Vibrational properties of the F A (Li+) center in alkali halides

Abstract

The on- or off-axis behavior and the vibrational properties of the F _A (Li⁺) center are investigated in several alkali halides by means of polarized resonant Raman scattering. The observed Raman modes are interpreted and classified according to their nature and frequency. A comparison between on- and off-axis systems and between the vibrational modes of the isolated Li⁺ and the F _A (Li⁺) center reveals a displacement of the Li⁺ equilibrium position parallel to the F _A (Li⁺) defect axis and, due to the small impurity size, away from the adjacent F center.     

Braided m-Lie Algebras

Braided m-Lie algebras induced by multiplication are introduced, which generalize Lie algebras, Lie color algebras and quantum Lie algebras. The necessary and sufficient conditions for the braided m-Lie algebras to be strict Jacobi braided Lie algebras are given. Two classes of braided m-Lie algebras are given, which are generalized matrix braided m-Lie algebras and braided m-Lie subalgebras of End _F M, where M is a Yetter–Drinfeld module over B with dimB < . In particular, generalized classical braided m-Lie algebras sl _{q, f} (GM _G (A), F) and osp _{q, t} (GM _G (A), M, F) of generalized matrix algebra GM _G (A) are constructed and their connection with special generalized matrix Lie superalgebra sl _{s, f} (GM _{Z_2}(A ^s ), F) and orthosymplectic generalized matrix Lie super algebra osp _{s, t} (GM _{Z_2}(A ^s ), M ^s , F) are established. The relationship between representations of braided m-Lie algebras and their associated algebras are established.This revised version was published online in March 2005 with corrections to the cover date.     

The Measurements of Photostimulated Luminescence in Alkali Doped BaFBr:Eu2☎ at Liquid Nitrogen Temperature

Considerable increase of the photostimulated luminescence (PSL) intensity and red shift of the excitation spectrum was obtained by alkali doping of BaFBr:Eu^2? crystals [1]. The band of the F_A(Br^?) centers about 0.1 eV shifted to low energy side against the “normal” F(Br^?) centers. The F_A(Br^?) centers are destroyed after heating to 330 K.     

Construction of Fredholm representations and a modification of the Higson-Roe corona

The Fredholm representation theory is well adapted to the construction of homotopy invariants of non-simply-connected manifolds by means of the generalized Hirzebruch formula [σ(M)] = 〈L(M)ch _A f*ξ, [M]〉 ∈ K _A ⁰(pt) ⊗ Q, where A = C*[π] is the C*-algebra of the group π, π = π ₁(M). The bundle ξ ∈ K _A ⁰(Bπ) is the canonical A-bundle generated by the natural representation π → A. Recently, the first author constructed a natural family of Fredholm representations that lead to a symmetric vector bundle on the completion of the fundamental group with a modification of the Higson-Roe corona, provided that the completion is a closed manifold.     

Reichenbach's common cause principle and quantum field theory

Reichenbach's principles of a probabilistic common cause of probabilistic correlations is formulated in terms of relativistic quantum field theory, and the problem is raised whether correlations in relativistic quantum field theory between events represented by projections in local observable algebrasA(V₁) andA(V₂) pertaining to spacelike separated spacetime regions V₁ and V₂ can be explained by finding a probabilistic common cause of the correlation in Reichenbach's sense. While this problem remains open, it is shown that if all superluminal correlations predicted by the vacuum state between events inA(V₁) andA(V₂) have a genuinely probabilistic common cause, then the local algebrasA(V₁) andA(V₂) must be statistically independent in the sense of C^*-independence.     

The BFKL-Regge phenomenology of deep inelastic scattering

We calculate the Regge trajectories of the subleading BFKL singularities and eigenfunctions for the running BFKL pomeron in the color dipole representation. We obtain a viable BFKL-Regge expansion of the proton structure function F _2p (x,Q ²) in terms of several rightmost BFKL singularities. We find large subleading contributions to F _2p (x,Q ²) in the HERA kinematical region which explain the lack of predictive power of GLDAP extrapolations of F _2p (x,Q ²) to the region of small x. We point out the relation of our early finding of precocious BFKL asymptotic behavior to the nodal structure of subleading BFKL eigenfunctions. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 3, 134–138 (10 August 1997) Published in English in the original Russian journal. Edited by Steve Torstveit     

