The radiative characteristics of the rovibronic states of the hydrogen molecule: IV. Relative probabilities of the r 3Π g ? , s 3Δ g ? → c 3Π u ± spontaneous transitions of the H2 molecule

A statistical analysis of the available literature data and data obtained in this work on the wave numbers of the lines that appear in triplet-triplet rovibronic transitions of the H₂ molecule was performed. This allowed us to verify and refine the controversial identification of spectral lines and find the optimum rovibronic level energy values for the c ³Π _u ^±, r ³Π _g ⁻, and s ³Δ _g ⁻ states. The ratios between the line strengths of the P, Q, and R branches of the (4dπ)r ³Π _g ⁻, (4dδ)s ³Δ _g ⁻ → (2pπ)c ³Π _u ^± band systems of the H₂ molecule were measured systematically. The calculation results obtained in the Frank-Condon approximation differed substantially (by up to two orders of magnitude) from the experimental data. The dependences of the ratios between rovibronic line strengths of the r ³Π _g ⁻ → c ³Π _u ^± and s ³Δ _g ⁻ → c ³Π _u ^± transitions on the rotational quantum number N′ of the upper level were found to correlate with each other. The deviations of adiabatic theory increase as N′ grows, which is evidence of an important role played by electronic-rotational interactions in the perturbation of transition probabilities. The experimental ratios between the probabilities of rovibronic transitions satisfactorily agree with the results of calculations within the framework of the simple nonadiabatic model taking into account electronic-rotational interaction of radiating adiabatic states in the approximation of pure precession. The dependences of transition probabilities on N′ were obtained for the first time for the first four diagonal bands of the r ³Π _g ⁻, s ³Δ _g ⁻ → c ³Π _u ^± transitions. Original Russian Text ? S.A. Astashkevich, B.P. Lavrov, A.V. Modin, I.S. Umrikhin, 2008, published in Khimicheskaya Fizika, 2008, Vol. 27, No. 2, pp. 22–38.     

Reverse current in metal/n-Al x Ga1−x Sb surface-barrier structures

The effect of ap inversion layer along the free surface of a solid solution and the reverse current for metal/n-Al _x Ga_1−x Sb surface barrier structures are analyzed. An algorithm is proposed for numerical solution of the system of equations which describes the “collection” of the current along the unbounded planar surface of a structure with a metallic contact of radiusr _c . During the calculations of the properties for surface barrier structures it was assumed that the positions of the Fermi level at the boundary with the metal and at the freen-Al _x Ga_1−x Sb surface are about the same. Calculations of the near-surface component of the reverse currentI _s for the structures with this assumption exceed the bulk componentI _b by more than an order of magnitude. The dependences ofI _s andI _b and the effective radius of the collection region of the current on the composition of the solid solution are found. We compared the calculated current-voltage characteristics with the experimental ones for Pd/Al_0.1 Ga_0.9Sb structures. Tomsk State University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 41, No. 12, pp. 46–51, December, 1998.     

Ethylene adsorption on the Pt-Cu bimetallic catalysts. Density functional theory cluster study

