Energy levels of a two-dimensional anharmonic oscillator: Hill determinant approach

The energy levels of the Schrödinger equation for the potentialx ²+y ²+λ[a _xxx⁴+2a _xyx² y ²+a _yyy⁴] are calculated using Hill determinant approach for several eigenstates and over a wide range of values of perturbation parameters. The obtained numerical results agree with those previously reported by other methods.     

Ru(III), Os(VIII), Pd(II) and Pt(IV) catalysed oxidation of glycyl–glycine by sodium N‐chloro‐p‐toluenesulfonamide: comparative mechanistic aspects and kinetic modelling

The Ru(III)/Os(VIII)/Pd(II)/Pt(IV)‐catalysed kinetics of oxidation of glycyl–glycine (Gly‐Gly) by sodium N‐chloro‐p‐ toluenesulfonamide (chloramine‐T; CAT) in NaOH medium has been investigated at 308 K. The stoichiometry and oxidation products in each case were found to be the same but their kinetic patterns observed are different. Under comparable experimental conditions, the oxidation‐kinetics and mechanistic behaviour of Gly‐Gly with CAT in NaOH medium is different for each catalyst and obeys the underlying rate laws:

• Rate = k [CAT]_t [Gly‐Gly]⁰ [Ru(III)][OH^?]^x
• Rate = k [CAT]_t[Gly‐Gly]^x [Os(VIII)]^y[OH^?]^z
• Rate = k [CAT]_t[Gly‐Gly]^x [Pd(II)][OH^?]^y
• Rate = k [CAT]_t[Gly‐Gly]⁰ [Pt(IV)]^x[OH^?]^y

Here, and x, y, z < 1 in all the cases. The anion of CAT, CH₃C₆H₄SO₂NCl^?, has been postulated as the common reactive oxidising species in all the cases. Under comparable experimental conditions, the relative ability of these catalysts towards oxidation of Gly‐Gly by CAT are in the order: Os(VIII) > Ru(III) > Pt(IV) > Pd(II). This trend may be attributed to the different d‐electronic configuration of the catalysts. Further, the rates of oxidation of all the four catalysed reactions have been compared with uncatalysed reactions, under identical experimental conditions. It was found that the catalysed reaction rates are 7‐ to 24‐fold faster. Based on the observed experimental results, detailed mechanistic interpretation and the related kinetic modelling have been worked out for each catalyst. Copyright © 2008 John Wiley & Sons, Ltd.     

Electrochemical Studies on Substituted Iron-Hexacyanoiron(III) Bi-Layered Thin Films at Glassy Carbon Electrode/Electrolyte Interface

Thin films (30–50 nm) of bilayered HCM (hexacyanometalates) were prepared using direct electrodeposition or electrochemically driven insertion-substitution of PB (Prussian Blue) or InHCF (Indium Hexacyanoferrate) or K..In _x [Fe{CN}₆] _y , as starting material. The redox behavior of the immobilized counter/central ions at GCE/electrolyte interface have been investigated in aqueous KCl (pH 1) electrolytes using dynamic voltammetric techniques. Studies show that when the counter Fe or In ion is replaced by expandable partially filled d orbits elements such as Ru³⁺ a redox wave of the inserted counter ion is observed. Furthermore, the substitution of Fe as a counter ion with other poly-valent cations was found to be reversible if PB was the starting material. Studies were extended to include the EC (electrochemical) behavior of related HCM compounds such as K...Al _x [Fe{CN}₆] _y K, Ni _x [Fe{CN}₆] _y Cu _x [Fe{CN}₆] _y , K..Zn _x [Fe{CN}₆] _y and, K..Ru[Fe{CN}₆]₃. Unlike studied 3d cations, GCE modified with thin films of copper-hexacyanoiron (III) KCu _x [Fe{CN}₆] _y or CHF showed two redox waves with E^o _f 0.6, 0.9 V vs Ag/AgCl. Studies showed that even immobilized Cu ions were capable of catalyzing the oxidation of hydrazine and sulfite. The mechanism for electro-oxidation is also included.     