The Multi-form Generalised Gleason Theorem

Arising from investigations of decoherence functionals in the “histories” approach to quantum mechanics, the following result is given by the methods of [14]. Let A ₁ and A ₂ be von Neumann algebras without Type I ₂ direct summands and let P(E _j ), (j=1,2) be their lattices of projections. Let m\colon; P(A ₁)×(P(A ₂)→ℂ be a bounded quantum bi-measure. Then there is a unique bounded bilinear functional M on A ₁×A ₂ which extends m. In this note we use a different approach to establish a generalisation of this result to k-fold, vector valued, quantum multi-measures. This tool is needed for further investigations of decoherence functionals in quantum theory. Received: 10 April 1998 / Accepted: 17 April 1998     

Airy Distribution Function: From the Area Under a Brownian Excursion to the Maximal Height of Fluctuating Interfaces

The Airy distribution function describes the probability distribution of the area under a Brownian excursion over a unit interval. Surprisingly, this function has appeared in a number of seemingly unrelated problems, mostly in computer science and graph theory. In this paper, we show that this distribution function also appears in a rather well studied physical system, namely the fluctuating interfaces. We present an exact solution for the distribution P(h_m,L) of the maximal height h_m (measured with respect to the average spatial height) in the steady state of a fluctuating interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h_m,L)=L^−1/2f(h_m L^−1/2) for all L>0 where the function f(x) is the Airy distribution function. This result is valid for both the Edwards–Wilkinson (EW) and the Kardar–Parisi–Zhang interfaces. For the free boundary case, the same scaling holds P(h_m,L)=L^−1/2F(h_m L^−1/2), but the scaling function F(x) is different from that of the periodic case. We compute this scaling function explicitly for the EW interface and call it the F-Airy distribution function. Numerical simulations are in excellent agreement with our analytical results. Our results provide a rather rare exactly solvable case for the distribution of extremum of a set of strongly correlated random variables. Some of these results were announced in a recent Letter [S.N. Majumdar and A. Comtet, Phys. Rev. Lett. 92: 225501 (2004)].     

FA(Ga+,In+,Tl+) tunable laser activity and interaction of halogen atoms (F,Cl,Br,I,At) at the (001) surface of KCl crystal: ab initio calculations

An attempt has been made to examine F_A(Ga⁺,In⁺,Tl⁺) tunable laser activity and adsorptivity of halogen atoms (F,Cl,Br,I,At) at the (0 0 1) surface of KCl crystal using an embedded cluster model, CIS and density functional theory calculations with effective core potentials. The ion clusters were embedded in a simulated Coulomb field that closely approximates the Madelung field at the host surface. The nearest neighbor ions to the defect site were then allowed to relax to equilibrium. Based on the calculated strength of electron–phonon coupling and Stokes-shifted optical transition bands, The F_A(Tl⁺) center was found to be the most laser active in agreement with the experimental observation that the optical emissions of F_A(In⁺) and F_A(Ga⁺) centers were strongly quenched. The disappearance of the anisotropy and np splitting observed in the absorption of F_A(Ga⁺,In⁺,Tl⁺) centers were monotonically increasing functions of the size of the impurity cation. The F_A(Ga⁺,In⁺,Tl⁺) defect formation energies followed the order F_A(Ga⁺)>F_A(In⁺)>F_A(Tl⁺). The Glasner–Tompkins empirical relationship between the principal optical absorption of F centers in solids and the fundamental absorption of the host crystal was generalized to include the positive ion species. As far as the adsorptivity of the halogen atoms is concerned, the F and F_A(In⁺,Tl⁺) centers were found to change the nature of adsorption from physical adsorption to chemical adsorption. The adsorption energies were monotonically increasing functions of the electronegativity of the halogen and the amount of charge transferred from the defect-free surface. The calculated adsorption energies were explainable in terms of the electron affinity, the effective nuclear charge and the electrostatic potentials at the surface. The spin pairing mechanism played the dominant role in the course of adsorbate–substrate interactions and the KCl defect-free surface can be made semiconducting by F or F_A(In⁺,Tl⁺) surface imperfections.     