The adsorption of ethylene on Cu₁₂Pt₂ clusters has been studied within the density functional theory (DFT) approach to understand the high ethylene selectivity of Cu-rich Pt-Cu catalyst particles in the reaction of hydrogen-assisted 1,2-dichloroethane dechlorination. The structural parameters for Cu₁₂Pt₂ clusters with D_4h, D_2d, and C_3v symmetry have been calculated. The relative stability of the isomeric Cu₁₂Pt₂ clusters follows the order: C_3v > D_2d > D_4h. Each isomer has an active site for ethylene adsorption that consists of a single Pt atom surrounded by Cu atoms. The interaction of ethylene with the active site yields a π-C₂H₄ adsorption complex. The strongest π-C₂H₄ complex forms with the cluster of C_3v symmetry; the bonding energy, ΔE_π(C₂H₄), is −15.6 kcal mol⁻¹. The bonding energies for the π-C₂H₄ complex with Cu₁₄ and Pt₁₄ clusters are −6.5 and −18.8 kcal mol⁻¹, respectively.The addition of Pt to Cu modifies the valence spd-band of the cluster as compared to a Cu₁₄ cluster. The DOS near the Fermi level increases when C₂H₄ adsorbs on the Cu₁₂Pt₂ cluster. As well, the center of the d-band shifts toward lower binding energies. Ethylene adsorption also induces a number of states below the d-band. These states correspond to those of gas-phase C₂H₄.The vibrational frequencies of C₂H₄ adsorbed on the clusters of D_4h and C_3v symmetry have been calculated. The phonon vibrations occur below 250 cm⁻¹. The intense bands around 200 cm⁻¹ are attributed to stretching vibrations of the Pt-Cu bonds normal to the cluster surface. The stretching vibrations of the Pt-C bonds depend on the local structure of the active site: ν_s(Pt-C) = 268 cm⁻¹ and ν_as(Pt-C) = 357 cm⁻¹ for the cluster of the D_4h symmetry; ν_s(Pt-C) = 335 cm⁻¹ and ν_as(Pt-C) = 397 cm⁻¹ for the cluster of the C_3v symmetry. Bands in the range of 800-3100 cm⁻¹ are attributed to vibrations of the adsorbed C₂H₄ molecule. The signature frequencies of the π-C₂H₄ adsorption complex are the δ_s(CH₂) deformation vibration at ∼1200 cm⁻¹ and the ν(C-C) stretching vibration at ∼1500 cm⁻¹. These vibration are absent for di-σ-C₂H₄ adsorption complexes.     

CP violation in KS, L → π+π?γ and KS, L → π+π?e+e? decays

The dependence of K _{S, L} → π ⁺ π ⁻ γ decay probabilities on photon polarization is calculated. The phases of the terms of the amplitude that arise from the pion-pion interaction are obtained by using a simple realistic model of pion-pion interaction via virtual ρ meson, instead of chiral perturbation theory (ChPT). The results are compared with those of other authors and the origin of the discrepancies is explained. It is shown that the standard ChPT approach for K _{S, L} → π ⁺ π ⁻ γ decays cannot reproduce the contribution of the ρ meson to the P-wave ππ interaction. The departure of the photon spectrum from pure bremsstrahlung due to the pion-loop contribution to the electric direct emission amplitude is calculated. It is shown that the interference between the terms of amplitude with different CP parity appears only when the photon is polarized (linearly or circularly). Instead of measuring the linear polarization, the angular correlation between the π ⁺ π ⁻ and e ⁺ e ⁻ planes in K _{S, L} → π ⁺ π ⁻ e ⁺ e ⁻ decay can be studied. From Yadernaya Fizika, Vol. 67, No. 2, 2004, pp. 332–345. Original English Text Copyright ? 2004 by Bulanov. This article was submitted by the author in English.     

Formation of multilayer strained-layer heterostructures by liquid epitaxy. II. Simulation of the fabrication of heterostructures based on indium-arsenic-antimony-bismuth solid solutions

The formation of InAs_1−x−y Sb_xBi_y/InSb and InAs_1−x−y Sb_xBi_y/InSb_yBi_y strained-layer heterostructures by “capillary” LPE is simulated. The laws governing the dependence of the gap width E _g and the thickness d of the epilayers on the conditions of the process are revealed. It is shown that because of the sharp increase in the rate of epitaxial deposition as the LPE temperature is raised, the successful growth of epilayers of subcritical thickness is possible only up to T<550 K. The influence of the rate of laminar flow of the liquid in the growth channel in a relaxation regime and in a continuous pumping regime on the uniformity of the distribution of E _g and d in the epitaxial heterostructures is analyzed. Effective combinations of parameters for carrying out the process, which ensure the achievement of E _g ≈0.1 eV (77 K) in the active layers with variable-band-gap layers of minimal thickness, are established. Zh. Tekh. Fiz. 67, 50–56 (July 1997)     

