Hyperfine Interaction of 140Ce(←140La) in CaB6

A ¹⁴⁰La(I ^π=3⁻, T _1/2=40.3 h)-doped layer has been produced in CaB₆ by means of radioactive isotope (RI) beam technique: ¹⁴⁰Cs(I ^π=1⁻, T _1/2=63.7 s) was implanted into CaB₆ and the radioactive equilibrium of ¹⁴⁰Ba–¹⁴⁰La was achieved. The concentration of La in CaB₆ was La/Ca ∼0.001. Obtained TDPAC spectra of the 2083 keV level of ¹⁴⁰Ce (I ^π=4⁺, T _1/2=3.4 ns, μ=+4.35±0.10 μ _N ) followed by the β decay of ¹⁴⁰La showed the existence of hyperfine magnetic fields: B _hyp=−15.0±0.5 T and −1.00±0.15 T. This revised version was published online in September 2006 with corrections to the Cover Date.     

Thomae Formula for General Cyclic Covers of $${{\mathbb {CP}}^1}$$

Let X be a general cyclic cover of \mathbbCP¹{\mathbb{CP}^{1}} ramified at m points, λ₁... λ _m . we define a class of non-positive divisors on X of degree g −1 supported in the pre images of the branch points on X, such that the Riemann theta function does not vanish on their image in J(X). We generalize the results of Bershadsky and Radul (Commun Math Phys 116:689–700, 1988), Nakayashiki (Publ Res Inst Math Sci 33(6):987–1015, 1997) and Enolskii and Grava (Lett Math Phys 76(2–3):187–214, 2006) and prove that up to a certain determinant of the non-standard periods of X, the value of the Riemann theta function at these divisors raised to a high enough power is a polynomial in the branch point of the curve X. Our approach is based on a refinement of Accola’s results for 3 cyclic sheeted cover (Accola, in Trans Am Math Soc 283:423–449, 1984) and a generalization of Nakayashiki’s approach explained in Nakayashiki (Publ Res Inst Math Sci 33(6):987–1015, 1997) for general cyclic covers.     

Integrability ofSU(N) spin chains with elliptic exchange

For some one-parameter setH _N of linear combinations ofN(N−1)/2 elementary transpositions {P _jk} (1≤j<k≤N) at arbitrary naturalN≥3 one can construct a variety {I _m} (3≤m≤N) of operators which commute withH _N. Being applied toSU(n) spin representations of the permutation group, this proves the integrability of 1D periodic spin chains with elliptic short-range interaction. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

Non-steady-state photo-EMF in nanostructured GaN and polypyrrole within porous matrices

We report an experimental investigation of the non-steady-state photoelectromotive force in nanostructured GaN within porous glass and polypyrrole within chrysotile asbestos. The samples are illuminated by an oscillating interference pattern created by two coherent light beams and the alternating current is detected as a response of the material. Dependences of the signal amplitude versus temporal and spatial frequencies, light intensity, and temperature are studied for two wavelengths λ=442 and 532 nm. The conductivity of the GaN composite is measured: σ=(1.1–1.6)×10⁻¹⁰ Ω⁻¹ cm⁻¹ (λ=442 nm, I ₀=0.045–0.19 W/cm², T=293 K) and σ=(3.5–4.6)×10⁻¹⁰ Ω⁻¹ cm⁻¹ (λ=532 nm, I ₀=2.3 W/cm², T=249–388 K). The diffusion length of photocarriers in polypyrrole nanowires is also estimated: L _D=0.18 μm.     

Holographic Dark Energy in Brans-Dicke Cosmology with Granda-Oliveros Cut-off

Motivated by the recent works of one of us (Karami and Fehri, Int. J. Theor. Phys. 49:1118, 2010; Phys. Lett. B 684:61, 2010), we study the holographic dark energy in Brans-Dicke gravity with the Granda-Oliveros cut-off proposed recently in literature. We find out that when the present model is combined with Brans-Dicke field the transition from normal state where w _D >−1 to the phantom regime where w _D <−1 for the equation of state of dark energy can be more easily achieved for than when resort to the Einstein field equations is made. Furthermore, the phantom crossing is more easily achieved when the matter and the holographic dark energy undergo an exotic interaction. We also calculate some relevant cosmological parameters and their evolution.     