Formality Theorem for Hochschild Cochains via Transfer

We construct a 2-colored operad Ger _∞ which, on the one hand, extends the operad Ger _∞ governing homotopy Gerstenhaber algebras and, on the other hand, extends the 2-colored operad governing open-closed homotopy algebras. We show that Tamarkin’s Ger _∞-structure on the Hochschild cochain complex C ^•(A, A) of an A _∞-algebra A extends naturally to a Ger⁺_￥{{\bf Ger}^+_{\infty}}-structure on the pair (C ^•(A, A), A). We show that a formality quasi-isomorphism for the Hochschild cochains of the polynomial algebra can be obtained via transfer of this Ger⁺_￥{{\bf Ger}^+_{\infty}}-structure to the cohomology of the pair (C ^•(A, A), A). We show that Ger⁺_￥{{\bf Ger}^+_{\infty}} is a sub DG operad of the first sheet E ¹(SC) of the homology spectral sequence for the Fulton–MacPherson version SC of Voronov’s Swiss Cheese operad. Finally, we prove that the DG operads Ger⁺_￥{{\bf Ger}^+_{\infty}} and E ¹(SC) are non-formal.     

The longitudinal structure function F L(x, Q 2) and the gluon distribution G(x, Q 2) at low x

We obtain a relation between the longitudinal structure function F _L(x, Q ²), F ₂(x, Q ²) and G(x, Q ²) at small x, using the formalism recently reported by one of the authors [2]. We also obtain a relation between F _L(x, Q ²), F ₂(x, Q ²) and its slope (dF ₂(x, Q ²))/(dlnQ ²). This provides us with the determination of the longitudinal structure function F _L(x, Q ²) from F ₂(x, Q ²) data and hence extract the gluon distribution G(x, Q ²).     

The role of OH ions in the stabilization of F colour centres in LiF

Thermally Stimulated Depolarisation Current (TSDC) and optical methods are applied to a range of alkali-fluoride crystals in order to establish a model for the stable F ₂ ⁺ - like colour centres in LiF:OH^-. The experimental results for LiF:OH^- suggest that the OH^- defects are partially destroyed under ionising irradiation or during crystal growth. The low-temperature dielectric relaxation signals in LiF:OH^- and LiF:Mg²⁺,OH^- are attributed to highly interacting hydroxide ions and products of their destruction located in extended lattice defects. In LiF:OH^-, in contrast to other alkali halides, the results advocate for a defect-structure model, which considers a neutral defect (ND, probably O₂ or H₂) sited at the anion vacancy of the O^2--V _a ⁺ dipole and which possibly is the “nucleus” for the F ₂ ⁺ centre. The proposed F ₂ ⁺ (ND, O^-) model seems to better explain the dielectric results, compared to the older F ₂ ⁺ (O^2-) and F ₂ ⁺ (O^-) models. The estimate for the electric dipole moment derived from the experimental TSDC bands, gives a value for the F ₂ ⁺ - like centre in LiF:OH^- between those of the F ₂ ⁺ (O^-) and F ₂ ⁺ (O^2-) defects, in good agreement with the proposed F ₂ ⁺ (ND,O^-) model. The reduction of the activation energy barrier of the (re)orientation process of the Mg²⁺V _c ^- (OH^-) complexes in LiF:Mg²⁺,OH^-, and the low-temperature shift of their TSDC band, compared to the single Mg ₂ ⁺ V _c ^- peak in LiF:Mg²⁺, are tentatively ascribed to an increase in the crystal-lattice parameters owing to the presence of OH^- and/or products of its destruction. Received 31 August 2001 / Received in final form 30 March 2002 Published online 9 July 2002     

High precision measurements of the hyperfine structure of seven metastable atomic states of57Fe by laser-Rf double-resonance

The hyperfine structure of the metastable atomic states (3d ⁷4s)⁵ F _2,3,4,5 and (3d ⁷ 4s)³ F _2,3,4 of⁵⁷Fe has been measured using theABMR- LIRF method (atomic beam magnetic resonance detected by laser induced resonance fluorescence). From these measurements the following hfs constantsA of the magnetic dipole interaction have been obtained (corrected for second order effects):A(⁵ F ₂)=55.994(7) MHzA(⁵ F ₃)=69.632(5) MHzA(⁵ F ₄)=78.435(4) MHzA(⁵ F ₅)=87.246(3) MHzA(³ F ₂)=143.328(4) MHzA(³ F ₃)=50.602(10) MHzA(³ F ₄)=13.456(5) MHz     

