ₀ of methanesulfonic acid (MSA) and its mixtures with N,N-dimethylformamide (DMF), 2-pyrrolidine (Pyr) and ethyl acetate (EA) with the ratios of MSA: DMF equal to 1: 1 and 2: 1, MSA: Pyr (2: 1) and MSA: EA, equal to 2: 1, 1: 1, and 1: 2 is investigated by the indicator method at 25°C. It is revealed that a change in the acidity of the solutions of MSA in the aprotic solvents can occur as a result of the influence of salts both on the equilibrium composition of the nascent complexes and on their ionizing ability (both of these factors change acidity on addition of salts to the mixture of MSA-EA (1: 1)). An explanation is proposed why CH₃SO₃Na and CH₃SO₃Bu₄N influence differently on the acidity of aqueous solutions of MSA. It is established that in the solutions of (TCE) the ionizing ability of MSA and its complexes with DMF, Pyr and EA, which have different degree of the proton transfer ($ K_{T_i } $ K_{T_i } ), depends on the concentration ratio of MSA: TCE and ($ K_{T_i } $ K_{T_i } ): TCE.     

Neutral meson oscillations and equivalence principle for particles and antiparticles

Oscillations of neutral meson (K ⁰-$ \overline {K^0 } $ \overline {K^0 } , D ⁰-$ \overline {D^0 } $ \overline {D^0 } , and B ⁰-$ \overline {B^0 } $ \overline {B^0 } are extremely sensitive to the meson and antimeson energies at rest. This energy is determined as mc ²—with the corresponding inertial mass—and as the energy of gravitational interaction. Assuming that the CPT theorem is correct for inertial masses and estimating the gravitational potential for which the largest contribution originates from the field of the galaxy center, we obtain the estimate from experimental data on K ⁰-$ \overline {K^0 } $ \overline {K^0 } oscillations:

The property of maximal transcendentality in the N \mathcal{N} = 4 SYM

We show results for the universal anomalous dimension γ_uni(j) of Wilson twist-2 operators in the $ \mathcal{N} $ \mathcal{N} = 4 Supersymmetric Yang-Mills theory in the first three orders of perturbation theory. These expressions are obtained by extracting the most complicated contributions from the corresponding anomalous dimensions in QCD.     

Scarcity of real discrete eigenvalues in non-analytic complex $$ \mathcal{P}\mathcal{T} $$-symmetric potentials

We find that a non-differentiability occurring whether in real or imaginary part of a complex $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric potential causes a scarcity of the real discrete eigenvalues despite the real part alone possessing an infinite spectrum. We demonstrate this by perturbing the real potentials x ² and |x| by imaginary $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric potentials ix/it|x| and ix, respectively.