One Dimensional Behavior of Singular N Dimensional Solutions of Semilinear Heat Equations

We consider u(x,t) a solution of u _t =Δu+|u| ^{p − 1} u that blows up at time T, where u:ℝ ^N ×[0, T)→ℝ, p>1, (N−2)p<N+2 and either u(0)≥ 0 or (3N−4)p<3N+8. We are concerned with the behavior of the solution near a non isolated blow-up point, as T−t→ 0. Under a non-degeneracy condition and assuming that the blow-up set is locally continuous and N−1 dimensional, we escape logarithmic scales of the variable T−t and give a sharper expansion of the solution with the much smaller error term (T−t)^{1, 1/2−η} for any η>0. In particular, if in addition p>3, then the solution is very close to a superposition of one dimensional solutions as functions of the distance to the blow-up set. Finally, we prove that the mere hypothesis that the blow-up set is continuous implies that it is C ^{1, 1/2−η} for any η>0. Received: 20 June 2001 / Accepted: 6 October 2001     

D-dimensional massless particle with extended gauge invariance

We propose the model ofD-dimensional massless particle whose Lagrangian is given by theN-th extrinsic curvature of world-line. The system hasN+1 gauge degrees of freedom constitutingW-like algebra; the classical trajectories of the model are space-like curves which obey the conditionsk _N+a=k_N−a, k_2N =0,a=1, ...,N−1,N≤[(D−2)/2], while the firstN curvaturesk _i remain arbitrary. We show that the model admits consistent formulation on the anti-DeSitter space. The solutions of the system are the massless irreducible representations of Poincaré group withN nonzero helicities, which are equal to each other. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

Absolute cross sections of electron attachment to molecular clusters. Part II: Formation of (H2O) N? , (N2O) N? , and (N2) N?

Absolute cross sections σ⁻(E, N) of electron attachment to clusters (H₂O) _N , (N₂O) _N , and (N₂) _N for varying electron energy E and cluster size N are measured by using crossed electron and cluster beams in a vacuum. Continua of σ⁻(E) are found that correlate well with the functions of electron impact excitation of molecules’ internal degrees of freedom. The electron is attached through its solvation in a cluster. In the formation of (H₂O) _N ⁻ , (N₂O) _N ⁻ , and (N₂) _N ⁻ , the curves σ⁻(N) have a well-defined threshold because of a rise in the electron thermalization and solvation probability with N. For (H₂O)₉₀₀, (N₂O)₃₅₀, and (N₂)₂₆₀ clusters at E = 0.2 eV, the energy losses by the slow electron in the cluster are estimated as 3.0 × 10⁷, 2.7 × 10⁷, and 6.0 × 10⁵ eV/m, respectively. It is found that the growth of σ⁻ with N is the fastest for (H₂O) _N and (N₂) _N clusters at E → 0 as a result of polarization capture of the s-electron. Specifically, at E = 0.1 eV and N = 260, σ⁻ = 3.0 × 10⁻¹³ cm² for H₂O clusters, 8.0 × 10⁻¹⁴ cm² for N₂O clusters, and 1.4 × 10⁻¹⁵ cm² for N₂ clusters; at E = 11 eV, σ⁻ = 9.0 × 10⁻¹⁶ cm² for (H₂O)₂₀₀ clusters, 2.4 × 10⁻¹⁴ cm² for (N₂O)₃₅₀ clusters, and 5.0 × 10⁻¹⁷ cm² for (N₂)₂₆₀ clusters; finally, at E = 30 eV, σ⁻ = 3.6 × 10⁻¹⁷ cm² for (N₂O)₁₀ clusters and 3.0 × 10⁻¹⁷ cm² for (N₂)₁₂₅ clusters. Original Russian Text ? A.A. Vostrikov, D.Yu. Dubov, 2006, published in Zhurnal Tekhnicheskoĭ Fiziki, 2006, Vol. 76, No. 12, pp. 1–15.     