Vibrational spectrum of perfluoroethane

We have obtained IR absorption spectra of a C₂F₆ gas and a C₂F₆ cryosolution in Xe (T = 163 K) in the fundamental and overtone ranges. We have interpreted 28 bands of ¹²C¹²CF₆ and three bands of ¹³C¹²CF₆. In the spectral ranges that correspond to vibrations that are combinations with ν₁, ν₇, and ν₅, we observe multiplets, which we attribute to interactions of the type of Fermi resonances between the states ν₁(A _1g ) ∼ ν₆(A _1g ), ν₇(E _g ) ∼ ν₆ + ν₁₁(E _g ) ∼ 2ν₈(E _g ), ν₅(A _2u ) ∼ ν₈ + ν ₁₁(A _2u ). We reveal an anomalous intensity distribution in the spectrum of an asymmetric isotopologue. For the basic and isotopic configurations of perfluoroethane, we calculate the coefficients of shapes of vibrations and the intensities of absorption bands. We reveal that the behavior of the groups ¹²CF₃ and ¹³CF₃ is indifferent to the excitation of doubly degenerate stretching vibrations ν₇(E _g ) and ν₁₀(Eu).     

Möbius Transformations in Noncommutative Conformal Geometry

We study the projective linear group PGL ₂(A) associated with an arbitrary algebra A and its subgroups from the point of view of their action on the space of involutions in A. This action formally resembles M?bius transformations known from complex geometry. By specifying A to be an algebra of bounded operators in a Hilbert space H, we rediscover the M?bius group μ _ev (M) defined by Connes and study its action on the space of Fredholm modules over the algebra A. There is an induced action on the K-homology of A, which turns out to be trivial. Moreover, this action leads naturally to a simpler object, the polarized module underlying a given Fredholm module, and we discuss this relation in detail. Any polarized module can be lifted to a Fredholm module, and the set of different lifts forms a category, whose morphisms are given by generalized M?bius tranformations. We present an example of a polarized module canonically associated with the differentiable structure of a smooth manifold V. Using our lifting procedure we obtain a class of Fredholm modules characterizing the conformal structures on V. Fredholm modules obtained in this way are a special case of those constructed by Connes, Sullivan and Teleman. Received: 2 October 1997 / Accepted: 11 August 1998     

Optical and electrical characterization of cadmium selenide doped with cobalt

The optical and electrical properties of Co²⁺ ions in CdSe have been investigated. Absorption, photoluminescence, electron paramagnetic resonance, and Hall measurements were used to characterize a cobalt-doped (1×10¹⁹ cm⁻³) single crystal. Infrared absorption and emission spectra associated with transitions between the ⁴A₂(F) ground state and the ⁴T₁(F) and ⁴T₂(F) excited states are described. At 10 K, spin-orbit splittings result in three structured absorption bands associated with the ⁴A₂(F) to ⁴T₁(F) transition having zero-phonon lines at 4926, 5101, and 5724 cm⁻¹. The ⁴A₂(F) to ⁴T₂(F) transition shows two zero-phonon lines at 2874 and 3286 cm⁻¹, also accompanied by vibronic structure. Intrinsic lattice modes explain most of the sharp-line structure observed at low temperature, except for a subset of peaks where local modes (25-30 cm⁻¹) are invoked. Using below-band-gap light, selective excitation allows detection of the ⁴T₁(F) to ⁴A₂(F) recombination at liquid-helium temperatures. The activation of free carriers in our n-type material containing shallow donors is affected by the presence of cobalt, and we find the Co^+/++ level to be about 34 meV below the conduction band of CdSe.     

Nucleon form factors of the isovector axial-vector current

The theoretical and experimental status of the isovector axial-vector current form factors G _A(q ²) and G _P(q ²) of the nucleon is reviewed. We also describe a new calculation of these form factors in manifestly Lorentz-invariant chiral perturbation theory (ChPT) with the inclusion of axial-vector mesons as explicit degrees of freedom.     

Dynamical Correlation Functions for an Impenetrable Bose Gas with Neumann or Dirichlet Boundary Conditions

Abstract

We study the time and temperature dependent correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditions ψ(x ₁, 0)ψ ^?(x ₂ , t) _±,T . We derive the Fredholm determinant formulae for the correlation functions, by means of the Bethe Ansatz. For the special case x ₁ = 0, we express correlation functions with Neumann boundary conditions ψ(0, 0)ψ ^?(x ₂ , t) _+,T , in terms of solutions of nonlinear partial differential equations which were introduced in [1] as a generalization of the nonlinear Schrödinger equations. We generalize the Fredholm minor determinant formulae of ground state correlation functions ψ(x ₁)ψ ^?(x ₂) _±,0 in [2], to the Fredholm determinant formulae for the time and temperature dependent correlation functions ψ(x ₁, 0)ψ ^?(x ₂ , t) _±,T , t ∈ R, T ≥ 0.