Signature splitting in two quasiparticle rotational bands of <Superscript>180,182</Superscript>Ta

The signature splittings in K^π = 1 ⁺: 7 /2[404] _π?9 /2[624] _ν, K^π = 0^?: 9 /2[514] _π?9 /2[624] _ν bands of ¹⁸⁰Ta and K^π = 0^?: 7 /2[404] _π?7 /2[503] _ν, K^π = 1^?: 5 /2[402] _π?3 /2[512] _ν, K^π = 1⁺: 7 /2[404] _π?9 /2[624] _ν bands of ¹⁸²Ta are analysed within the framework of two-quasiparticle rotor model. The phase as well as magnitude of the experimentally observed signature splitting in K^π = 1⁺ band of ¹⁸⁰Ta, which could not be explained in earlier calculations, is successfully reproduced. The conflict regarding placement of a 12 ⁺ level in K^π = 1 ⁺: 7 /2 ⁺[404] _π?9 /2 ⁺[624] _ν ground-state rotational band of ¹⁸⁰Ta is resolved and tentative nature of K^π = 0^?: 7 /2[404] _π?7 /2[503] _ν, K^π = 1⁺: 7 /2[404] _π?9 /2[624] _ν bands observed in ¹⁸²Ta is confirmed. As a future prediction for experimentalists, these two-quasiparticle structures observed in ¹⁸⁰Ta and ¹⁸²Ta are extended to higher spins.     

Spin fluctuations and unconventional pairing on the Lieb lattice

The spin fluctuations and superconducting pairing symmetries in the dispersive band of Lieb lattice are studied by fluctuation exchange approximation. The antiferromagnetic spin density wave is found to exist on the A sublattice (the lattice sites with four nearest neighbors) at half filling. When slightly doped away from half filling, a balance between the combined effects of the (π,π$\pi ,\pi$) and (0.4π,0$0.4\pi ,0$) spin fluctuations and the gaining of the condensation energy leads to the nearly degenerate _dx2−y2$d_{x^2-y^2}$- and _gxy(x2−y2)$g_{xy(x^2-y^2)}$-wave pairing states. After further doped, the _dxy$d_{xy}$-wave state is favored via the intra-sublattice spin fluctuations with a wave vector (π,0$\pi ,0$). We emphasize that the sublattices' contribution and the renormalization of the spectral function play a crucial role on the spin fluctuations and the pairing symmetry. The effect of the imbalance of the on-site energy at different sublattices is also discussed.     

Inclusive particle spectra in p(π+)n interactions at 195 GeV/c

We present results on single-particle inclusive distributions in p(π⁺)n reactions from a Fermilab experiment using the hybrid 30″ bubble chamber and PWC facility. Distributions in rapidity, y, Feynman x and p²_T for π⁺ and π^? are presented and compared with other experiments. The effects of different targets and projectiles (neutrons, protons and pions) on the distributions are demonstrated and discussed in terms of projectile and target fragmentation. The average transverse momentum 〈P_T〉 is studied as a function of x, y and multiplicity.     

A closed-form solution of the Schroedinger equation describing the harmonic oscillator with time dependent frequency and acted on by a time dependent perturbative force

A new form of the semiclassical quantum conditions in non-separable systems is proposed. In two dimensions (2D) it has the form (? = 1)

where C_Σ is the path of a classical trajectory closed in phase space, N_x and N_y are the number of circuits in the x and y ‘senses’ on the invariant toroid and J_x and J_y are the ‘good’ action variables on the toroid; these action variables, J_x and J_y , must have the values 2π(n ₁ + ½) and 2π(n ₂ + ½) respectively where n ₁ and n ₂ are the integer quantum numbers. Closed classical trajectories occur only for the exceptional toroids with rational frequency ratios. In the general case we imply that the trajectory has closed on itself to some arbitrary accuracy. Results for the 2D potentials studied are in agreement with previously published work. It is shown how the method may be extended to 3D systems.     

Thin film Co[TCNE]2 and VyCo1−y[TCNE]2 magnetic materials

A chemical vapor deposition method has been developed for the synthesis of both solvent-free Co[TCNE]₂ and V_yCo_1−y[TCNE]₂ thin films. Both materials have been previously synthesized by solution methods, but contain solvent. The Co[TCNE]₂ thin films were characterized by infrared spectroscopy and magnetic studies, and albeit solvent-free were determined to be similar to the analogous solution-prepared samples as they are paramagnetic with slight antiferromagnetic coupling. In contrast to the solution-based synthesis, V_yCo_1−y-[TCNE]₂ showed no dependence of coercive field based on the composition of the films, even though infrared spectroscopic data indicates formation of a solid-solution thin film, and not a physical mixture.     

