Phenomenological Estimate of the Binding Energy of Heavy Dimesons

 A phenomenological estimate is derived such that the binding energies of dimesons are expressed as combinations of masses of different mesons and baryons. The estimate is almost model-independent, the only major assumptions being that the wave functions of the two light quarks in Λ _c , Λ _b and in the and dimesons are very similar, and that for heavy quarks the QQ interaction is half as strong as the interaction. We get (I = 0, J = 1) bound by about 100 MeV and unbound. Received July 4, 2000; revised November 28, 2000; accepted for publication February 5, 2001     

Separation of different wave components in the Bethe–Salpeter wave function

The scalar products of polarization tensor and unit vectors are presented explicitly in spherical coordinate system expanded in terms of spherical harmonic functions. By applying the obtained formulae, different wave components in the Salpeter wave function can be shown explicitly, and the results are consistent with the results obtained by L–S coupling analysis. The cancelation formula is given, by which the terms with pure L = J + 1 wave components in the Salpeter wave function for the bound state with h_P=(-1)^J\eta_{\rm P}=(-1)^J can be obtained by separating the L = J − 1 wave components from mixing terms. This separation provides the basis for studying higher-order contributions from the coupling of L = J − 1 and J + 1 wave states, and for solving the Salpeter equation exactly without approximation.     

Scattering of Heavy Charged Particles on Hydrogen Atoms

 Low-energy scattering of heavy positively charged particles on hydrogen atoms (H) is investigated by solving Faddeev equations in configuration space. A resonant value of the pH scattering length, a = 750 ± 5 a.u., in the pp antisymmetric state was found. This large value indicates the existence of a first excited state with a binding energy B = 1.14 × 10⁻⁹ a.u. below the H ground state. Resonances for non-zero angular-momenta states are predicted. Received November 4, 2001; accepted for publication November 12, 2001     

Fitting Cosmological Data to the Function <Emphasis Type="Italic">q</Emphasis>(<Emphasis Type="Italic">z</Emphasis>) from GR Theory: Modified Chaplygin Gas

In the Friedmann cosmology, the deceleration of the expansion q plays a fundamental role. We derive the deceleration as a function of redshift q(z) in two scenarios: ΛCDM model and modified Chaplygin gas (MCG) model. The function for the MCG model is then fitted to the cosmological data in order to obtain the cosmological parameters that minimize χ ². We use the Fisher matrix to construct the covariance matrix of our parameters and reconstruct the q(z) function. We use Supernovae Ia, WMAP5, and BAO measurements to obtain the observational constraints. We determined the present acceleration as q ₀ = − 0.65 ±0.19 for the MCG model using the Union2 dataset of SNeIa, BAO, and CMB and q ₀ = − 0.67 ±0.17 for the Constitution dataset, BAO and CMB. The transition redshift from deceleration to acceleration was found to be around 0.80 for both datasets. We have also determined the dark energy parameter for the MCG model: Ω _X0 = 0.81 ±0.03 for the Union2 dataset and Ω _X0 = 0.83 ±0.03 using the Constitution dataset.     

Spectra of Stimulated Electromagnetic Emission of the Ionosphere Upon Sweeping of the Pump Wave Frequency Near Gyroharmonics. I. Experimental Results

We present the results of experimental studies of the spectra of the stimulated electromagnetic emission excited in the ionosphere by powerful radio waves during the pump wave frequency sweeping near the forth (n = 4) and fifth (n = 5) harmonics of the electron cyclotron frequency nf _ce. The frequency sweep was carried out for long (continuous) pumping in vertical and inclined directions (at 14° and 18° south of the zenith), as well as for the pulse diagnostic wave both with and without additional pumping far from the gyroharmonics. The dependences of the spectral features of the stimulated electromagnetic emission on the ratio between the pump-wave frequency f ₀ (or on the diagnostic-wave frequency f_DW) and nf _ce were analyzed. It is found that near the multiple gyroresonance, different spectral features of the stimulated emission are quenched at the same frequency for different pump-wave frequencies. For a sufficiently large inclination of the pump wave beam from the vertical direction, the intensity of the stimulated electromagnetic emission is notably decreased for f ₀ ≲ nf _ce as compared with f ₀ > nf _ce. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 6, pp. 461–476, June 2008.     