Magnetic susceptibility anisotropy and low-dimensional antiferromagnetism of CuO

The anisotropy of the magnetic susceptibility χ and the influence of oxygen vacancies in CuO single crystals on it are investigated. The temperature dependences of χ(T) along the a, b, and c axes in the range 60<T<600 K and the behavior of the field dependence of the magnetization σ(H) above and below the Néel temperature T _N are plotted for a crystal before and after heat treatment. The χ(T) curves have the form characteristic of low-dimensional systems, which become three-dimensional when the temperature is lowered. The character of the χ(T) curves remains unchanged after annealing. Oxygen vacancies have practically no influence on the a-axis magnetic susceptibility, but they alter the absolute values of the b-and c-axis susceptibilities. The significant effects of reducing the oxygen concentration include a decrease in the magnitude of the low-temperature anomaly (increase) in χ and an increase in the minimum value of χ. The results of the calculations of the exchange parameter I/k and the g factor are discussed in terms of the Heisenberg and Ising models for a one-dimensional system. Zh. éksp. Teor. Fiz. 113, 1026–1035 (March 1998)     

Dynamic magnetic permeability of a thin, high-T c superconducting wafer

The field dependence of the vibrational contribution to the dynamic magnetic permeability μ _V(H) is calculated for a thin (of thickness d∼λ) high-T _c superconducting wafer in a magnetic field parallel to the surface. The resulting curves are plotted on the basis of an exact numerical analysis of the vortex structures both for the thermodynamic-equilibrium vortex lattice and in the presence of pinning forces and the Bean-Livingston surface barrier. It is shown that the μ _V(H) curves are highly sensitive to the size factor (d/λ) and exhibit abrupt changes corresponding to a change in the number of vortex rows. The equilibrium μ _V(H) curve is found to be similar in its general behavior and absolute value (obtained with allowance for the distribution of grain sizes and with appropriate values of λ and ϰ) to the experimental μ _V(H) curve plotted at nitrogen temperature for fine-grained YBa₂Cu₃O_x with grain diameters 〈D〉∼λ in an increasing magnetic field. It is established that the main cause of the experimentally observed irreversible behavior of the μ _V(H) curves during cyclic variation of the applied magnetic field is the existence of a surface barrier to the exit of vortices from the superconductor. The lower limit H _min(B) of stability of the mixed state in the presence of an ideal surface barrier in a thin, high-T _c superconducting wafer (d∼λ) is determined, along with the range of the vortex state (H _max-H _min) for a fixed number of vortices in micrometer-size grains of the investigated YBaCuO samples. Fiz. Tverd. Tela (St. Petersburg) 39, 1943–1947 (November 1997)     

Modeling of anisotropic spheres in extended teleparallel theory with matter coupling

This work is devoted to investigate the structures of compact stars by using spherically static symmetric space-time in the background of $f(\tau ,T)$ gravity, where $\tau$ represents the torsion scalar and $T$ represents the trace of the energy momentum tensor. We develop the field equations by using the concept of quintessence to discuss the motion by using anisotropic fluid distribution with a spherically symmetric metric. We use the convention of junction conditions to evaluate the unknown parameters used in the study of the compact stars. In this study we use the available data of three different compact objects $4U1608-52,$ $CenX-3$ and $EXO1785-240$. We discuss the physical and analytical existence of compact stars by satisfying some standard properties of compact stars like the behavior of the energy density, quintessence density, radial and tangential pressures, anisotropy, to elaborate the anisotropic nature of the star. We discuss the sound speeds and casuality conditions to show the stability of the system. Equilibrium of the star is justified by the TOV equation. Red-shift function, compactness, and mass function states the physical existence of the star. It is examined that all these parameters show the viability and stability of the model used in the effects of $f(\tau ,T)$ gravity.     