The emission spectrum of <Emphasis Type="Italic">p</Emphasis>-AlGaAs/GaAsP/<Emphasis Type="Italic">n</Emphasis>-AlGaAs diodes under uniaxial compression

New experimental data are presented on the effects of uniaxial compression of up to 4 kbar along the [110] and [1$ \bar 1 $ \bar 1 0] crystallographic directions on the spectra of electroluminescence and the current-voltage characteristics of diodes based on n-Al _x Ga_{1 − x} As/GaAs _y P_{1 − y} /p-Al _x Ga_{1 − x} As (y = 0.84) heterostructures that were designed for injection lasers. With increasing pressure, the spectra show a shift to shorter wavelengths, reaching 25 meV at 3 kbar; the intensity increases 2–3 times as well. Numerical calculations were carried out on the band structure of the investigated heterostructures under compression along the [110] axis, which indicate the increase in the effective band gap in the quantum well (QW) GaAs _y P_{1 − y} , with a pressure coefficient of about 8.5 meV/kbar and reduction of the barrier height at the boundaries of the QW. The calculations predict the possibility that light and heavy holes crossover at pressures above 4.5–5 kbar. The increase in the effective band gap completely describes the experimental data on the shift of the electroluminescence spectra. The mixing of light and heavy holes when approaching the band crosspoint is the probable cause of an increase in the intensity of radiation under uniaxial compression.     

Analytical potential energy function for the electronic states 2^∏1/2 and 2^∏3/2 of O^x2 （x=＋1, -1）

The splitting of potential energy levels for ground state X^2∏g of O^x2 （x = ＋1,-1） under spin-orbit coupling （SOC） has been calculated by using the spin-orbit （SO） multi-configuration quasi-degenerate perturbation theory （SO-MCQDPT）. Their Murrell-Sorbie （M S） potential functions are gained, and then the spectroscopic constants for electronic states 2^∏1/2 and 2^∏3/2 are derived from the M S function. The vertical excitation energies for O^x2 （x = ＋1,-1） are v[O2＋1^（2∏3/2→X^2∏1/2）] =195.652cm^-1, and v[O2^-1（2^∏1/2 →X^2∏3/2）] =182.568cm^-1, respectively. All the spectroscopic data for electronic states 2^∏1/2 and 2^∏3/2 are given for the first time.     

High-temperature operation of AlGaInAs/InP lasers1994

We discuss the design of uncooled lasers which minimizes the change in both threshold current and slope efficiency over the temperature range from–40 to +85°C [1]. To prevent carrier overflow under high-temperature operation, the electron confinement energy is increased by using the Al _x Ga _y In_1–x–y As/InP material system [1] instead of the conventional Ga _x In_1–x As _y P_1–y /InP material system. Experimentally, we have investigated strained quantum well lasers with three different barrier layers and confirmed that the static and dynamical performance of the lasers with insufficient carrier confinement degrades severely under high-temperature operation [2]. With an optimized barrier layer, the Al _x Ga _y In_1–x–y As/InP strained quantum well lasers show superior hightemperature performance, such as a small drop of 0.3 dB in slope efficiency when the heat sink temperature changes from 25 to 100°C [3], a maximum CW operation temperature of 185°C [4], a thermally-limited 3-dB bandwidth of 13.9 GHz at 85°C [2], and a mean-time-to-failure of 33 years at 100°C and 10 mW output power [5].     