Measurement of the Tensor-Analyzing Power A yy in Deuteron Breakup at 4.5 GeV/c and 80 mr

 The tensor-analyzing power A _yy in inclusive breakup of 4.5 GeV/c deuterons on beryllium has been measured at ∼ 80 mr of the detected proton angle. The analyzing power remains positive up to the highest measured momentum of the proton, that is in definitive contradiction with the predictions of the existing models based on the standard deuteron wave functions. The results suggest that the deuteron structure at short distances may depend on more than one independent variable. E-mail address: ladygin@sunhe.jinr.ru Received October 2, 2001; accepted July 19, 2002     

On the Uniqueness of Gravitational Centre

The dual volume of order α of a convex body A in R ⁿ is a function which assigns to every a ∈ A the mean value of α-power of distances of a from the boundary of A with respect to all directions. We prove that this function is strictly convex for α > n or α < 0 and strictly concave for 0 < α < n (for α = 0 and for α = n the function is constant). It implies that the dual volume of a convex body has the unique minimizer for α > n or α < 0 and has the unique maximizer for 0 < α < n. The gravitational centre of a convex body in R³ coincides with the maximizer of dual volume of order 2, thus it is unique.      

Plasma-filled rippled wall rectangular backward wave oscillator driven by sheet electron beam

Performance of the backward wave oscillator (BWO) is greatly enhanced with the introduction of plasma. Linear theory of the dispersion relation and the growth rate have been derived and analysed numerically for plasma-filled rippled wall rectangular waveguide driven by sheet electron beam. To see the effect of plasma on the TM₀₁ cold wave structure mode and on the generated frequency, the parameters used are: relativistic factor γ = 1.5 (i.e. v/c = 0.741), average waveguide height y ₀ = 1.445 cm, axial corrugation period z ₀ = 1.67 cm, and corrugation amplitude ε = 0.225 cm. The plasma density is varied from zero to 2 ×10¹² cm^− 3. The presence of plasma tends to raise the TM₀₁ mode cut-off frequency (14 GHz at 2 ×10¹² cm^− 3 plasma density) relative to the vacuum cut-off frequency (5 GHz) which also causes a decrease in the group velocity everywhere, resulting in a flattening of the dispersion relation. With the introduction of plasma, an enhancement in absolute instability was observed.     

Bound States in n Dimensions (Especially n = 1 and n = 2)

 We stress that in contradiction with what happens in space dimensions n ≥ 3, there is no strict bound on the number of bound states with the same structure as the semi-classical estimate for a large coupling constant. We give, in two dimensions, examples of weak potentials with one or infinitely many bound states. We derive bounds for one and two dimensions which have the “right” coupling-constant behaviour for large coupling. Received November 22, 2001; accepted for publication November 28, 2001     

Ergodic Jacobi Matrices and Conformal Maps

We study structural properties of the Lyapunov exponent γ and the density of states k for ergodic (or just invariant) Jacobi matrices in a general framework. In this analysis, a central role is played by the function w = − γ + iπ k as a conformal map between certain domains. This idea goes back to Marchenko and Ostrovskii, who used this device in their analysis of the periodic problem.     

Effect of externally injected radiation on amplified spontaneous emission in CO

The effect of externally injected radiation on the two-photon laser-induced amplified spontaneous emission (TP-LIASE) is reported. The wave generated via the same LIASE process in a seeder cell acts as a seeder field for the inverted medium created in a main cell. A nearly tenfold gain is achieved in the B¹ Σ ⁺ ?A¹ Π (0, 3) transition of the CO molecule. We demonstrate that the single rotational transition in the B¹ Σ ⁺ ?A¹ Π (0, 4) band is selectively amplified by injection of laser radiation. This pump and seed arrangement facilitates detection of molecular spectra by simply tuning the seed-laser frequency. The polarization effect of the input laser radiation is briefly discussed. Received: 9 June 2000 / Revised version: 2 October 2000 / Published online: 21 February 2001     

