How accurate is the cancelation of the first even zonal harmonic of the geopotential in the present and future LAGEOS-based Lense-Thirring tests?

The strategy followed so far in the performed or proposed tests of the general relativistic Lense-Thirring effect in the gravitational field of the Earth with laser-ranged satellites of LAGEOS type relies upon the cancelation of the disturbing huge precessions induced by the first even zonal harmonic coefficient J ₂ of the multipolar expansion of the Newtonian part of the terrestrial gravitational potential by means of suitably designed linear combinations of the nodes Ω of more than one spacecraft. Actually, such a removal does depend on the accuracy with which the coefficients of the combinations adopted can be realistically known. Uncertainties of the order of 2 cm in the semimajor axes a and 0.5 milliarcseconds in the inclinations I of LAGEOS and LAGEOS II, entering the expression of the coefficient c ₁ of the combination of their nodes used so far, yield an uncertainty δc ₁ = 1.30 × 10⁻⁸. It gives an imperfectly canceled J ₂ signal of 10.8 milliarcseconds per year corresponding to 23% of the Lense-Thirring signature. Uncertainties of the order of 10–30 microarcseconds in the inclinations yield δc ₁ = 7.9 × 10⁻⁹ which corresponds to an uncanceled J ₂ signature of 6.5 milliarcseconds per year, i.e. 14% of the Lense-Thirring signal. Concerning a future LAGEOS-LAGEOS II-LARES combination with coefficients k ₁ and k ₂, the same uncertainties in a and the less accurate uncertainties in I as before yield δk ₁ = 1.1 × 10⁻⁸, δk ₂ = 2 × 10⁻⁹; they imply a residual J ₂ combined precession of 14.7 milliarcseconds per year corresponding to 29% of the Lense-Thirring trend. Uncertainties in the inclinations at ≈ 10 microarcseconds level give δk ₁ = 5 × 10⁻⁹, δk ₂ = 2 × 10⁻⁹; the uncanceled J ₂ effect is 7.9 milliarcseconds per year, i.e. 16% of the relativistic effect.     

On the frequency dependence of the transition temperature in spin glasses

For the first time, the frequency dependence of T_f (temperature of the maximum of the a.c. susceptibility of spin-glasses) is shown to obey a Fulcher law $\text{τ = τ}{}_{\mathrm{o}}\text{exp}\text{[}\text{E}{}_{\mathrm{a}}\text{k(}\text{T}{}_{\mathrm{f}}\text{?}\text{T}{}_{\mathrm{f}}\text{)}\text{]}$. This is observed as well in the case of dilute alloys (or R.K.K.Y. spin-glasses : $\text{Cu}$Mn, $\text{Au}$Fe, …) as for frustrated systems (Eu_1?xGd_xS, Eu_xSr_1?xS …). For R.K.K.Y. spin-glasses, only in the case of a very small amplitude, V_o of the R.K.K.Y. interaction, this time dependence approaches an Arrhenius law. In the case of “frustrated” spin-glasses the concentration is the main parameter to determine the kind of frequency dependence of T_f. These properties are evidence for a glass-like phase transition in spin-glasses. The scaling of the frequency dependence of T_f with V_o is justified for R.K.K.Y. spin-glasses from present data.     

Correlations entre defauts ponctuels et proprietes de transport dans PbF2 dope

The investigation of the transport properties of the Pb_1−xM²⁺ⁿ_xF_2+nx(n = 1,2) solid solutions shows a maximum of the activation energy ΔE_max associated to a minimum of the conductivity for a very small value of x : x_min. (x_min. ≅ 0.01 for n = 1; x_,in ≅ 0.005 for n = 2). The value of ΔE_max. depends closely on the nature of the substituting cation. Correlations have been established between the transport properties and the nature of the point defects which are supposed to occur in the considered composition range (nn or innn pairs) by analogy with similar alkali-earth fluorides. The size difference Δr between host and substitutional cations seems to play an essential role. The evolution of ΔE_max. and the preferential stability of the nn or nnn pairs is discussed as a function of Δr.     