Formation and quenching mechanisms of excited particles in an oxygen-iodine laser medium

New values of a number of kinetic constants of processes proceeding in oxygen-iodine laser media are presented. The total probabilities of formation of I₂(X, 15 ≤ v ≤ 24) and I₂(X, 25 ≤ v ≤ 47) molecules in the course of quenching of I* atoms by I₂(X) are found to be 0.9 and 0.1, respectively. The quantum yield of singlet oxygen in the reaction O(¹ D) + N₂O → N₂ + O₂(a ¹Δ) is close to 100%. The quenching rate constants of I₂(A’) by O₂, H₂O, CO₂, I₂, and Ar and of I(² P _1/2) by O(³ P), O₃, NO₂, N₂O₄, and N₂O are presented.     

Metastability and Low Lying Spectra¶in Reversible Markov Chains

We study a large class of reversible Markov chains with discrete state space and transition matrix P _N . We define the notion of a set of metastable points as a subset of the state space Γ _N such that (i) this set is reached from any point x∈Γ _N without return to x with probability at least b _N , while (ii) for any two points x, y in the metastable set, the probability T ^{− 1} _{x , y} to reach y from x without return to x is smaller than a _{N − 1}< b _N . Under some additional non-degeneracy assumption, we show that in such a situation: (i) To each metastable point corresponds a metastable state, whose mean exit time can be computed precisely. (ii) To each metastable point corresponds one simple eigenvalue of 1 −P _N which is essentially equal to the inverse mean exit time from this state. Moreover, these results imply very sharp uniform control of the deviation of the probability distribution of metastable exit times from the exponential distribution. Received: 1 August 2000 / Accepted: 19 November 2001     

LSP spectral changes correlating with SERS activation and quenching for R6G on immobilized Ag nanoparticles

In terms of chemical enhancement in Surface Enhanced Raman Scattering (SERS), we investigated the effect of halide and other anions to rhodamine 6G (R6G) adsorbed Ag particles that were immobilized on the substrates. The residual species on chemically prepared Ag particles such as citrate or a-carbon were thoroughly substituted by various anions, e.g., Cl⁻, Br⁻, I⁻, SCN⁻, CN⁻, or S₂O₃ ²⁻ anions, whose adsorption features are elucidated by the formation constants for AgX₂ ^(m−1)−, here X denotes the above anions. In particular, Cl⁻, Br⁻, or SCN⁻ ions activated SERS of R6G via intrinsic electronic interaction with Ag, whereas CN⁻, S₂O₃ ²⁻, or I⁻ anions quenched it due to their exclusive adsorption onto the Ag surfaces. We found that the activation process with the anions commonly yields a marked blue-shift of the coupled plasmon peak from ca. 650–700 to 500–550 nm in elastic scattering. It is rationalized by slight increase of the gap size between adjacent Ag nanoparticles by only ca. 1 nm based on theoretical simulations. This is probably caused by slight dissolution, oxidative etching, of the particles according to large formation constants of the complexes. Consequently, partly remaining negative charges on the Ag surface, and a slight increase in the gap size, providing huge electric field, facilitated R6G cations to adsorb on the nanoparticles, especially at the junction.     