A Fast Algorithm for Wave Propagation from a Plane or a Cylindrical Surface

The newly developed Taylor-Interpolation-FFT (TI-FFT) algorithm dramatically increases the computational speeds for millimeter wave propagation from a planar (cylindrical) surface onto a “quasi-planar” (“quasi-cylindrical”) surface. Two different scenarios are considered in this article: the planar TI-FFT is for the computation of the wave propagation from a plane onto a “quasi-planar” surface and the cylindrical TI-FFT is for the computation of wave propagation from a cylindrical surface onto a “quasi-cylindrical” surface. Due to the use of the FFT, the TI-FFT algorithm has a computational complexity of O(N ² log₂  N ²) for an N × N computational grid, instead of N ⁴ for the direct integration method. The TI-FFT algorithm has a low sampling rate according to the Nyquist sampling theorem. The algorithm has accuracy down to −80 dB and it works particularly well for narrow-band fields and “quasi-planar” (“quasi-cylindrical”) surfaces.     

Four-Nucleon States in the Continuum: A Means to Probe the Nucleon-Nucleon Interaction

 Four-nucleon states in the continuum are studied through exact microscopic calculations based on the solution of the AGS equations for four nonrelativistic quantum particles. Our studies include calculations of cross sections and analyzing powers for all two-body reactions of interest, but here we only show results for n ³He → n ³He. The NN interactions we use are Bonn-CD, Nijmegen II, and Bonn-B. Compared to existing quality data, one finds large discrepancies and some sensitivity to the choice of NN force model. The calculated n + ³He elastic phase shifts show a very strong inelastic resonance at about 0.3 MeV which is not supported by the total cross-section data. This result is due to the existence of a ³ P ₀ (0⁻) resonance in isospin I = 0 at this energy and the undesirable coincidence of n + ³He and p + ³H thresholds in our calculation due to lack of Coulomb repulsion between protons. This interpretation is supported by R-matrix analyses of the data on the basis of coincident thresholds. Calculated 0⁺ and 0⁻ states are compared with modified R-matrix analyses. Received October 30, 2001; accepted for publication November 7, 2001     

Synthesis, crystal structure, thermal and dielectric properties of bis(p-phenylenediammonium) chloride hexachlorobismuthate(III) monohydrate [C6H4(NH3)2]2ClBiCl6.H2O

Synthesis, crystal structure, and dielectric properties of [C₆H₄(NH₃)₂]₂ClBiCl₆.H₂O are reported. The compound crystallizes in the monoclinic system with space group P2₁/n. The unit cell dimensions are a = 9.836(5), b = 19.582(5), c = 13.082(5) ?, β = 104.731(5)° with Z = 4. The atomic arrangement can be described by an alternation of organic and inorganic layers. The anionic layer is built up of octahedral of [BiCl₆]^3- arranged in sandwich between the organic layers. The crystal packing is governed by means of the ionic N–H···Cl hydrogen bonds, forming a three-dimensional network. The dielectric properties have been investigated at temperature range from 297 to 410 K at various frequencies (10 Hz–100 kHz). Dielectric studies were performed to confirm results obtained with thermal analysis. The evolution of dielectric constant as a function of temperature and frequency of single crystal has been investigated in order to determine some related parameters.     

Contribution of the Δ(1232) to the (e, e'p) reaction along with Coulomb distortion effects

The Δ-resonance contribution has been included in the (e, e'p) reaction along with Coulomb distortion effects. We treat the resonance via a non-relativistic Δ current operator and use a Dirac Hartree single-particle model for the ground-state single-particle wave function and a relativistic optical model for the knocked-out proton wave function. It is assumed that the π-meson created by the virtual photon is absorbed in the target nucleus following the production of a Δ-resonance. Our DWBA calculation shows that the Δ-resonance contribution to the (e, e'p) reaction cross-section is 10-15% for an energy of 250 MeV transfered to the proton knocked out of the s-shell of ⁴⁰Ca, in the parallel and perpendicular kinematics. Received: 21 July 2001 / Accepted: 21 March 2002     