Pressure dependence of the electric field gradient in Sb and Sb1−x M x (M=ln,Zn, Ge,Pb, Cd,Sn) at the site of111Cd

Using the¹¹¹Cd-TDPAC (time differential perturbated angular correlation) method, the pressure dependence of the electric field gradient (EFG) in Sb and Sb_1–x M _x (M=ln, Zn, Ge, Pb, Cd, Sn) was investigated. The application of a phenomenological ansatz for the parametrisation of the pressure and temperature dependence of the EFG made it possible to combine temperature data gained in former studies [1], [2] with the pressure dependent data presented in this paper. The resulting pressure dependence of –2±0.2 MHz/kbar is shown to be independent of concentration and element of admixture. Results for the volume and explicit temperature dependence agree with existing information on the mixed system Sb_1–x M _x (M=ln, Zn, Ge, Pb, Cd, Sn); the investigation of the EFG in Sb_1–x–y M _x Pb _y showed that the resulting EFG may be interpreted as the weighted sum of the individual contributions of the two metals.This paper is dedicated to Prof. Dr. W. Kreische on the occasion of his 60th aniversary on 02.02.1995     

New class of T′-structure cuprate superconductors

High-temperature superconductivity has been discovered in La_2−xBa_xCuO₄ [J.G. Bednorz, K.A. Müller, Z. Phys. B 64 (1986) 189. [1]], a compound that derives from the undoped La₂CuO₄ crystallizing in the perovskite T-structure. In this structure oxygen octahedra surround the copper ions. It is common knowledge that charge carriers induced by doping in such an undoped antiferromagnetic Mott-insulator lead to high-temperature superconductivity [V.J. Emery, Phys. Rev. Lett. 58 (1987) 2794; C.M. Varma, S. Schmitt-Rink, E. Abrahams, Solid State Commun. 62 (1987) 681; E. Dagotto, Rev. Mod. Phys. 66 (1994) 763. [2], [3] and [4]]. The undoped material La₂CuO₄ is also the basis of the electron-doped cuprate superconductors [Y. Tokura, H. Takagi, S. Uchida, Nature (London) 337 (1989) 345. [5]] of the form La_2−xCe_xCuO_4+y [M. Naito, M. Hepp, Jpn. J. Appl. Phys. 39 (2000) L485; A. Sawa, M. Kawasaki, H. Takagi, Y. Tokura, Phys. Rev. B 66 (2002) 014531. [6] and [7]] which, however, crystallize in the so-called T′-structure, i.e. without apical oxygen above or below the copper ions of the CuO₂-plane. It is well known that for La_2−xCe_xCuO_4+y the undoped T′-structure parent compound cannot be prepared due to the structural phase transition back into the T-structure occurring around x∼0.05. Here, we report that if La is substituted by RE=Y, Lu, Sm, Eu, Gd, or Tb, which have smaller ionic radii but have the same valence as La, nominally undoped La_2−xRE_xCuO₄ can be synthesized by molecular beam epitaxy in the T′-structure. The second important result is that all these new T′-compounds are superconductors with fairly high critical temperatures up to 21 K. For this new class of cuprates La_2−xRE_xCuO₄, which forms the T′-parent compounds of the La-based electron doped cuprates, we have not been able to obtain the Mott-insulating ground state for small x before the structural phase transition into the T-structure takes place.     

An inclusive study of π-, K0 and a production from pn reactions at 11.6 GeV/c

Cross sections, multiplicities and particle inclusive spectra are presented for π^-, K⁰ and Λ produced in pn reactions at 11.6 GeV/c beam momentum. The results are compared with the data from pp interactions in the same energy range. Correlations between two π^- are also discussed. The main results are: the π^-, K⁰ and Λ all behave similarly as a function of transverse momentum squared; π^- in the forward c.m. hemisphere have spectra in x and y consistent with that of pp interactions, whereas the spectra of π^- in the backward hemisphere fall off more slowly with ∥x∥ and ∥y∥ than those in the forward hemisphere, suggesting n-fragmentation effects. The K⁰ and Λ have x and y distribution roughly similar to those in pp interactions. The K⁰ and Λ are consistent with a modified form of KNO scaling.     

Magnetostriction and anisotropy of CoxFe3xO4 (x≤0.1) single crystals

Using the strain gauge technique, the magnetostriction constants λ_[100] and λ_[111] have been measured on single crystals of Co_xFe_3-xO₄ with compositions 0.0005≤x≤0.1 in the temperature range between 100 and 300 K and using magnetic fields up to 23 kOe. The presence of Co²⁺-ions gives rise to a very large negative value of λ_[100] and a fairly large positive value of λ_[111]. A linear relationship is found between the magnetostriction constants and the cobalt concentration.Some conclusions about the anisotropic beheviour of the samples can be made, based on the magnetostriction measurements. The change of the direction of easy magnetization from [111] to [100] in the temperature range just above the Verwey transition, is illustrated and discussed. It turned out to be possible to determine an effective anisotropy constant K'₁ through a curve fitting procedure. It is found that 1n K'₁ varies linearly with T.     

