Ligand polarization contributions to lanthanide 4f → 4f magnetic dipole transition moments and rotatory strengths

Radiation-induced (dynamic) polarizations of electronic charge distributions on ligands may contribute to both the electric- and magnetic-dipole moments of 4f → 4f transitions in lanthanide complexes. These ligand-polarization effects on magnetic-dipole transition moments are examined in the present study, and their possible influence on the rotatory strengths of 4f → 4f transitions in chiral lanthanide systems is given special attention. The ligand-polarization mechanism for magnetic-dipole transition moments is not likely to contribute significantly to the total dipole strengths of 4f → 4f transitions in noncentrosymmetric lanthanide systems. However, this mechanism may contribute significantly (or detectably) to the rotatory strengths of certain 4f → 4f transitions in chiral lanthanide systems. The relative importance of these contributions will be greatest for transitions with predominantly |ΔJ| ≥ 2 character and with relatively large U ^λ(λ = 2, 4, and 6) matrix elements.     

Validity of the Anderson and Hubbard models for the description of metallic Ce and cerium heavy fermion compounds

The importance of the inclusion of inter-site f-f hybridization in electron structure calculations for metallic Ce and cerium heavy fermion compounds was studied. We demonstrate that for heavy-fermion systems such as cerium compound CeCu₂Si₂ f-f hybridization can be neglected and Anderson model application is well justified. On another hand for cerium metal f-f hybridization is strong enough to provide the contribution to hybridization function comparable to hybridization between 4f and itinerant electrons. We argue that in the case of Ce only the most general Hamiltonian combining the Hubbard and Anderson models should be used.     

Effect of electron-phonon interaction and temperature dependence of resistivity in some heavy fermion systems

Here we have considered the electron-phonon interaction in the Periodic Anderson Model (PAM) to describe the temperature dependence of resistivity in some heavy fermion (HF) systems. Since the resistivity is related to the imaginary part of the electron self energy, the expression of the same is evaluated from electron Green function by the double time temperature dependant Green function technique of the Zubarev type. In order to understand the effect of electron-phonon interaction in these systems, we couple the phonons to both the f-electrons as well as to the electrons of the hybridization band of both conduction and f-electrons. The influence of various model parameters, namely, the position of 4f level E ₀, the electron-phonon coupling strengths f ₁(q) and f ₂(q), the effecting coupling strength g = N(0)γ ₀²/ω ₀ have been studied on the temperature dependence of resistivity in HF systems. The numerical analysis is performed for q = 0 and for finite temperature in the static limit. The analysis of the results gives satisfactorily in comparison to the experimental observations.     

Resonant photoemission from 4f systems,especially Ce

Resonant photoemission has provided important new means to study the properties of the 4f electron states in the light lanthanides. These investigations have revealed unexpectedly complex 4f spectral shapes. This has led to new insight into the problem of the 4f systems. Some recent results for Ce are reviewed and it is shown how these disprove the previously accepted promotional model for Ce. The results are briefly discussed in terms off-hybridization and possible band formation. Some expected future experimental developments are also discussed.     

Crystallization of electrons confined to a lattice

A necessary condition for electron crystallization is the dominance of the electronic Coulomb repulsion as compared with the kinetic energy. We show that 4f systems are good candidates for electron or hole crystallization to occur since the small radius of the 4f shell leads to small hybridizations and hence kinetic energy of the f electrons. Crystallization may take place in lattices with several equivalent 4f sites per unit cell when the electron or hole number is less than the number of sites. We give evidence that charge ordering in Yb₄As₃ is an example of the mechanism considered here. We also compare it with those considered by Wigner, Verwey, Mott and Hubbard.     

