Anisotropic Universe Models with Perfect Fluid and Dark Energy with Time Varying G and Λ

We have investigated general Bianchi type I cosmological models which containing a perfect fluid and dark energy with time varying G and Λ that have been presented. The perfect fluid is taken to be one obeying the equation of state parameter, i.e., p=ωρ; whereas the dark energy density is considered to be either modified polytropic or the Chaplygin gas. Cosmological models admitting both power-law which is explored in the presence of perfect fluid and dark energy too. We reconstruct gravitational parameter G, cosmological term Λ, critical density ρ _c , density parameter Ω, cosmological constant density parameter Ω _Λ and deceleration parameter q for different equation of state. The present study will examine non-linear EOS with a general nonlinear term in the energy density.     

Investigation of the excitation of metastable states of 197Pt and 197Hg in (γ, n) and (d, 2n) reactions

The isomeric ratios of the ^197m,g Pt and ^197m,g Hg yields in the respective (γ, n) reactions are measured for the first time in the energy range 8–17 MeV. The isomeric ratios σ _m/σ_g for ^197m,g Hg in the (d, 2n) reaction are measured in the energy range 8–50 MeV. The experimental data are compared with the results of theoretical calculations. The effect of the structure of low-lying states and of the yrast line on the behavior of σ _m/σ_g is revealed. __________ Translated from Yadernaya Fizika, Vol. 67, No. 5, 2004, pp. 899–905. Original Russian Text Copyright ? 2004 by Zheltonozhsky, Mazur, Bigan.     

A Cyclic Model of Universe with Energy Exchange between Radiation,Matter and Vacuum Energy

We further extend the cosmological scenario with energy exchange by Barrow and Clifton and our previous work to the more complex case with energy exchange between three fluids: radiation, matter and vacuum energy. By prescribing the form of energy exchange function, we construct an infinitely cyclic cosmological model, in which the universe undergoes an endless sequence of cosmic epoch and each consisting of expansion and contraction, and the cosmological parameters, such as the Hubble parameter H, deceleration parameter q, transition red-shift Z _T, and densities ρ _r ,ρ _m , and ρ _Λ are consistent with the present observed values.     

The Landauer resistance of a one-dimensional metal with periodically spaced random impurities

We find the dependence of the ensemble-averaged resistance, 〈ρ _L〉, of a one-dimensional chain consisting of periodically spaced random delta-function potentials of the chain length L, the incident-electron energy, and the chain disorder parameter w. We show that generally the 〈ρ _L〉 vs L dependence can be written as a sum of three exponential functions, two of which tend to zero as L℩∞. Hence the asymptotic expression for 〈ρ _L〉 is always an exponential function of L. Such an expression for 〈ρ _L〉 means that the electronic states are indeed localized and makes it possible (which is important) to find the dependence of the localization radius on the incident-electron energy and the force with which an electron interacts with the sites of the chain. We also derive a recurrence representation for 〈ρ _L〉, which proves convenient in numerical calculations. Zh. éksp. Teor. Fiz. 111, 575–584 (February 1997)     

Effect of the velocity-dependent potentials on the energy eigenvalues of the Morse potential

We investigate the effect of the isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Morse potential for any quantum states. When the velocity-dependent term is used as a constant parameter, ρ(r) = ρ ₀, the energy eigenvalues can be obtained analytically by using the Pekeris approximation. When the velocity-dependent term is considered as an harmonic oscillator type, ρ(r) = ρ ₀ r ², we show how to obtain the energy eigenvalues of the Morse potential without any approximation for any n and ℓ quantum states by using numerical calculations. The calculations have been performed for different energy eigenvalues and different numerical values of ρ ₀, in order to show the contribution of the velocity-dependent potential on the energy eigenvalues of the Morse potential.     