Antisymmetry in Strangeness −1 and −2 Three-Baryon Systems

 Using the generalized Pauli principle by adding particle labels to the usual space and spin labels a symmetric Hamiltonian and a corresponding antisymmetric wave function are constructed for systems of three baryons in the strangeness sectors S = −1 and −2. Applications are the ΞNN-ΛΛN and NNΛ-NNΣ systems. Minimal sets of generalized coupled Faddeev equations for breakup and rearrangement operators as well as (possible) bound states are derived that have the ordinary Pauli principle for identical particles built in. The equations found confirm our previous sets of coupled Faddeev equations whose derivation was made for distinguishable particles and not using the generalized Pauli principle. Received August 21, 2000; accepted for publication September 29, 2000     

Cuspons and Smooth Solitons of the Degasperis–Procesi Equation Under Inhomogeneous Boundary Condition

This paper is contributed to explore all possible single peakon solutions for the Degasperis–Procesi (DP) equation m _t  + m _x u + 3mu _x  = 0, m = u − u _xx . Our procedure shows that the DP equation either has cusp soliton and smooth soliton solutions only under the inhomogeneous boundary condition lim_|x|→ ∞ u =A ≠0, or possesses the regular peakon solutions ce ^{− |x − ct|} ∈ H ¹ (c is the wave speed) only when lim_|x|→ ∞ u = 0 (see Theorem 4.1). In particular, we first time obtain the stationary cuspon solution of the DP equation. Moreover we present new cusp solitons (in the space of ) and smooth soliton solutions in an explicit form. Asymptotic analysis and numerical simulations are provided for smooth solitons and cusp solitons of the DP equation.      

Spectrum of the H− Ion in the s-Wave Model

 The H⁻ ion in the s-wave model has one bound state and a Rydberg series of resonances, one associated with each inelastic threshold of the electron hydrogen system. We calculate the energy of the bound state and the energies of the resonances as well as their total widths up to N = 9 and partial widths up to N = 7. Received July 5, 1999; revised February 18, 2000; accepted for publication February 22, 2000     

Understanding the proton spin “puzzle” with a new “minimal” quark model

We investigate the spin structure of the nucleon in an extended Jaffe-Lipkin quark model. In addition to the conventional 3q structure, different (3q)(Q ) admixtures in the nucleon wave function are also taken into account. The contributions to the nucleon spin from various components of the nucleon wave function are discussed. The effect due to the Melosh-Wigner rotation is also studied. It is shown that the Jaffe-Lipkin term is only important when antiquarks are negatively polarized. We arrive at a new “minimal” quark model, which is close to the naive quark model, in order to understand the proton spin “puzzle”. Received: 4 November 2000 / Accepted: 23 October 2001     

Acidichromism and Ionochromism of Luteolin and Apigenin,the Main Components of the Naturally Occurring Yellow Weld: A Spectrophotometric and Fluorimetric Study

Luteolin and apigenin, extracted from Reseda luteola L., were spectrophotometrically and fluorimetrically studied. The spectra were investigated as a function of pH in methanol/water solutions (1/2, v/v) in the 2–12 pH range. The absorption spectra markedly shifted to the red by increasing the pH. Three acid–base dissociation steps were detected for luteolin (pK _a = 6.9; 8.6; 10.3) and two for apigenin (pK _a = 6.6; 9.3). Fluorescence emission was very weak or undetectable (Φ _F < 10⁻⁴) in acidic solution, but increased in intensity with increasing the pH. Both molecules exhibited a great propensity towards complex formation with metal ions, with association constants on the order of 10⁵–10⁷ for the first complexation step; in the presence of excess Al³⁺ ions, multiple equilibria were detected. A marked fluorescence enhancement was observed upon complexation with Al³⁺ ions (Φ _F ∼ 1 for luteolin and ∼10⁻² for apigenin).