The structure of mixed fluorides Ca1?xSrxF2 and Sr1?xBaxF2 and the luminescence of Eu2+ in these crystals

The structure of the mixed fluorites Ca_1−x Sr_xF₂ and Sr_1−x Ba_xF₂, as well as the structure of the Eu²⁺ impurity center in these crystals, is calculated within the framework of the virtual-crystal method realized in the shell model and pair-potential approximation. The phenomenological dependence of the position of the lower level of the 4f ⁶5d configuration of the Eu²⁺ ion on distance to the Eu²⁺-ligand is derived. The dependences of the Stokes shift and the Huang-Rhys factor on x are calculated for the yellow luminescence in Sr_1−x Ba_xF₂:Eu²⁺. The value of x at which the lower level of the 4f ⁶5d configuration of the Eu²⁺ ion in Sr_1−x Ba_xF₂:Eu²⁺ falls within the conduction band is found. __________ Translated from Fizika Tverdogo Tela, Vol. 45, No. 5, 2003, pp. 823–826. Original Russian Text Copyright ? 2003 by Nikiforov, Zakharov, Chernyshev, Ugryumov, Kotomanov.     

Nonlinear dynamics of vortices pinned to unidirectional twins

The nonlinear resistive properties of superconductors in the mixed state in the presence of a system of unidirectional planar defects (twins) have been investigated theoretically within the framework of the two-dimensional stochastic model of anisotropic pinning based on the Fokker-Planck equations with a concrete form of the pinning potential. These equations allow one to obtain an exact analytical solution of the problem. Formulas are obtained for experimentally observable even and odd (relative to reversal of the direction of the external magnetic field) nonlinear longitudinal and transverse magnetoresistivities ρ _‖,⊥ ^± ( j,t,α,ε) as functions of the transport current density j, temperature t, the angle α between the directions of the current and the twins, and the relative volume fraction ε occupied by the twins. In light of the great variety of types of nonlinear resistive dependences contained in these expressions for ρ _‖,⊥ ^± the most characteristic of them are presented in the form of graphs with commentary. The desired nonlinear dependences ρ _‖,⊥ ^± are linear combinations of the even and odd parts of the function v(j,t, α,ε), which has the sense of the probability of overcoming the potential barrier of the twins; this makes it possible to give a simple physical treatment of the nonlinear regimes. New scaling relations for the Hall conductivity are obtained and investigated which differ from the previously known relations for isotropic pinning. The interaction of vortex motion directed along the twins and the Hall effect is considered for Hall constants which are arbitrary in magnitude and sign, and it is shown that in the case of small Hall viscosity vortex motion directed along the twins has an effect on the odd magnetoresistivities ρ _‖ ⁻ and ρ _⊥ ⁻ , whereas the reverse effect can be neglected. It is shown that pinning anisotropy is sufficient to manifest the new nonlinear (in the current) magnetoresistivities ρ _⊥ ⁺ and ρ _‖ ⁻ . Zh. éksp. Teor. Fiz. 116, 2103–2129 (December 1999)     

Low temperature optical study of Gadolinium molybdate and influence of an external magnetic field

We describe the optical absorption spectrum of a single crystal of Gadolinium Molybdata (GMO) at the temperature of liquid helium. We observe a set of sharp lines in the near ultra violet region; we clasify the lines into three groups A, B, and C. We study the positions of the lines as functions of the orientation of the crystal relative to the polarization of the incident light and we investigate the Zeeman effect on the lines of the groups A and B. We suggest that the observed lines of all three groups are due to transitions between the ground ${}^8\text{S}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ state and the excited ${}^6\text{P}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$, ${}^6\text{P}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ and ${}^6\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ states of the Gd³⁺ ion in the crystal.     

Symmetry enforced gauge invariance of nuclear magnetic shielding constants

E.S.R. experiments performed at 1·3 K by optical detection are reported for the photo-excited triplet state of palladiumporphin in a single crystal of n-octane, and the observation of a level anticrossing signal is described.

In the crystal the orbital degeneracy of the ³ E _u state of the free molecule is lifted by the crystal field and in n-octane the energy difference between the two orbital components |x> and |y> is found to be 58 ± 2 cm^-1. The spinorbit coupling (SOC) and the orbital Zeeman interaction couple the triplet manifolds of |x> and |y>, and for a proper understanding of the magnetic properties of these states it is necessary to work in the basis of the six spin-orbit functions deriving from the ³ E _u state of the free molecule. It is shown that either of the two triplet states can be described by an effective spin hamiltonian of the common form and expressions for the zero-field parameters D and E and the principal values of the g tensor are given. The experimental values of the parameters in the lowest triplet state are D = -24·38 ± 0·03 GHz, |E| = 320 ± 60 MHz, g _‖ = 1·677 ± 0·001 and g _⊥ = 1·989 ± 0·002. The matrix element of the SOC connecting the |x> and |y> triplet manifolds amounts to qZ = 15 ± 3 cm^-1 and the vibronic orbital angular momentum (in units of ?) in the ³ E _u state of the free molecule to qΛ = 1·5 ± 0·3. A tentative value of 0·63 for the orbital reduction factor q is obtained by comparison with a theoretical estimate of Λ. The value of q is indicative of weak Jahn-Teller coupling.     