Magnetic-nonmagnetic transitions in intermediate-valence systems

We investigate the coexistence of ferromagnetism and intermediate valence in 4f-systems, which have ferromagnetic ground states in the normal valence phase and fluctuate between a magnetic (J0) and a nonmagnetic (J=0) configuration in the intermediate valence phase. We use the well-knowns-f model, which is extended by a hybridization term and an intraatomicf-Coulomb-interaction, for systems with ferromagnetics-f exchange. The alloy analogy of this model is solved within a CPA-scheme. We inspect the stability of the localf-momentm _f , the valencen _f and relevant quasiparticle densities of states in terms of the Bloch bandwidthW (closely related to external pressure!), thef-level positionE _f (alloying!), and the hybridization matrix elementV.     

I/f noise in systems showing stochastic resonance

Stochastic resonator systems with input and/or output 1/f noise have been studied. Disordered magnets/dielectrics serve as examples for the case of output 1/f noise with white noise (thermal excitation) at the input of the resonators. Due to the fluctuation-dissipation theorem, the output noise is related to the out-of-phase component of the periodic peak of the output spectrum. Spin glasses and ferromagnets serve as interesting examples of coupled stochastic resonators. A proper coupling can lead to an extremely large signal-to-noise ratio. As a model system, a l/f-noise-driven Schmitt trigger has been investigated experimentally to study stochastic resonance with input 1/f noise. Under proper conditions, we have found several new nonlinearity effects, such as peaks at even harmonics, holes at even harmonics, and 1/f noise also in the output spectrum.     

Local scaling transformation function and atomic shell structure in density functional theory

The method of local scaling transformation in density functional theory calculates a transformation function (TRF) in order to generate an optimized atomic N-electron wave function from a trial density and a reference density/wave function. The TRFsf(r) for several atomic systems are studied and it is observed that the number of minima in df(r)/dr equals the number of atomic shells, except whenρ=ρ ₀ andf=r.     

On the nonexistence of Liouvillian first integrals for generalized Liénard polynomial differential systems

We consider generalized Liénard polynomial differential systems of the form ? = y, ? = -g(x) - f (x) y, with f (x) and g(x) two polynomials satisfying deg(g) ≤ deg(f). In their work, Llibre and Valls have shown that, except in some particular cases, such systems have no Liouvillian first integral. In this letter, we give a direct and shorter proof of this result.     

Design of a hybrid diffractive/refractive achromatized telecentric f·θ lens

The design of a hybrid diffractive/refractive achromatized telecentric f·θ lens with a field of view (FOV) 50° and an effective focal length of 750 mm is presented. The optical stop is placed at the front focal plane so that it is a telecentric system. The design is based on a traditional refractive counterpart, and the designed system consists of a hybrid diffractive/refractive lens and four refractive lenses. The designed f·θ lens shows a considerable reduction in weight with a simplified structure, and exhibits superior performance compared to the refractive system. It is emphasized that the designed f·θ lens can be applied to modern color scanning systems that operate in the visible wavelength range with high performance. It can also be applied to high-energy scanning systems. When applying the designed hybrid diffractive/refractive f·θ lens to the high-energy scanning system, a big laser operating in one longitudinal mode can be replaced by a small multi-mode laser, and the scanning system can be simplified greatly with the accuracy improved.     

Triangle Distribution and Equation of State for Classical Rigid Disks

The triangle distribution function f ⁽³⁾ for three mutual near neighbors in the plane describes basic aspects of short-range order and statistical thermodynamics in two-dimensional many-particle systems. This paper examines prospects for constructing a self-consistent calculation for the rigid-disk-system f ⁽³⁾. We present several identities obeyed by f ⁽³⁾. A rudimentary closure suggested by scaled-particle theory is introduced. In conjunction with three of the basic identities, this closure leads to an unique f ⁽³⁾ over the entire density range. The pressure equation of state exhibits qualitatively correct behaviors in both the low-density and the close-packed limits, but no intervening phase transition appears. We discuss extensions to improved disk closures, and to the three-dimensional rigid-sphere system.     