Higher-twist effects in QCD,deep inelastic scattering,and the Drell-Yan process

Inclusion of specific effects associated with constituent binding in hadronic wave functions is shown to lead to important non-scaling, nonfactorizing 1/Q ² contributions to cross sections for semi-inclusive deep-inelastic scattering, the Drell-Yan process, and other hard scattering reactions. These 1/Q ² higher-twist terms are predicted to be dominant in well defined kinematic regions such as largex and/or largez. The provide angular distributions typical of longitudinally polarized virtual photons andW's, including sin² θ terms in meson induced Drell-Yan processes and ine ⁺ e ^?→πX, as well as unusual (1?y) terms in deep-inelastic scattering. Calculations are also presented of the quark structure functions of the pionq _π(x, Q ²) and for the quark to pion fragmentation functionD _π(z, Q ²). Predictions are made for the azimuthal angle dependence of the cross sections for \(\pi N \to \mu {\text{ }}\bar \mu X\) andlN→l′πX.     

Structural investigation of xAg2O·(100−x)·[2B2O3·As2O3] glasses doped with manganese ions

Structural analysis of x[(100−y)Ag₂O·yMnO]·(100−x)[2B₂O₃·As₂O₃] glasses, with x=10 mol% and 0≤y≤10 mol%, was performed by means of FT-IR and FT-Raman spectroscopies. The purpose of this work is to investigate the structural changes that appear in the xAg₂O·(100−x)·[2B₂O₃·As₂O₃] glasses with the addition and increase in manganese ions content. FT-IR measurements revealed the presence of pyro-, ortho-, di-, tri-, tetra- and penta-borate groups and structural units characteristic to As₂O₃ in the structure of the studied glasses. FT-IR spectroscopy measurements also show that BO₃ units are the main structural units of the glass system. The presence of structural units characteristic to Ag₂O were not directly evidenced by FT-IR spectroscopy. In addtition, the FT-Raman analysis evidenced the presence of boroxol rings in the structure of the studied glasses.     

Analyses of intrinsic inhomogeneity and metal segregation in samples of Ag–Ge–Se glasses

Ge_ySe_(1−y) glasses are semiconductors but when Ag is added above certain threshold concentration, Ag_x[Ge_ySe_(1−y)]_(100−x) glasses behave as fast ionic conductors [Ureña et al., Solid State Ionics 176 (2005) 505]. This peculiar behavior may be attributed to the intrinsically inhomogeneous nature of these glasses where zones rich in metals coexist with zones of the host material. The conductivity transformation may be ascribed to the percolation of the Ag rich phase [Pradel et al., J. Phys.: Condens. Matter 15 (2003) S1561].Ag_x[Ge_0.25Se_0.75]_(100−x) glasses either massive or as films were obtained by melt quenching and pulsed laser deposition (PLD), respectively, in compositions belonging to the Se rich corner of the ternary phase diagram. Their amorphous nature and intermediate range order was checked employing X-ray diffractometry (XRD), the short range order was characterized by extended X-ray absorption fine structure (EXAFS) (Ge and Se K absorption edge) and their microstructure was characterized by scanning electron microscopy (SEM) and small angle X-ray scattering (SAXS).     

Atomic structure and lattice dynamics of strain-compensated Si1-x-yGexCy layers

The local atomic structure and lattice dynamics are studied for strain compensated Si_1-x-yGe_xC_y layers grown by molecular beam epitaxy on Si (001) substrates. The layers were characterized by transmission electron microscopy, x-ray diffraction, and Raman scattering and modeled using a valence-force field model. For a [Ge]/[C] ratio of approximately ten, the lattice constant in the growth direction is equal to that of the substrate, indicating an absence of macroscopic strain. Experimental and theoretical results are compatible with Vegard's rule. To handle the large bond length distortions near C atoms properly, the valence-force field model used includes anharmonic effects via bond-length-dependent interatomic force constants which were determined from ab initio density-functional calculations. The dependence of the Raman spectra on strain and composition of Si_1-x-yGe_xC_y layers can be explained by the model calculations.