Overall values of conventional discrepancy indices for crystals with heavy atoms. Part II. Results for monoclinic and orthorhombic crystals when the heavy-atom part alone constitutes the model

Theoretical expressions of 〈y _N〉, 〈|y _N − σ₁ y _P ^c |〉 and 〈|y _N ² −σ ₁ ² (y _P ^c )²|〉 (wherey _N andy _P ^c are the normalized structure amplitudes of the structure and the model respectively) are derived in terms of the heavy atom contributionσ ₁ ² for monoclinic and orthorhombic crystals containing a few (i.e., 1 or 2) heavy atoms of the same kind per asymmetric unit by taking the heavy atom part alone as the model. Results are obtained for both the related and unrelated cases. The local values of 〈y _N〉 and 〈|y _N ⁿ − σ ₁ ⁿ (y _P ^c ) ⁿ |〉, (n=1, 2) calculated from these expressions can be used to calculate the overall values of the conventionalR-indicesR(F) andR(I) for the related and unrelated cases. These overall values could be used to check the correctness of heavy atoms located in the structure. Contribution No. 550     

Hyperfine Interactions of N Isotopes in TiO2 and Quadrupole Moment of 16N

Hyperfine interactions of ^12,14N in BN(hexagonal) crystal were studied by detecting β-NQR(¹²N) and FT-NMR(¹⁴N). A β-NMR of ¹⁶N (I ^π=2⁻,T _1/2=7.13 s) in MgO crystal was detected to determine the magnetic moment of ¹⁶N to be |μ(¹⁶N:2⁻)|=(1.986±0.001)μ_N. Also, the β-NQR of ^12,16N in TiO₂ crystal were detected to determine |Q(¹⁶N:2⁻)|=(17.9±1.7) mb. An abnormally small effective charge for neutrons is required to account for |Q(¹⁶N:2⁻)|. This revised version was published online in September 2006 with corrections to the Cover Date.     

Characteristic features of the photoconductivity and spin conversion of electron-hole pairs in doped amorphous molecular semiconductors in the dye absorption region

The photoconductivity of doped poly-N-epoxypropylcarbazole films in the absorption region of a cationic polymethine dye is observed to increase when the BF ₄ ⁻ ion is replaced by Cl⁻ and I⁻. The effect of a magnetic field on the photoluminescence is investigated at room temperature. The photoconductivity is studied as a function of the electric field intensity and wavelength of light. The dependence of the photoconductivity on the nature of the anion can be explained by a change in the probability of intercombination conversion in ionic and electron-hole pairs. Fiz. Tverd. Tela (St. Petersburg) 41, 44–48 (January 1999)     

Exact Analytical Solution of the Schrödinger Equation for an N-Identical Body-Force System

A mathematical method is presented for solving the Schr?dinger equation for a system of identical body forces. The N-body forces are more easily introduced and treated within the hyperspherical harmonics. The problem of the N-body potential has been used at the level of both classical and quantum mechanics. The hypercentral interacting potential is assumed to depend on the hyperradius x = (ξ₁² + ξ₂² + ⋯ + ξ_N−1²)^1/2 only, where ξ₁,ξ₂,…,ξ_N−1 are Jacobi relative coordinates which are functions of N-particle relative positions r₁₂,r₂₃,…,r_N1. The problem of the harmonic oscillator and the Coulomb-type potential has been widely studied in different contexts. Using the N-body potential V(x) = ax² + bx − (c/x) as an example, and assuming an ansatz for the eigenfunction, an exact analytical solution of the Schr?dinger equation for an N-body system in three dimensions is obtained. This method is also applicable to some other types of potentials for N-identical interacting particles.     

Rational Design of Novel Benzimidazole-Based Sensor Molecules that Display Positive and Negative Fluorescence Responses to Anions