Theoretical analysis of the centrifugal distortion contributions to the rotational spectra of 2Π diatomics

The centrifugal distortion contributions to the rotational energies of diatomic molecules are derived from the resolution of the vibration-rotation wave equation. The unknown radial dependence of the fine structure constants is taken into account by means of a Taylor expansion around the equilibrium distance. Hence, one obtains the expressions of the centrifugal corrections associated with each fine structure constant in terms of the equilibrium values of its radial derivatives. The case of ²Π states is examined in detail. The dependence of the centrifugal distortion effects upon the choice of the coupling scheme representation is exhibited and a ²Π energy matrix containing the centrifugal constants of any order is proposed. Such a matrix is appropriate to fit the data for any value of the rotational quantum number. The theoretical expressions of the energy levels are related to the experimental data and the correlations between the spin-orbit centrifugal and spin-rotation contributions are put in evidence. It is shown that very compact formulas can be derived allowing a straightforward evaluation of the successive radial derivatives of the spin-orbit function in terms of the spectroscopic data $\text{A}{}^{\mathrm{(1)}}\text{? ?α}{}_{\mathrm{A}}\text{(}\text{w}{}_{\mathrm{e}}\text{B}{}_{\mathrm{e}}\text{)}$; $\text{A}{}^{\mathrm{(2)}}\text{? ?(1 +}\text{α}{}_{\mathrm{B}}\text{w}{}_{\mathrm{e}}\text{2B}{}_{\mathrm{e}}{}^2\text{)A}{}^{\mathrm{(1)}}$; …. Application of these results to the case of several molecules is considered and discussed.     

On generalized Clifford groups II

The earlier study of the irreducible representations of the generalized Clifford groups G^m_n in the case where m is a prime number, is now extended to the case where m is any integer. The analysis of class structure and hence the construction of the irreducible representations of G^m_n for a non-prime integer m is found to be more complicated. This investigation also requires the properties of the generalized Clifford algebras C^m_n(I) which are studied in Section 2 of the paper. The case of infinite generalized Clifford group, i.e. G^∞_n involving the infinite- order root of unity as well as the physical relevance of the generalized Clifford groups are briefly dealt with.     

Formation mechanism of the Si(1 1 1)7×7 reconstruction studied by scanning tunneling microscopy: Zipper-like restructuring in the sequential size changes of isolated single faulted-halves

The formation mechanism of the 7×7 reconstruction on annealed Si(1 1 1) surfaces has been demonstrated at the atomic level. In situ observations of unreconstructed regions (‘1×1’) on terraces after rapid quenching to 380 °C were done using scanning tunneling microscopy (STM) with a scanning speed of 1.7 s per frame. In the narrow ‘1×1’ regions, we imaged isolated single-faulted (F) halves of the dimer-adatom-stacking-fault (DAS) structure from “birth” to “death”. During “life”, the isolated single F-halves frequently changed their size. The size changes between odd-sized F-halves always took place through even-sized F-halves of intermediate sizes: 5×5-F^′↔6×6-F↔7×7-F^′↔8×8-F↔9×9-F^′↔10×10-F↔11×11-F^′↔12×12-F↔13×13-F^′, where the 5×5-F^′, 7×7-F^′ and so forth are irregular-type structures of the odd-sized F-halves. Even-sized F-halves and the irregular-type structures are necessary in the size changes, whereas the regular-type structures have never been involved. Lifetimes of the 10×10-F, 8×8-F, and 6×6-F at 380 °C are about 10.5, 6, and 2-3 s, respectively, which are much shorter than those of the isolated irregular-type structures of the odd-sized F-halves. With the aid of room temperature STM images of a rapidly quenched surface, we determined the atomic structures of the even-sized F-halves. We have proposed a sequential size change (SSC) model, including undiscovered parts of the size changes ‘1×1’ ↔2×2-F↔3×3-F^′↔4×4-F↔5×5-F^′, as the formation and decay mechanism of isolated single F-halves in the ‘1×1’ region. The SSC model has the following sequence: ‘1×1’ ↔ 2×2-F↔3×3-F^′↔4×4-F↔5×5-F^′↔6×6-F↔7×7-F^′↔8×8-F↔9×9-F^′↔10×10-F↔11×11-F^′↔12×12-F↔13×13-F^′. It was found by collecting statistics of size-change directions that one of two equivalent sides of the irregular-type structures, which have a mirror symmetry, is involved in the size changes thus indicating that other parts of the F-halves remain unchanged. Based on such findings, we have proposed the atomic processes for bond-rearrangements in the SSC model. The bond-rearrangements proceed along one side of a triangular F-half by breaking the existing dimers and forming new dimers like a “zipper”. Proposed atomic processes of the zipper-like restructuring are illustrated by a ball-and-stick model. The reason for the appearance of the even-sized F-halves and the irregular-type structures of the odd-sized ones is discussed in terms of the energy barrier heights along a reaction path in the size change of single F-halves.     

