A measurement of the electromagnetic form factor of the eta meson and of the branching ratio for the eta Dalitz decay

In an optical spark chamber experiment we have obtained a sample of 80 eta Dalitz decays (η → e⁺e^?γ) and have measured the eta electromagnetic form factor to be F(X) = 1.0?(0.22 ±0.45)X, where X=M_ee²/M_η², and the branching ratio (η→e⁺e^?γ/(η→π⁺π^?π⁰)= (0.0082 ± 0.0020).     

On the effective viscosity for the Darcy-Brinkman equation

Up-scaling of the Stokes equations with non-slip boundary condition describing the flow in a porous medium, leads to the Darcy-Brinkman equation

?_βμ_βv_D,β=-K_β·(∇P_m,β-ρ_βg)+K_β·μ_β∇²v_D,β.     

On the invariants of the complex Ginzburg-Landau equation

Using Lie group theory, both the invariants and the similarity variables of the complex Ginzburg—Landau equation V_xx = a(V_t + bV) + cV|V|^2kwherea,b,c?Iandk?I are constructed.     

On the nonrelativistic limit of the Dirac theory

The relation between a “nonrelativistic” Hamiltonian of the formH ^∞=(A+B)²+C and a corresponding family of “Dirac-Hamiltonians”H(c) in the limitc → ∞ is investigated. It is shown that the resolvent (z ?H(c))^?1 and the relativistic perturbation of isolated eigenvalues ofH ^∞ are analytic in 1/c for sufficiently large |c|.     

On the shape consistency in the deformed shell-model approach

We show that the shape inconsistency (β^V_λ ? β^ρ_λ) between the average potential and the corresponding nucleonic density is generally small (～? 5%) for λ = 2, 3, 4 in both Nilsson and Woods-Saxon models. The properties of (β^V_λ ? β^?_λ) are analysed in detail and understood in terms of the extended Thomas-Fermi model. Approximate formulas β^ρ_λ = β^ρ_λ(β^V) are given and the microscopic reasons for the shape inconsistency discussed.     

On the fractal dimension of the Henon attractor

We re-measured the fractal dimension of the Hénon attractor by direct box-counting. We paid special attention to (a) optimal speed and use of storage, and (b) systematic corrections due to the finiteness of the number of iterations. Covering with grids of up to 9600 × 9600 boxes, we observe that the number N(?, n) of boxes visited after n iterations obeys a scaling law N(?, ∞) - N(?, n) ≈ const × ?^-αn^-β (for n → ∞) with α = 2.42 ± 0.15, β = 0.89 ± 0.03. Using this extrapolate to n → ∞, we obtain D = 1.28 ± 0.01 in disagreement with previous box-counting estimates, but in agreement with a recent indirect evaluation.     

Field effect on the dynamics of the Ising spin glass near the percolation threshold

The effect of a uniform field H on the dynamics of the Ising spin glass Fe_xZn_1-xF₂, x=0.25, is studied through Monte Carlo simulations. The correlation function data are consistent with the droplets picture, with a single scaling variable t/t_w, where t_w is the waiting time under H, activation over logarithmic energy barriers near the percolation threshold, x_p=0.24, and considerable change of the glassy phase for intermediate and high H.     

Evolution of the nucleon structure in the lightest nuclei

We show that the pattern of the oscillation of the structure functions ratio r^A(x)=F₂^A/F₂^N(D) varies with A by changing the position of the cross-over point x₃ in which r^A(x)=1, unlike the pattern for nuclei with masses A>4, where only the amplitude of the oscillation changes. In particular we find that the pattern of F₂(x) modifications is controlled with the values (1−x₃)=0.32 (D/N), 0.16 (³He/D) and 0.08 (⁴He/D). The obtained results follow from the relativistic approach and allow one to define the class of modifications of the bound nucleon structure.     

Hyperfine anomaly in the spectrum of the osmium atom. effect of the spatial distribution of nuclear charge

Contributions of the superposition of configurations ns ²5d ⁸+ns5d ⁸ n′s (n=1–5, n′=6–10) and ns ²5d ⁶+ns5d ⁶ n′s (n=1–6, n′=7–10) to parameters a _5d ⁰¹ , a _5d ¹² , and a _5d ¹⁰ of the hyperfine structure in the spectrum of the osmium atom OsI are calculated. It is shown that the nonzero contribution is made only to a _5d ¹⁰ . The effect of the spatial distribution of nuclear charge on the parameters of the hyperfine structure in the spectra of ¹⁸⁷Os and ¹⁸⁹Os isotopes and on the hyperfine anomaly for the 5d ⁷6s levels in the spectrum of these isotopes is estimated.     