Electron screening in backward elastic scattering

Abstact: The elastic scattering cross sections, σ (E,θ), for the systems He+Ta and He+W have been measured at θ_lab=165° and E _lab=76.1 keV to 3.988 MeV using targets with a thickness of a few atomic layers. The results are smaller than the results given by the Rutherford scattering law, σ_R(E,θ), due to the effects of electron screening and can be described by σ(E,θ)/σ_R(E,θ)=(1+U_e/E)⁻¹, where U _e is an atomic screening potential energy. The deduced average value, U _e=28 ± 3 keV, is consistent with the Moliére- and Lenz-Jensen-models as well as electron binding energies. Received: 25 May 1998     

Spectral rigidity and eigenfunction correlations at the Anderson transition

The statistics of energy levels for a disordered conductor are considered in the critical energy window near the mobility edge. It is shown that, if the critical wave functions are multifractal, the one-dimensional gas of levels on the energy axis is compressible, in the sense that the variance of the level number in an interval is 〈 (δN)²〉∼χ〈N〉 for 〈N〉≫1. The compressibility, χ=η/2d, is given exactly in terms of the multifractal exponent η =d−D ₂ at the mobility edge in a d-dimensional system. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 5, 355–360 (10 September 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Coherent and incoherent π0 photoproduction from the deuteron

Differential cross-sections for the reactions d (γ,π⁰)d and d (γ,π⁰)pn have been measured at MAMI with the TAPS detector setup in the energy range 140 MeV < E _γ < 306 MeV. By use of the Glasgow tagging spectrometer an 0.8 MeV energy resolution for photons incident on the target was achieved. The π⁰ missing energy resolution was sufficient for a reliable separation of coherent and incoherent channels. The data for the break-up channel exhibit very strong final state interaction effects, whereas the observed angular dependence of the inclusive process d (γ,π⁰)X is in quantitative agreement with predictions for a quasi-free process. The observed absolute d (γ,π⁰)X cross-sections, on the other hand, are significantly smaller than predicted by the quasi-free process for E _γ >∼ 250 MeV. Associating this failure with the π⁰ photoproduction on the neutron would suggest that its cross-section is up to 25% below the presently believed value. Received: 13 February 2001 / Accepted: 13 April 2001     

The sign of interband interaction and stability of the superconducting ground state in the multiband model

Summary It is stressed that the stability of the superconducting ground state in the two-band model is guaranteed for both signs of the leading interband interactionW. Thereby the requirement for the energy minimum fixed the phase differences of two order parameters as |ϕ₁-ϕ₂|=0,2π, … ifW<0 and |ϕ₁-ϕ₂|=π 3π, … ifW>0, and this difference is reflected in the ground-state wave function.     

Emission of light nuclei (<Emphasis Type="Italic">p,d, t</Emphasis>, α) in the process of annihilation of slow antiprotons in nuclear emulsion

The annihilation of slow (∼7 MeV) antiprotons in nuclear emulsion has been studied. The yields and energy spectra of p, d, t, and α particles in the evaporation region have been measured. The shape of the spectra of p, d, and t is in agreement with the Maxwell distribution and the excitation energy of a nucleus is consistent with a theoretical estimate for evaporation from the equilibrium state. The probability of the absorption of antiprotons inside the nucleus estimated from the multiplicity of h particles is ɛ = (2.0 ± 0.6) × 10⁻². The relative d/p yield coincides with a similar ratio appearing in the capture of slow π⁻ mesons by nuclei in the nuclear emulsion. The yields of t and α particles in the process of the annihilation of antiprotons are much higher than those in a similar process for pions. To identify g particles (0.29 < β < 0.70), energy losses dE/dx on ionization and multiple scattering have been measured. In this velocity region, the yields of p, d, t, and pions have been observed. The ratios (n _d /n _p ) _g , (n _d /n _p ) _b , and n _d /n _p measured in the capture of π⁻ mesons are almost the same. In this velocity range (g particles), α particles have not been observed.     

Radiative energy loss of high-energy quarks in finite-size nuclear matter and quark-gluon plasma

The induced gluon radiation of a high-energy quark in a finite-size QCD medium is studied. For a sufficiently energetic quark produced inside a medium we find the radiative energy loss ΔE _q∝L ², where L is the distance traveled by quark in the medium. It has a weak dependence on the initial quark energy E _q. The L ² dependence turns to L ¹ as the quark energy decreases. Numerical calculations are performed for a cold nuclear matter and a hot quark-gluon plasma. For a quark incident on a nucleus we predict ΔE _q ≈0.1E _q (L/10fm) ^β , with β close to unity. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 8, 585–589 (25 April 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Composite-meson model and meson exchange currents

We study the meson exchange currents (MEC) mechanism for the pion double-charge exchange (DCX) reaction in a composite-meson model. The model assumes that the mesons are two-quark systems and can interact with each other only through quark loops. The contributions of the ρ, σ, and f₀ mesons, the four-quark box diagram as well as a contact diagram has been taken into account. It is shown that the contribution of the ρ, σ, and f₀ mesons increases the forward scattering cross-section in an average by 25% and decreases with energy.     

