Jahn–Teller effect and superparamagnetism in zn substituted copper-gallate ferrite

Spinel ferrite CuFe₂O₄ and solid solution of Cu_1−xZn_xFe_2−yGa_yO₄ with 0.0?x?0.5 are synthesized through the usual ceramic method. X-ray diffraction measurements confirm the presence of single-phase tetragonal structure with c/a>1for CuFe₂O₄ and compositions with x?0.1. The formation of the tetragonal phase in these samples is attributed to the presence of the cooperative Jahn–Teller Cu ion at the octahedral B-site in the spinel lattice. At the compositional parameter x?0.2, tetragonal-to-cubic transformation occurred and the lattice parameter a for the cubic unit cell is found to decrease with increasing Zn content x. ⁵⁷Fe Mössbauer measurements at 293 K for these compounds reveal superparamagnetic phase for samples with 0.0?x?0.2. In contrast, Mössbauer spectra at 12 K for these materials show well ordered spectra where, the cation distribution and the hyperfine parameters are determined.     

Theoretical study of the spin-orbit coupling in the X2Π state of OH

The spin-orbit coupling constant, A(r), as a function of internuclear distance (r) was computed for the X²Π state of OH, using the microscopic spin-orbit Hamiltonian, extended basis sets, and extensive configuration-interaction wavefunctions. Our best theoretical results are in excellent agreement with the “experimental” A(r) functions deduced from an inversion of the observed A_v. Our calculated first-order contributions to A_v, v ≤ 10, obtained by vibrationally averaging our theoretical A(r) function using the X²Π RKR potential, differ from experiment by less than 0.12%. A minimum occurs in the A_v at v = 7 in agreement with experiment, reflecting the local minimum in A(r) near 2.8 bohr. The second-order contributions to A_v are only about 0.1% for v ≤ 10. They arise mainly from the A²Σ⁺ state for the lower vibrational levels, but each of the A²Σ⁺, B²Σ⁺, (1)²Σ^?, (1)⁴Σ^?, and (1)²Δ states contributes significantly for higher vibrational levels. Spin-orbit centrifugal distortion parameters, A_Dv and a_Dv, are reported for v ≤ 6. The theoretical A_Dv are also in excellent agreement with experiment when the “experimental” A(r) function has the same slope at the equilibrium separation as that obtained from the effective spin-rotation constants of OH, OD, and OT.     

The Nambu,Jona-Lasinio model and low energy effective meson Lagrangians

Using standard techniques, the Nambu-Jona-Lasinio Lagrangian with its chirally invariant four-fermion couplings is transformed into a bosonized form which includes scalar, pseudo-scalar, vector and axial-vector fields. Then, after eliminating the scalar and axialvector fields in an appropriate way, we obtain the Lagrangian given by Bando et al. based on the “hidden” local symmetry approach, except that in the present approach the free parametera of their model is now uniquely given by a=(1? M _V ² /M _A ² )^?1 in terms of the vector and axial-vector meson massesM _V andM _A. The value ofa=2, which led them to remarkable phenomenological successes is therefore directly connected with the Weinberg mass relation M_A=√2M_V in this model. The formal equivalence between the hidden symmetry approach and the massive Yang-Mills scheme is clearly demonstrated in the present approach, which derives an effective meson theory starting from a Lagrangian at the underlying quark level.     