The effect of the valence nucleons off the shells with <Emphasis Type="Italic">Z</Emphasis> = 82 and <Emphasis Type="Italic">N</Emphasis> = 126 on rotational characteristics of actinide nuclei

Our earlier results obtained for moments of inertia (M) in the case of 54 rotational level bands built on the ground state of actinide nuclei are taken for further analysis. In the current paper, resulting dynamic rotational characteristics, such as a ₀, a ₁, s ₀ and the R _4/2 parameter, are studied from the standpoint of their dependence on the valence nucleon number product N _p N _n and on the variable P = N _p N _n /(N _p + N _n ). New features of the nuclei deformation phenomenon in the actinide area arise when their dynamic rotational characteristics, mentioned above, are plotted in such a way as shown in the current work. The method of analysis presented here makes it possible to reveal nuclei with valence nucleon numbers for which the nuclear interactions are notable and those in which they are inconspicuous. E. g. when N _p N _n < 200 and P < 6 the strength of nuclear interaction gradually decreases with the increase of these variables. The strength of the nuclear interaction does not change significantly for N _p N _n > 200 and P > 6 — the rotational characteristics stabilise. Moreover, it is possible to establish the P variable as representing the effective number of interactions of each valence nucleon with those of the other type.     

Experimental study of the electronic and lattice contributions to the VO2 transition

The contributions of electronic and crystallographic components to the semiconductor → metal transition in VO₂ have been estimated from resistivity, E.P.R., and calorimetric measurements of the electronic and thermodynamic properties of Ga_xV_?xO₂, where 0 < x < 0.0130. E.P.R. and resistivity measurements indicate a decrease in the metallic character of the high-temperature R phase with increasing x, and calorimetric measurements of the energetics of the transition show a decrease in the enthalpy and entropy of the transition with increasing levels of doping. This concomitant decrease in enthalpy and metallic character with increasing x implies a strong contribution of the electronic entropy to the transition. An extrapolation of the combined electronic and calorimetric data for Ga_xV_?xO₂ to pure VO₂ suggest that the electronic entropy comprises about 60% of the total entropy of transition in VO₂.     

Acceleration and inhibition of amyloid-β fibril formation by peptide-conjugated fluorescent-maghemite nanoparticles