Analytic solution of the BCS gap equation inD dimensions (D=1, 2, 3), at finite temperatures

The Bardeen-Cooper-Schrieffer (BCS) gap equation is solved analytically in one, two and three dimensions, for temperatures close to zero andT _c. We work in the weak coupling limit, but allow the interaction widthν≡ħω _m/E _F to lie in the interval (0, ∞) Here,ħω _m is the maximum energy of a force-mediating boson, andE _F denotes the Fermi energy. We obtain expressions forT _c and ΔC, the jump in the electronic specific heat acrossT=T _c, in the limitsν≪1 (the usual phonon pairing) andν>1 (non-phononic pairing). This enables us to see howT _c scales with the mediating boson cut off. Our results predict a larger jump in the specific heat for the caseν>1, compared toν≪1. We also briefly touch upon the role of a van Hove singularity in the density of states.     

Variations of ionic binding energies and the distribution of charge carriers in orthorhombic La2−x Sr x CuO4

The significance of heterovalent, substitutional disorder for the distribution of charge carriers in La_2−x Sr _x CuO₄ has been investigated. Disorder is shown to cause strong variations of binding energies of the ions ranging to some eV for Sr contentsx=0.1. Balancing the energy for a hole transport, Cu³⁺+O²⁻→Cu²⁺+O⁻, and taking binding energy variations into account, the process is realized to become possible without consuming energy for a subset Θ for allx Cu³⁺ in one formula unit of La_2−x Sr _x CuO₄. The functions Θ(x) are presented for hole transports to apex and in-plane oxygens, respectively. The delocalization of charge carriers is interpreted to be caused by valency disorder on metal lattice sites.     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

Spectroscopic and structural proprieties of LiAr and LiAr<Subscript>2</Subscript> molecules

We determined and tried to understand the spectroscopic and structural properties of small LiAr and LiAr₂ molecules within a simple model considering LiAr as a result of interaction between a valence electron and a LiAr⁺ molecular ion. Potential energy curves, spectroscopic constants, and vibrational levels corresponding to the Li(2s, 2p, 3s, and 3p)+Ar dissociation are reported for the LiAr molecule. The depth of the potential well for the X ²Σ⁺ ground state is found to be 50 cm⁻¹ (the corresponding experimental value is (42.5±1.2) cm⁻1 [1]). R _e is determined to be 9.36 a.u. (the experimental value is 9.24 a.u.). For the first excited state A, R _e = 4.97 a.u. and D _e = 993cm ⁻¹ (the corresponding experimental values are 4.68 a.u. and (925−40) cm⁻¹, respectively [1]). The spacing between the vibrational levels for the ground and first excited states is in very good agreement with the experiment. For the ground state, the difference between our results and the data of the most recent experiment is about 1 cm⁻¹. The model has been extended to study the LiAr₂ molecule in two forms (linear and triangular). We have determined the potential energy surfaces of the states dissociating to Li(2s, 2p)+Ar₂ and thus found the triangular form to be more stable as compared to the linear one. We have also calculated the transition energy between the ground state and first excited states of this molecule. The emission spectrum of the Li(2s)+Ar₂→Li(2p)+Ar₂ transition in both forms redshifts as compared to the Li(2s)→Li(2p) atomic transition.     

The multiphoton ionization rate and the energy shift of atoms interacting with weak dichromatic fields with commensurate frequencies are simple functions of the phase difference