Jeans-Buneman instability in a dusty plasma

A self consistent formulation of the Jeans instability of a dusty plasma with proper inclusion of charge dynamics is described. It is shown that charge fluctuations significantly affect the Jeans as well as the Buneman mode. For plasma particles (electrons and ions) in local thermal equilibrium, the Jeans lengthλ _J is given byλ _J≈λ _g F(R, ε, β/η), whereλ _g is the Debye length of the charged grains,R is the square of the ratio of the Jeans to the plasma frequency of the grains,ε is the square of the ratio of the Debye length of the grains and the plasma particles andβ/η is the ratio of the attachment to the decay frequency of the electronic charges to the grain surface. The functional form ofF is given in the text. Numerical investigation of the Jeans-Buneman mode for a two and three component plasma shows that the Jeans mode dominates atkλ _D≪1 (wherek is the wave number andλ _D is the Debye length of plasma particles), whereas atkλ _D≫1 only the Buneman mode operates. Charge fluctuations reduce the area of overlap of the two modes. Furthermore, in the absence of gravity, there exists a new, charge fluctuation induced unstable mode in a streaming dusty plasma. Astrophysical applications of the results are discussed.     

Investigation of thermal expansion,phase diagrams,and barocaloric effect in the (NH4)2WO2F4 and (NH4)2MoO2F4 oxyfluorides

The thermal expansion along the principal crystallographic axes of the (NH₄)₂WO₂F₄ and (NH₄)₂MoO₂F₄ oxyfluorides has been studied. The anomalous behavior of α _i (T) due to the phase transitions has been revealed at T ₁ = 271.4 K and T ₂ ≈ 180 K for the molybdate and at T ₁ = 201.5 K and T ₂ ≈ 161 K for the tungstate. The quantities dT/dp and dT/dσ _i , which characterize the dependence of the phase transition temperatures on the hydrostatic and uniaxial pressures, have been determined from analyzing the results of studies of the thermal expansion and heat capacity with the use of the Pippard relations. The p-T and α _i -T phase diagrams reflect different characters of the influence of the pressure on the stability of the initial and distorted phases of the oxyfluorides. The magnitudes of the extensive and intensive barocaloric effects determined in the vicinity of the structural phase transitions are as follows: ΔS _BCE varies from approximately −10 to −17 J/mol K and ΔT _AD ≈ 8−17 K for the molybdate and ΔS _BCE varies from approximately −10 to −17 J/mol K and ΔT _AD ≈ 8−13 K for the tungstate.     

Construction of the Incipient Infinite Cluster for Spread-out Oriented Percolation Above 4 + 1 Dimensions

 We construct the incipient infinite cluster measure (IIC) for sufficiently spread-out oriented percolation on ℤ ^d × ℤ₊, for d +1 > 4+1. We consider two different constructions. For the first construction, we define ℙ ⁿ (E) by taking the probability of the intersection of an event E with the event that the origin is connected to (x,n)  ℤ ^d × ℤ₊, summing this probability over x  ℤ ^d , and normalising the sum to get a probability measure. We let n → ∞ and prove existence of a limiting measure ℙ_∞, the IIC. For the second construction, we condition the connected cluster of the origin in critical oriented percolation to survive to time n, and let n → ∞. Under the assumption that the critical survival probability is asymptotic to a multiple of n ⁻¹, we prove existence of a limiting measure ℚ_∞, with ℚ_∞ = ℙ_∞. In addition, we study the asymptotic behaviour of the size of the level set of the cluster of the origin, and the dimension of the cluster of the origin, under ℙ_∞. Our methods involve minor extensions of the lace expansion methods used in a previous paper to relate critical oriented percolation to super-Brownian motion, for d+1 > 4+1. Received: 13 December 2001 / Accepted: 11 July 2002 Published online: 29 October 2002 RID="*" ID="*" Present address: Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. E-mail: rhofstad@win.tue.nl     

Beam quality of radial Gaussian Schell-model array beams

Taking the Rayleigh range z_R and the M²-factor as the characteristic parameters of beam quality, the beam quality of radial Gaussian Schell-model (GSM) array beams is studied. The analytical expressions for the z_R and the M²-factor of radial GSM array beams are derived. It is shown that for the superposition of the cross-spectral density function z_R is longer and the M²-factor is lower than that for the superposition of the intensity. For the two types of superposition, z_R increases and the M²-factor decreases with increase in beam coherence parameter, and both z_R and the M²-factor increase with increase in inverse radial fill-factor. For the superposition of the cross-spectral density function, z_R increases and the M²-factor decreases with increase in beam number, while for the superposition of the intensity both the z_R and M²-factor are independent of the beam number.     