EPR study of Fe3+ and Mn2+ in CeO2 and ThO2

Attempts were made to grow CeO₂ and ThO₂ single crystals doped with transition metal ions. Only Fe³⁺ and Mn²⁺ could be detected by the EPR technique. The EPR spectrum of Fe³⁺ in CeO₂ exhibits the well-known fine structure in cubic fields. The parameters areg=2.0044(1) anda=15.6(1)·10^?4 cm^?1. The hyperfine constantA for⁵⁷Fe in hexahedral coordination was found to be 8.9(1)·10^?4 cm^?1. The EPR spectrum of Mn²⁺ in CeO₂ reveals two cubic Mn²⁺ centers. The parameters for center 1 areg=1.9999(1) andA=86.9(1)·10^?4 cm^?1 and for center 2g=1.9984(1) andA=87.0(1)·10^?4 cm^?1. Heating the Mn doped CeO₂ samples in hydrogen, the Mn²⁺ centers transform from cubic into trigonal centers with approximate values ofg=1.9988(2),A=84.5(6)·10^?4 cm^?1 andD=203(1)·10^?4 cm^?1. The two observed Mn²⁺ centers in ThO₂ exhibita priori axial symmetry with approximate values ofg=2.0006(2),A=88.9(4)·10^?4 cm^?1 andD=33(3)·10^?4 cm^?1.     

Asymptotic inverse spectral problem for anharmonic oscillators

We study perturbationsL=A+B of the harmonic oscillatorA=1/2(??²+x ²?1) on ?, when potentialB(x) has a prescribed asymptotics at ∞,B(x)～|x|^?α V(x) with a trigonometric even functionV(x)=Σa _mcosω _m x. The eigenvalues ofL are shown to be λ _k =k+μ _k with small μ _k =O(k ^?γ), γ=1/2+1/4. The main result of the paper is an asymptotic formula for spectral fluctuations {μ _k }, $$\mu _k \sim k^{ - \gamma } \tilde V(\sqrt {2k} ) + c/\sqrt {2k} ask \to \infty ,$$ whose leading term \(\tilde V\) represents the so-called “Radon transform” ofV, $$\tilde V(x) = const\sum {\frac{{a_m }}{{\sqrt {\omega _m } }}\cos (\omega _m x - \pi /4)} .$$ as a consequence we are able to solve explicitly the inverse spectral problem, i.e., recover asymptotic part |x ^?α|V(x) ofB from asymptotics of {µ _k }. ₁ ^∞      

Anomalous phonon intensities in the Raman spectrum of disordered CsMg1−xCoxCl3

The five Raman-active $\text{k}\text{= 0}$ phonons have been measured at low temperatures and for a range of x in the disordered lattice CsMg_1-xCo_xCl₃. While the E_2g^a, E_2g^b, E_2g^c and A_1g modes at 55.0, 132.0, 189.0 and 255.0 cm^?1 for x = 0 exhibit normal one-mode behaviour, the intensity of the E_1g phonon at 127.5 cm^?1 has a most unusual concentration dependence which requires a new theory.     

Self dual solutions of the temperature SU(2) Yang-Mills theory

Continuing previous work we elaborate on the method of “heating” the self-dual axially symmetric fields of the SU(2) Yang-Mills theory to finite temperature. Heating consists of performing—in certain Ansatz functions which are two-dimensional (2D) conformally invariant—a 2D conformal transformation x = x₀ + i ∥x∥ → y(x), where the analytic function y(x) is periodic in the Euclidean time variable x₀. Solutions are preserved by this manipulation, which automatically changes zero-temperature fields into finite temperature ones. One can exploit this simple fact in various ways. The Harrington-Shepard caloron solution of the temperature Yang-Mills theory can be gotten from the T = 0 instanton by the transformation y(x) = (πT)^?1 tan πTx. One can generate a multicaloron solution from the T = 0 one instanton solution by a conformal transformation. Generally, self-dual axially symmetric Yang-Mills fields can be heated without spoiling self duality. The caloron and three other temperature solutions are studied in some detail. One of the new solutions is a generalized caloron with interesting properties. Our study reveals a remarkable property of the self-dual sector of the temperature Yang-Mills theory: it is full of Wu-Yang (color) monopoles at high temperature. At low temperature these monopoles disappear.     