The formation of amyloid aggregates by association of peptides into ordered structures is hallmark of certain neurodegenerative disorders. Exploring the effect of specific nanoparticles on the formation of amyloid fibrils may contribute toward a mechanistic understanding of the aggregation processes, leading to design nanoparticles that modulate the formation of toxic amyloid plaques. Uniform maghemite (γ-Fe₂O₃) magnetic nanoparticles, containing fluorescein covalently encapsulated within (F-γ-Fe₂O₃)_, were prepared. These F-γ-Fe₂O₃ nanoparticles of 14.0 ± 4.0 nm were then coated with human serum albumin (HSA) via a precipitation process. Covalent conjugation of the spacer arm succinimidyl polyethylene glycol succinimidyl ester (NHS–PEG–NHS) to the F-γ-Fe₂O₃~HSA nanoparticles was then accomplished by interacting the primary amine groups of the HSA coating with excess NHS–PEG–NHS molecules. Covalent conjugation of the peptides amyloid-β 40 (Aβ₄₀) or Leu-Pro-Phe-Phe-Asp (LPFFD) onto the surface of the former fluorescent nanoparticles was then performed, by interacting the terminal activated NHS groups of the PEG derivatized F-γ-Fe₂O₃~HSA nanoparticles with primary amino groups of the peptides. Kinetics of the Aβ₄₀ fibrillation process in the absence and presence of varying concentrations of the Aβ₄₀ or LPFFD conjugated nanoparticles were also elucidated. The non-peptide conjugated fluorescent nanoparticles do not affect the Aβ₄₀ fibrillation process significantly. However, the Aβ₄₀-conjugated nanoparticles (F-γ-Fe₂O₃~HSA–PEG–Aβ₄₀) accelerate the fibrillation process while the LPFFD-conjugated nanoparticles (F-γ-Fe₂O₃~HSA–PEG–LPFFD) inhibit it. By applying MRI and fluorescence imaging techniques simultaneously these bioactive fluorescent magnetic iron oxide nanoparticles can be used as an efficient tool to study and control the Aβ₄₀ amyloid fibril formation process.     

The zeta function of the quartic oscillator

We investigate the levels of the quartic oscillator ($\text{?}\text{d}{}^2\text{d}\text{q}{}^2\text{+ q}{}^4$) by means of the associated zeta function. By using several versions of the semiclassical approach, we prove exact results concerning the locations of the real zeros and of the poles of that function, the residues of which are essentially the coefficients of the semiclassical expansion of the Bohr-Sommerfeld quantization rule. We also compute the derivative of the zeta function at the origin, by relating it to the Fredholm determinant of the operator. These results translate as sum rules for the eigenvalues and thus are helpful for their precise computation, and a further analysis allows one to split them into separate rules for even and odd levels; the extension to higher anharmonic oscillators ($\text{?}\text{d}{}^2\text{d}\text{q}{}^2\text{+ q}{}^{\mathrm{2M}}$) is immediate. Finally we propose an asymptotic formula for large negative arguments of the zeta function, based on the nature and location of the complex singularities of the partition function of the operator $\text{(}\text{?}\text{d}{}^2\text{d}\text{q}{}^2\text{+ q}{}^4\text{)}{}^{\mathrm{<mtext>3</mtext><mtext>4</mtext>}}$.     

Superconductivity of (Sn1−z Pbz)1−x InxTe alloys

The temperature dependences of the electrical resistivity of (Sn_1?z Pb_z)_1?x In_xTe alloys with different concentrations of lead (z=0–0.60) and indium (x=0.03–0.20) were studied at temperatures T=0.4–4.2 K in magnetic fields from zero to H=15 kOe. A resistivity drop of no less than three-four orders of magnitude was observed in this range of alloy compositions. Application of a magnetic field above a critical level resulted in a recovery of the sample resistivity to the original value. The observed resistivity drop is identified with a superconducting transition. The critical parameters of the superconducting transition (T _c and H _c2) were determined at the drop to one half the normal resistivity level. Experimental dependences of the critical supercon-ducting-transition temperature T _c and of the second critical magnetic field H _c2 on the contents of lead (z) and indium (x) were measured. The data obtained confirm a strong localization of the In impurity states and are evidence of the extrinsic nature of superconductivity in the class of materials under study. It was established that as the Pb content in (Sn_1?z Pb_z)_1?x In_xTe increases, T _c and H _c2 decrease as the Fermi level E _F (fixed in the In impurity resonance band) leaves the Δ extremum and the superconductivity breaks down when E _F leaves the LΣ saddle point in the valence-band energy spectrum.     