Spin transistor and quantum spin Hall-effects in CdBxF2−x–p-CdF2–CdBxF2−x sandwich nanostructures

Planar CdB_xF_2−x–p-CdF₂–CdB_xF_2−x sandwich nanostructures prepared on the surface of the n-type CdF₂ bulk crystal are studied to register the spin transistor and quantum spin Hall-effects. The current–voltage characteristics of the ultra-shallow p⁺–n junctions verify the CdF₂ gap, 7.8 eV, and the quantum subbands of the 2D holes in the p-type CdF₂ quantum well confined by the CdB_xF_2−xδ-barriers. The temperature and magnetic field dependencies of the resistance, specific heat and magnetic susceptibility demonstrate the high temperature superconductor properties for the CdB_xF_2−xδ-barriers. The value of the superconductor energy gap, 2Δ = 102.06 meV, determined by the tunneling spectroscopy method appears to be in a good agreement with the relationship between the zero-resistance supercurrent in superconductor state and the conductance in normal state, πΔ/e, at the energies of the 2D hole subbands. The results obtained are evidence of the important role of the multiple Andreev reflections in the creation of the high spin polarization of the 2D holes in the edged channels of the sandwich device. The high spin hole polarization in the edged channels is shown to identify the mechanism of the spin transistor and quantum spin Hall-effects induced by varying the top gate voltage, which is revealed by the first observation of the Hall quantum conductance staircase.     

The a-type rotational spectrum of isocyanic acid,HNCO, in the excited bending states

Rotational transitions of HNCO in the v₄ = 1, v₅ = 1, and v₆ = 1 vibrational states have been measured. The assignment of the a-type ^qR_K and ^qQ₁ branches has been made with the help of a qualitative discussion of the vibration-rotation interactions. Effective rotational and centrifugal distortion constants have been determined precisely for each vibrational K_a-rotational state, up to K_a = 4 for the lowest excited state and K_a = 3 for the other two excited states. The K_a dependence of the effective rotational constants B and D was observed to be quite anomalous for some of the transitions because of the a-type Coriolis interactions and accidental b-type Coriolis resonances. From a discussion of the selection rules and the effect on B and D of the interactions, the first excited state of the out-of-plane vibration, ν₆, has been assigned definitely to the second lowest excited vibrational state of HNCO.     

S wave of pion-pion scattering from data on the reaction π?p → π0π0n

The results of recent experiments performed at KEK, Brookhaven National Laboratory, the Institute for High-Energy Physics (Protvino), and CERN to study the reaction π ⁻ p → π ⁰ π ⁰ n are analyzed in detail. For S-wave pion-pion scattering in the channel of isospin I=0, new data are obtained for the phase shift δ ₀ ⁰ and the inelasticity parameter η ₀ ⁰ . Difficulties that arise in using, for the amplitudes of the S and D waves of the final π ⁰ π ⁰ system, physical solutions selected on the basis of partial-wave analyses are discussed. It is noteworthy that other solutions are preferable in principle in the region of the invariant mass m of the π ⁰ π ⁰ system above 1 GeV. With the aim of clarifying the situation and further studying the properties of the f ₀(980) resonance, it is proposed to perform, in the reaction π ⁻ p → π ⁰ π ⁰ n, an especially careful examination of the m region in the vicinity of the threshold. __________ Translated from Yadernaya Fizika, Vol. 67, No. 7, 2004, pp. 1380–1391. Original Russian Text Copyright ? 2004 by Achasov, Shestakov.     

On the question of fine structure in νp and EK for 233U and 235U

The question of fine structure in the variation of the average number of prompt neutrons, $\text{ν}{}_{\mathrm{<mtext>p</mtext>}}$, emitted per fission with energy in the neutron fission of ²³³U and ²³⁵U has been examined. Consistent structure has been found in measurements of both $\text{ν}{}_{\mathrm{<mtext>p</mtext>}}\text{and}\text{E}{}_{\mathrm{<mtext>K</mtext>}}$ (the average total fission fragment kinetic energy) for ²³³U. Channel analysis of the neutron fission cross section of ²³³U allows the structure to be calculated quantitatively provided the collective energy at the second hump in the fission barrier is weakly coupled to the nuclear degrees of freedom at scission. A similar calculation for neutron fission of ²³⁵U supports the case for the absence of fine structure in $\text{ν}{}_{\mathrm{<mtext>p</mtext>}}\text{and}\text{E}{}_{\mathrm{<mtext>K</mtext>}}$ for this nucleus.     