On condensation in the free-boson gas and the spectrum of the Laplacian

We prove the convergence of the thermodynamic functions of a free boson gas for ad-dimensional (d=3,4,...) van Hove sequence of convex regions. The thermodynamic functions behave singularly at a critical densityρ _c which is independent of the geometrical details of the sequence. We are led to define a second critical densityρ _m depending on the geometrical details of the sequence. For densities betweenρ _c andρ _m none of the single particle states is macroscopically occupied. We derive a sufficient condition on the sequence such thatρ _m =ρ _c .     

On the definition of the pressure of an infinite system

A microcanonical system $\text{L}$^o_Λ is considered together with a manometer $\text{M}$_Λ. The thermodynamic limit Λ → ∞ is taken for the system $\text{L}$_Λ composed of $\text{L}$^o_Λ and $\text{M}$_Λ. This yields a definition of the pressure P(v, ε) of $\text{{}\text{L}{}^{\mathrm{o}}{}_{\mathrm{\Lambda }}\text{; Λ → ∞}}$ for given values ε and v of the energy and particle densities. P(v, ε) is shown to be equal to the thermodynamic function p(z, β) derived from the grand canonical ensemble for almost all values of ε and v provided the appropriate equilibrium values of the temperature β^?1 and the chemical potential μ = β^?1 log z are inserted.     

Effects of the velocity dependence of the collision frequency on the Dicke line narrowing

The effect of the velocity (v) dependence of the transport collision frequency ν_trv on the Dicke line narrowing is analyzed in terms of the strong-collision model generalized to velocity-dependent collision frequencies (the so-called kangaroo model). This effect has been found to depend on the mass ratio of the resonance (M) and buffer (M _b) particles, β = M _b/M: it is at a minimum for β ? 1 and reaches a maximum for β ? 3. A power-law particle interaction potential, U(r) ∝ r ^?n , is used as an example to show that, compared to ν_trv (v) = const (n = 4), the line narrows if ν_trv (v) decreases with increasing v (n < 4) and broadens if ν _trv (v) increases with v(n > 4). At β ? 3, the line width can increase [compared to ν_trv (v) = const] by 5 and 12% for the potentials with n = 6 and n ? 10, respectively; for the potentials with n = 1 (Coulomb potential) and n = 3, it can decrease by more than half and 6%, respectively. The line profile I(Ω) has been found to be weakly sensitive to ν_trv (v) at some detuning Ω_c of the radiation frequency Ω. Dicke line narrowing is used as an example to analyze the collisional transport of nonequilibrium in the resonance-particle velocity distribution in a laser field. The transport effect is numerically shown to be weak. This allows simpler approximate one-dimensional quantum kinetic equations to be used instead of the three-dimensional ones to solve spectroscopic problems in which it is important to take into account the velocity dependence of the collision frequency when the phase memory is preserved during collisions.     

Prediction of the one pion exchange contribution to the processπ − p→π − pω with the help of the Veneziano model

The one pion exchange contribution to the differentialπ ^? p→π ^? pω cross-section is calculated assuming that theπ→πω amplitude associated with one of the vertices is described by the Veneziano formula, and that only a trivial dependence of the latter on the mass of the exchanged pion needs to be taken into account. The remaining unknown overall constant is then fixed by considering the decayω→3π. A rough comparison with preliminary data from a 16 GeV/cπ ^? p experiment shows that the one pion exchange model could possibly describe the reactionπ ^? p→π ^? pω forπω masses above 1.4 GeV.     

Temperature derivatives at constant volume of the elastic constants of the alkali halides

Values of dC/dT)_V have been computed from experimental dC/dT)_P and dC/dP)_T for the three elastic constants (expressed as $\text{B}{}_{\mathrm{T}}\text{, C}{}_{44}\text{and}\text{(C}{}_{11}\text{?C}{}_{12}\text{)}\text{2)}$ of each of the 16 Li, Na, K, and Rb halides. The dC/dT)_V measure the explicit dependence of C on T, the effect of thermal expansion having been removed. The dC/dT)_V are all small (compared with dC/dT)_P), are all negative, and vary quite systematically and smoothly with anion, with cation and with the three elastic constants. Negative dB_T/dT)_V is accounted for both thermodynamically and by available lattice dynamical calculations. dC/dT)_V for shear constant is expressed in terms of two vibrational mode parameters, whose values can then be estimated from the observed value, and the trend of dC/dT)_V with Debye temperature.     