Heavy SUSY Higgs bosons at e + e − linear colliders

The production mechanisms and decay modes of the heavy neutral and charged Higgs bosons in the Minimal Supersymmetric Standard Model are investigated at future e ⁺ e ^? colliders in the TeV energy regime. We generate supersymmetric particle spectra by requiring the MSSM Higgs potential to produce correct radiative electroweak symmetry breaking, and we assume a common scalar mass m₀, gaugino mass m_1/2 and trilinear coupling A, as well as gauge and Yukawa coupling unification at the Grand Unification scale. Particular emphasis is put on the low tan β solution in this scenario where decays of the Higgs bosons to Standard Model particles compete with decays to supersymmetric charginos/neutralinos as well as sfermions. In the high tan β case, the supersymmetric spectrum is either too heavy or the supersymmetric decay modes are suppressed, since the Higgs bosons decay almost exclusively into b and τ pairs. The main production mechanisms for the heavy Higgs particles are the associated AH production and H ⁺H^? pair production with cross sections of the order of a few fb.     

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.     

Quark confinement and the baker-ball-zachariasen approximation

The Yang-Mills effective action ?1/4∫dxxF _μv ^a (D ²/M ²)F _μv ^a recently proposed by Baker et al., and also much earlier by the author and R.L. Stuller, is considered. An extension of the effective action to include Fermions is constructed in which quarks can be confined. The Schwinger-Dyson equation for the quark propagator is studied, and conditions are derived for the quark mass to be driven selfconsistently to infinity.     

The one-site distribution of Gibbs states on Bethe lattice are probability vectors of period⩽2 for a nonlinear transformation

We prove that the one-site distribution of Gibbs states (for any finite spin setS) on the Bethe lattice is given by the points satisfying the equation π=T ²π, whereT=h·A·?, with?(x)=x ^(q?1/q,h(x)=(x∥x∥ _q ) ^q ,A=(a(r, s)∶r, s∈S), and $$a(r,s) = \exp (K[r,s] + (1/q)[N,r + s])$$ We also show that forA a symmetric, irreducible operator the nonlinear evolution on probability vectorsx(n+1)=Ax(n) ^p ∥Ax(n) ^p ∥₁ withp>0 has limit pointsξ of period?2. We show thatA positive definite implies limit points are fixed points that satisfy the equationAξ ^p=λξ. The main tool is the construction of a Liapunov functional by means of convex analysis techniques.     

Visible light activated photo-catalytic effect and local structure of iron silicate glass prepared by sol-gel method

A relationship between methylene blue (MB) decomposition ability under visible light and local structure of xFe₂O₃·(100-x)SiO₂ glass abbreviated as xFS prepared by sol-gel method was investigated by ⁵⁷Fe-Mössbauer spectroscopy, X-ray diffractometry (XRD) and ultraviolet-visible light absorption spectroscopy (UV-Vis). Mössbauer spectra of xFS glass with x of 10, 30 and 50 annealed at 1000 °C for 3 h were mainly composed of a paramagnetic doublet due to fayalite (Fe₂SiO₄), and magnetic sextets due to magnetite (Fe₃O₄) or hematite (α-Fe₂O₃). The absorption area (A) of α-Fe₂O₃ gradually increased from 0.0 to 10.3 and 100 % with the increasing Fe₂O₃ content (x) of annealed xFS glass. A leaching test performed by 20 mL of MB aqueous solution and 40 mg of annealed 50FS glass showed that MB concentration decreased from 16.2 to 4.7 μmol L^?1 after 2 h with the first order rate constant of 1.8 × 10^?4 s^?1. These results prove that annealed iron silicate glass containing α-Fe₂O₃ can decompose MB effectively under visible light irradiation.     