By implementing a time-independent, nonperturbative many-electron, many-photon theory (MEMPT), cycle-averaged complex eigenvalues were obtained for the He atom, whose real part gives the field-induced energy shift, Δ(ω ₁, F ₁;ω ₂, F ₂,ϕ), and the imaginary part is the multiphoton ionization rate, Γ(ω ₁, F ₁;ω ₂, F ₂,ϕ), where ω is the frequency, F is the field strength and ϕ is the phase difference. Through analysis and computation we show that, provided the intensities are weak, the dependence of Γ(ω ₁, F ₁;ω ₂, F ₂,ϕ) on ϕ is simple. Specifically, for odd harmonics, Γ varies linearly with cos(ϕ) whilst for even harmonics it varies linearly with cos(2ϕ). In addition, this dependence on ϕ holds for Δ(ω ₁, F ₁;ω ₂, F ₂,ϕ) as well. These relations may turn out to be applicable to other atomic systems as well, and to provide a definition of the weak field regime in the dichromatic case. When the combination of (ω ₁, F ₁) and (ω ₂, F ₂) is such that higher powers of cos(ϕ) and cos(2ϕ) become important, these rules break down and we reach the strong field regime. The herein reported results refer to Γ(ω ₁, F ₁;ω ₂, F ₂,ϕ) and Δ(ω ₁, F ₁;ω ₂, F ₂,ϕ) for He irradiated by a dichromatic ac-field consisting of the fundamental wavelength λ = 248 nm and its 2nd, 3rd and 4th higher harmonics. The intensities are in the range 1.0×10¹²-3.5×10¹⁴ W/cm², with the intensity of the harmonics being 1-2 orders of magnitude smaller. The calculations incorporated systematically electronic structure and electron correlation effects in the discrete and in the continuous spectrum, for ¹S, ¹P, ¹D, ¹F, ¹G, and ¹H two-electron states of even and odd parity. Received 9 July 2000 and Received in final form 2 November 2000     

On Convergence to Equilibrium Distribution,I.¶The Klein–Gordon Equation with Mixing

Consider the Klein–Gordon equation (KGE) in ℝ ⁿ , n≥ 2, with constant or variable coefficients. We study the distribution μ _t of the random solution at time t∈ℝ. We assume that the initial probability measure μ₀ has zero mean, a translation-invariant covariance, and a finite mean energy density. We also assume that μ₀ satisfies a Rosenblatt- or Ibragimov–Linnik-type mixing condition. The main result is the convergence of μ _t to a Gaussian probability measure as t→∞ which gives a Central Limit Theorem for the KGE. The proof for the case of constant coefficients is based on an analysis of long time asymptotics of the solution in the Fourier representation and Bernstein's “room-corridor” argument. The case of variable coefficients is treated by using an “averaged” version ofthe scattering theory for infinite energy solutions, based on Vainberg's results on local energy decay. Received: 4 January 2001 / Accepted: 2 July 2001     

Experimental and theoretical studies of optical properties on alloys of the intermetallic systems Li2Ag2−x In x and Li2Cd2−x In x

X-ray and neutron diffraction experiments and optical studies were done on several alloys of the quasibinary series Li₂Ag_2−x In _x , Li₂Cd_2−x In _x , and Li₂Zn_2−x Cd _x . Within a wide region the alloys crystallize homogenous in an NaTl-type structure (1≦x≦1.5 for Li₂Ag_2−x In _x ; 0.6≦x≦1 for Li₂Cd_2−x In _x ; 1.2≦x≦1.6 for Li₂Zn_2−x Cd _x ). Most of the alloys investigated are colored and the color changes continuously as a function ofx. Measurements of the reflectivityr and the dielectric constants (ɛ₁ and ɛ₂) were done in the energy range 1.5 eV≦E≦3.3 eV by the method of elliptical analysis. In this energy range the curvesr(E) have minima which shift with increasingx to lower energy values. Calculations of the energy bands of LiAg, LiIn, LiCd, and Li₂AgIn on the basis of the augmented plane wave method and the determination of the joint density show that the optical data can be interpretated on the assumption of interband transitions between the valence and the conduction bands and of transitions between the 4d-bands of silver and the energy states at the Fermi level.     

Exact self-consistent plane-symmetric solutions of the equations of two interacting fields (spinor field and scalar field)

A spinor field interacting with a zero-mass neutral scalar field is considered for the case of the simplest type of direct interaction, where the interaction Lagrangian has the formL _int =1/2 ϕ_αϕ_,α F(S) whereF(S) is an arbitrary function of the spinor field invariantS=ψψ. Exact solutions of the corresponding systems of equations that take into account the natural gravitational field in a plane-symmetric metric are obtained. It is proved that the initial system of equations has regular localized soliton-type solutions only if the energy density of the zero-mass scalar field is negative as it “disengages” from interaction with the spinor field. In two-dimensional space-time the system of field equations we are studying describes the configuration of fields with constant energy densityT ₀₀ , i.e., no soliton-like solutions exist in this case. Russian People’s Friendship University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 69–75, July, 1998.