Specific features of praseodymium-doping induced changes in the critical temperature and energy spectrum parameters of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> in the presence of calcium ions in the lattice

The results of the experimental study of the specific features of changes in the temperature and concentration dependences of the thermopower coefficient and the critical temperature in the Y_{0.85 − x} Ca_0.15Pr _x Ba₂Cu₃O _y system as the praseodymium content increases are presented. The results obtained have been analyzed based on the narrow band model, the energy spectrum and charge carrier system parameters have been determined, and their behavior with an increase in the doping level has been analyzed. It has been found that both superconducting properties and parameters of the normal state of Y_{0.85 − x} Ca_0.15Pr _x Ba₂Cu₃O _y vary differently in various doping ranges. Based on a comparison of the results obtained with the available data for the case of single doping of YBa₂Cu₃O _y with praseodymium, conclusions have been drawn regarding the mechanism of the energy spectrum modification in the studied compound. The Fermi-level pinning effect has been revealed in the region of a local peak of the density-of-states function, and the energy position of this peak has been determined. It has been shown that the consideration of the Fermi level dynamics caused by the specific features of the structure and transformation of the Y_{0.85 − x} Ca_0.15Pr _x Ba₂Cu₃O _y energy spectrum upon doping makes it possible to explain the observed dependence of the critical temperature on the praseodymium content.     

On electrostatic models of a metal-insulator phase transition in crystalline semiconductors with hydrogen-like impurities

Two well-known models for calculating the critical density N _C of a metal-insulator transition, as a function of the Bohr radius a _H of an isolated impurity as temperature T→0 K, are refined by making allowance for the screening of ions by electrons hopping along impurities. In one model, the transition at N _C1 is explained by the appearance of delocalized electrons as the impurity band is displaced into the allowed-energy band as a result of a decrease in the electron (hole) affinity of ionized impurities. In the other model the transition is explained by an unbounded increase in the static permittivity of the crystal as the density of impurity atoms increases to N _C2. The obtained approximations N _C1 ^1/3 a _H≈0.24 and N _C2 ^1/3 a _H≈0.20 for the degree of compensation K=0.01 describe existing experimental data for 1<a _H<10 nm. Fiz. Tverd. Tela (St. Petersburg) 40, 147–151 (January 1998)     

The Birth of the Infinite Cluster:¶Finite-Size Scaling in Percolation

We address the question of finite-size scaling in percolation by studying bond percolation in a finite box of side length n, both in two and in higher dimensions. In dimension d= 2, we obtain a complete characterization of finite-size scaling. In dimensions d>2, we establish the same results under a set of hypotheses related to so-called scaling and hyperscaling postulates which are widely believed to hold up to d= 6. As a function of the size of the box, we determine the scaling window in which the system behaves critically. We characterize criticality in terms of the scaling of the sizes of the largest clusters in the box: incipient infinite clusters which give rise to the infinite cluster. Within the scaling window, we show that the size of the largest cluster behaves like n ^d π _n , where π _n is the probability at criticality that the origin is connected to the boundary of a box of radius n. We also show that, inside the window, there are typically many clusters of scale n ^d π _n , and hence that “the” incipient infinite cluster is not unique. Below the window, we show that the size of the largest cluster scales like ξ ^d π_ξ log(n/ξ), where ξ is the correlation length, and again, there are many clusters of this scale. Above the window, we show that the size of the largest cluster scales like n ^d P _∞, where P _∞ is the infinite cluster density, and that there is only one cluster of this scale. Our results are finite-dimensional analogues of results on the dominant component of the Erdős–Rényi mean-field random graph model. Received: 6 December 2000 / Accepted: 25 May 2001     

Structure of the superconducting state of superconductors near the critical field Hc2 for values of the Ginzburg-Landau parameter kclose to unity

It is shown that near the transition temperature T _c the coefficients of the second and third terms in the expansion of the free energy in powers of H _c2−B (B is the magnetic field induction inside the superconductor) go to zero simultaneously for a value of κ=1 for the Ginzburg-Landau parameter. Thereby the structure of the mixed state near H _c2 for a value of the parameter κ close to unity is determined by the temperature correction to the coefficient for the third power and the coefficient for the fourth power in the expansion of the free energy in powers of H _c2−B. The values of these coefficients depend on the type of vortex lattice. Zh. éksp. Teor. Fiz. 112, 1499–1509 (October 1997)