Das Neutralgasprofil und die Elektronentemperatur in der Freifallsäule bei hohem Ionisationsgrad

The neutral gas flux from the wall into the column - connected with the ion flux to the wall - and the anisotropy of the velocity distribution of the neutral gas are included into the theory of the steady-state positive column. d/l_n and v_n0/v₀ occur as characteristic parameters. d denotes the radius of the column, l_n the mean free path of the neutral atoms for ionization, v_n0 the mean velocity of the neutral atoms re-emitted from the wall, v₀ = (2kT_e/M)^1/2, M the ion mass, T_e the electron temperature. On the axis the neutral gas density N_n is decreasing, if d/l_n is rising. At the wall N_n is increasing for v_n0 ? v₀, but it is almost constant or decreasing for v_n0 ? v₀ at the same time. In the plasma the total number of the atoms and the ions is taken as constant. In the case of small v_n0 the degree of ionization is high only for d ? l_n. However, it is already high for d ≈ l_n in the case of high v_n0. Therefore, the radial profiles of the neutral gas densities of different gases in a column can differ from each other. Almost full ionization can be reached near the axis. These results hold, too, if the initial velocity of the ions and a magnetic field are taken into account. d/l_n, the degree of ionization, and the electron temperature are given as functions of the electric power input and of the total number of the neutrals and the ions. The velocities of the re-emitted atoms depend on the accomodation coefficient of the ions recombining at the wall. With rising d/l_n an increasing number of the neutral atoms is re-emitted with superthermal velocities and the total number of the neutrals and the ions can be decreased. The anisotropy of the velocity distribution of the neutral atoms and the ions must be taken into account for the interpretations of spectroscopical measurements.     

The influence of free quintessence on gravitational frequency shift and deflection of light with 4D momentum

On the basis of the 4D momentum, the influence of quintessence on the gravitational frequency shift and the deflection of light are examined in modified Schwarzschild space. We find that the frequency of a photon depends on the state parameter of the quintessence w _q: the frequency increases for −1<w _q<−1/3 and decreases for −1/3<w _q<0. Meanwhile, we adopt an integral power number a (a=3ω _q+2) to solve the orbital equation of photon. The photon’s potentials become higher with the decrease of ω _q. The behavior of the bending light sensitively depends on the state parameter ω _q. In particular, for the case of ω _q=−1, there is no influence on the deflection of light by quintessence. Furthermore, according to the H-masers of the GP-A redshift experiment and long-baseline interferometry, the constraints on the quintessence field in the solar system are presented here.     

Mechanism of the production of the <Emphasis Type="Italic">a</Emphasis><Subscript>0</Subscript>(980) resonance in the γγ → π<Superscript>0</Superscript>η reaction

High-statistics Belle data on the γγ → π⁰η reaction have been analyzed in order to reveal the mechanism of two-photon production and the nature of the a ₀(980) resonance. The solution obtained for the γγ → π⁰η amplitude is in agreement with the predictions of the chiral theory for the πη-scattering length; with the strong coupling of the a ₀(980) resonance with the πη, K $ \bar K $ \bar K , and πη′ channels; and with the key role of the a ₀(980) → (K $ \bar K $ \bar K + π⁰η + π⁰η′) → γγ rescattering mechanisms in the a ₀(980) → γγ decay. This picture is much in favor of the q ² $ \bar q $ \bar q ² nature of a ₀(980) resonance and is consistent with the properties of its partners, σ₀(600) and f ₀(980) resonances, in particular, with those manifested in the γγ → ππ reactions. The important role of vector exchanges in the formation of the nonresonant background in the γγ → π⁰η reaction has been revealed. Preliminary information on the π⁰η → π⁰η reaction has been obtained.