New measurements of the radiative decay modes of the φ-meson

The radiative decay models of the φ-meson have been studied: e⁺e^?→φ→ηγ→3γ; e⁺e^?→φ→π^oγ→3γ. Cross sections σ_{φ→ηγ→3γ} and σ_{φ→π^oγ→3γ} have been measured at five energies in the φ-meson energy region and clearly show the φ-resonance in the ηγ → 3γ mode as well as in the π^oγ → 3γ mode. From a Breit-Wigner fit to the experimental data the values of the branching ratios are deduced: B_φ→ηγ = (1.5 ± 0.4) × 10^?2; B_φ→π^oγ = (1.4 ± 0.5) × 10^?3.     

Main channels of the decay of the giant dipole resonance in the 20,22Ne nuclei and isospin splitting of the giant dipole resonance in the 22Ne nucleus

Data published in the literature on various photonuclear reactions for the ^20,22Ne isotopes and for their natural mixture are analyzed with the aim of exploring special features of the decay of giant-dipole-resonance states in these two isotopes. With the aid of data on the abundances of the isotopes and on the energy reaction thresholds, the cross sections for the reactions ^20,22Ne[(γ, n)+(γ, np)] and ^20,22Ne[(γ, p)+(γ, np)] are broken down into the contributions from the one-nucleon reactions (γ, n) and (γ, p) and the contributions from the reactions (γ, np). The cross sections for the reactions ^20,22Ne(γ, n)^19,21Ne and ^20,22Ne(γ, p)^19,21F in the energy range E _γ=16.0–28.0 MeV and the cross sections for the reactions ^20,22Ne(γ, np)^18,20F in the energy range E _γ=23.3–28.0 MeV are estimated. The behavior of the cross-section ratio r=σ(γ, p)/σ(γ, n) for the ²²Ne nucleus as a function of energy is analyzed, and the isospin components of the giant dipole resonance in the ²²Ne nucleus are identified. The contributions of the isospin components of the giant dipole resonance in the ²²Ne nucleus to the cross sections for various photonuclear reactions are determined on the basis of an analysis of the diagram of the excitation and decay of pure isospin states in the ²²Ne nucleus and in nuclei neighboring it, which are members of the corresponding isospin multiplets. The isospin splitting of the giant dipole resonance and the ratio of the intensities of the isospin components are determined to be ΔE=4.57±0.69 MeV and R=0.24±0.04, respectively.     

Small Values of the Maximum for the Integral of Fractional Brownian Motion

We consider the integral of fractional Brownian motion (IFBM) and its functionals ξ _T on the intervals (0,T) and (?T,T) of the following types: the maximum M _T , the position of the maximum, the occupation time above zero etc. We show how the asymptotics of P(ξ _T <1)=p _T ,T→∞, is related to the Hausdorff dimension of Lagrangian regular points for the inviscid Burgers equation with FBM initial velocity. We produce computational evidence in favor of a power asymptotics for p _T . The data do not reject the hypothesis that the exponent θ of the power law is related to the similarity parameter H of fractional Brownian motion as follows: θ=?(1?H) for the interval (?T,T) and θ=?H(1?H) for (0,T). The point 0 is special in that IFBM and its derivative both vanish there.     

Investigation of the angular dependence of the analyzing powers in the deuteron-proton elastic scattering at the nuclotron

New polarimeter based on the asymmetry measurement in dp-elastic scattering has been constructed at internal target at Nuclotron (JINR). The result on the deuteron analyzing powers A _y , A _yy and A _xx in the deuteron-proton (dp) elastic scattering at the energies of 880 and 2000 MeV are presented. They are compared with different theoretical approaches.     

On the Determination of the Equilibrium Structure of the PH3 Molecule

Values of the r_e and α_e equilibrium structural parameters of the PH₃ molecule have been determined on the basis of experimental data on the fundamental bands of the PH₂D and PHD₂ species only, without any knowledge of the force-constant-type parameters of the PH₃ molecule. The functions of the equilibrium rotational parameters A^e, B^e, and C^e have been determined. These functions are totally independent of the values of any resonance interaction parameters. Then these functions have been used to determine r_e and α_e constants. The obtained values r_e=(1.416 776±0.000 164) Å and α_e=(93.56±0.29)° differ a little from those found in the earlier literature.