Electron Paramagnetic Resonance and Electron Spin Echo Studies of Co2+ Coordination by Nicotinamide Adenine Dinucleotide (NAD+) in Water Solution

Co²⁺ binding to the nicotinamide adenine dinucleotide (NAD⁺) molecule in water solution was studied by electron paramagnetic resonance (EPR) and electron spin echo at low temperatures. Cobalt is coordinated by NAD⁺ when the metal is in excess only, but even in such conditions, the Co/NAD⁺ complexes coexist with Co(H₂O)₆ complexes. EPR spin-Hamiltonian parameters of the Co/NAD⁺ complex at 6 K are g _z  = 2.01, g _x  = 2.38, g _y  = 3.06, A _z  = 94 × 10^?4 cm^?1, A _x  = 33 × 10^?4 cm^?1 and A _y  = 71 × 10^?4 cm^?1. They indicate the low-spin Co²⁺ configuration with S = 1/2. Electron spin echo envelope modulation spectroscopy with Fourier transform of the modulated spin echo decay shows a strong coordination by nitrogen atoms and excludes the coordination by phosphate and/or amide groups. Thus, Co²⁺ ion is coordinated in pseudo-tetrahedral geometry by four nitrogen atoms of adenine rings of two NAD⁺ molecules.     

Magnetic properties of (Mn1 − x Fe x )1.68Sn solid solutions

Solid solutions in the (Mn_{1 ? x} Fe _x )_1.68Sn system (x ≤ 0.5) with a Ni₂In-type structure are synthesized by the solid-phase reaction method in a stepwise temperature regime. The unit cell parameters a and c decrease with an increase in the iron concentration in the alloys and become equal to a = 0.430 nm and c = 0.538 nm for the (Mn_0.5Fe_0.5)_1.68Sn alloy. A superstructure with the unit cell parameters a _ss = 3a and c _ss = c is revealed in alloys of the system under investigation. The specific magnetization of the alloys increases nonlinearly from 53 G cm³ g^?1 in the Mn_1.68Sn alloy to 72 G cm³ g^?1 in the (Mn_0.5Fe_0.5)_1.68Sn solid solution. The Curie temperature changes from 270 K in the initial alloy of the composition Mn_1.68Sn to 365 K in the alloy of the composition (Mn_0.5Fe_0.5)_1.68Sn. All solid solutions in the (Mn_{1 ? x} Fe _x )_1.68Sn (x ≤ 0.5) system exhibit metallic conductivity in the temperature range from 77 to 450 K.     

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.     

Solutions of the Yang-Mills field equations independent of the x4 variable

Two families of classical solutions of the SU(2) Yang-Mills field equations in the four-dimensional euclidean space, which are independent of the x₄ variable, are presented. One of them depends on an arbitrary function and the other on an arbitrary solution of the three-dimensional Laplace equation.     

The decay of the Bethe-Salpeter kernel inP(ϕ)2 quantum field models

We extend methods of high temperature expansions to show that for even weakly coupledP(?)₂ quantum field models the Bethe-Salpeter kernel has 4 particle decay. More precisely ifK denotes the Euclidean Bethe-Salpeter kernel $$|K(x_1 ,x_2 ,x_3 ,x_4 )| \leqq Oe^{ - m_0 (1 - \varepsilon )d_2 } ,$$ wherex=(x ⁰,x ¹),d ₂=2|x ₁ ⁰ +x ₂ ⁰ ?x ₃ ⁰ ?x ₄ ⁰ |+|x ₁ ⁰ ?x ₂ ⁰ |+|x ₃ ⁰ ?x ₄ ⁰ | and ε(λ)→0 as λ→0. Our methods apply to otherr particle irreducible kernels.     

Paramagnetic resonance of V in tetragonal GeO2

Anisotropic g and A tensors are found for V⁴⁺ in single crystal tetragonal GeO₂. The orbital mixing parameter λ, normalized radial average 〈1/r³〉/N and core polarization x/N are calculated, and λ is not anomalously low as reported from polycrystalline measurements.     

Multiple meron solutions of the classical Yang-Mills equation

We give a construction for multiple meron-antimeron solutions to the classical SU(2) Yang-Mills field equations. The corresponding charge density is $\text{Q(x) =}\text{1}\text{2}\text{∑ ± γ(x?x}{}_{\mathrm{i}}\text{)}$, with the x_i distinct points on a line. The problem is reduced to the solution of a scalar φ⁴ equation. We obtain a model with merons connected in pairs.