Two novel and neutral benzimidazole derivatives-based anion receptors bearing a 1,10-phenanthroline fluorophore, N,N′-di-(2′-benzimidazolyl-methylene)-1, 10-phenanthroline-2,9-diamide (1) and N,N′-di-[2′-(benzimidazolyl-2′-) ethyl-]-1,10-phenanthroline-2,9-diamide (2), which exhibited turn-on and turn-off fluorescence responses to various anions, were rationally designed and synthesized and their fluorescent response toward anions was investigated in DMSO solution. In the process of anions binding, there were two different fluorescent responses in presence of anions: a quenching of the fluorescence emission for F^- and AcO^- and an enhancement of the fluorescence emission for Cl⁻, Br⁻ and I⁻. Two different luminescent mechanisms of the receptors 1 and 2 resulting from various anions were exploited to rationalize quenching and enhancement of the fluorescence emission: a photo-induced electronic transfer mechanism (PET) and the increase of the rigidity of the host molecules, respectively. In particular, chloride could be recognized selectively from the anions tested according to changes of fluorescence spectrum. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Josephson and single-particle currents between partially dielectricized superconductors with charge-density waves

The amplitudes of the nonstationary Josephson current I ¹, the interference current I ², and the quasiparticle current J through symmetric and asymmetric tunnel junctions, including superconductors with charge density waves, are calculated. In the symmetric (s) case the dependence of the Josephson current I _s ¹ on the voltage V on the junction has a logarithmic singularity at |eV|=2Δ, Δ+D, and 2D, where , Δ and Σ are the superconducting and dielectric order parameters, and e is the unit charge. At temperatures T≠0 jumps appear in the current-voltage characteristics I _s ¹ (V) at |eV|=D−Δ. Jumps and singularities are observed in the currents I _s ² and J _s at the same voltages at which singularities and jumps appear in I _s ¹ , respectively. In the nonsymmetric (ns) junctions which include an ordinary superconductor, singularities and jumps occur at |eV|=D+Δ_BCS, Δ+Δ_BCS, and (for T≠0) |D−Δ_BCS| and |Δ−Δ_BCS|, where Δ_BCS is the order parameter of an ordinary superconductor. The quasiparticle current J _ns is an asymmetric function of the voltage V and does not depend on the sign of Σ. The results are compared with experiment. Fiz. Tverd. Tela (St. Petersburg) 39, 991–999 (June 1997)     

Focal switch of cosine-Gaussian beams

The focal switch of cosine-Gaussian (CsG) beams passing through a system with the aperture and lens separated is studied analytically and numerically. It is shown that the focal switch of CsG beams can appear not only for the apertured case, but also for the unapertured case. The necessary condition for the focal switch is that truncation parameter α > α_c and the beam parameter β > β_c, α_c, β_c being the corresponding critical values. There exists a maximum of the relative transition height Δz _sw as α varies, and Δz _sw increases with increasing β and decreasing N _w. The normalized axial intensity minimum I _min / I _max decreases with an increase of α and β, and I _min / I _max remains unchanged as N _w varies.     

Entropic Repulsion for the High Dimensional Gaussian Lattice Field Between Two Walls

The main aim of this paper is to discuss the entropic repulsion of random interfaces between two hard walls. We consider the d (≥ 3)-dimensional Gaussian lattice field on ℝ^λ _N , λ _N = [−N, N] ^d ∩ ℤ ^d and identify the repulsion of the field as N → ∞ under the condition that the field lies between two hard walls at the height level 0 and L in Λ _N where L is large enough but finite. We also study the same problem for two layered interfaces case.     

KNΛ and KNΣ coupling constants from the Chiral Bag Model

The KNΛ and KNΣ coupling constants have been calculated in the framework of the Chiral Bag Model(CBM). We find −3.88 ≤g _KNΛ≤−3.67 and 1.15 ≤g _KNΣ≤ 1.24 by taking into account pseudoscalar mesons (π, K) and vector mesons (ρ, ω, K ^*) field effects. Particularly, it is shown that vector mesons make significant contributions to the coupling constants g _KNΛ and g _KNΣ. Our values are existing within the experimental limits compared to the phenomenological values extracted from the kaon photoproduction and kaon-nucleon scattering experiments. Also, form factors are suggested for the πNN, πNΔ, KNΛ and KNΣ couplings. Received: 17 August 1998 / Revised version: 22 December 1998