The influence of the dynamics of ionic multiplets onto electronic transport properties of heavy-fermion systems: a semi-phenomenological approach

We present calculations of the electronic transport properties of heavy-fermion systems within a semi-phenomenological approach to the dynamical mean field theory. In this approach the dynamics of the Hund's rules 4f (5f )-ionic multiplet split in a crystalline environment is taken into account. Within the scope of this calculation we use the linear response theory to reproduce qualitative features of the temperature-dependent resistivity and hall conductivity, the magneto-resistivity and the thermoelectric power typical for heavy-fermion systems. The model calculations are directly compared with experimental results on CeCu ₂ Si ₂. Received 30 June 2000 and Received in final form 15 December 2000     

Investigation of magnetic field effect on surface and finite-site free energy in one-dimensional Ising model of nanosystems

We investigate a one-dimensional (1-D) Ising model for finite-site systems. The finite-site free energy and the surface free energy are calculated via the transfer matrix method. We show that, at high magnetic fields, the surface free energy has an asymptotic limit. The absolute surface energy increases when the value of f (the ratio of magnetic field to nearest-neighbor interactions) increases, and for f?≥?10 approaches a constant value. For the values of f?≥?0.2, the finite-site free energy also increases, but slowly. The thermodynamic limit in which physical properties approach the bulk value is also explored.     

Small-angle neutron scattering studies of aqueous solutions of short-chain amphiphiles

We present small angle neutron scattering measurements on binary aqueous solutions of some short-chain amphiphiles (diols, triols, glycols and diglycols) at room temperature. The spectra were analysed in terms of the Teubner-Strey phenomenological formula which allows to obtain a measure for the amphiphilicity strength of each system (amphiphilicity factor f _a). In some systems, however, other models, valid for micellar solutions, give also a good representation of the spectra. As a result, we find that, independently of the type of hydrophilic group side (oxydrilic or oxirane), these systems cover the entire accessible amphiphilicity scale ( -1 < f _a < 1). Some disordered systems ( f _a > 1) presumably are able to form micelle-like aggregates. Received 12 June 2002 Published online: 16 April 2003 RID="a" ID="a"e-mail: giovanni.darrigo@uniroma1.it     

U-perturbation treatment of heavy fermion systems

Heavy fermion systems are described by the periodic Anderson Model (PAM), i.e. a lattice of localized, highly correlatedf-electron states hybridized with the delocalized states of a conduction band. We treat the PAM within the second orderU perturbation theory around the non-magnetic Hartree-Fock solution (U on site Coulomb correlation between thef-electrons). This treatment has the advantage that Fermi liquid relations (Luttinger theorem) are automatically fulfilled. Thef-electron selfenergy and spectral function are calculated for different temperatures, and, for the symmetric PAM, we obtain single-particle peaks near toE _f andE _f +U and in addition many-particle (Kondo) resonance peaks near to the chemical potential (E _f baref-electron energy). The resonance peaks are strongly temperature dependent and vanish on a characteristic temperature scaleT _K. For the symmetric PAM and a constant on-site hybridization the Fermi energy falls into a hybridization gap. A second, smaller characteristic temperature scaleT _coh (coherence temperature), on which the hybridization gap vanishes, is observed within this approach. For the non-symmetric PAM (i.e.E _f andE _f +U not symmetric around the chemical potential) we obtain a similar behaviour, but the single-particle peaks are no longer at the correct positionsE _f andE _f +U. The proper behaviour for the symmetric PAM but less satisfactory behaviour for the non-symmetric PAM can be understood from the fact that only for the symmetric PAM the exactly solvable limit of a vanishing hybridization is reproduced within this approach.     

Spectral intensities of lanthanide complexes

The effects of solvents and complex formation with nitrogen donor ligands on the spectral intensities of the f→f transitions in Nd(III) ion have been reported. The intensity parameters T_λ have been calculated for 14 systems and are compared with oxygen donor ligands.     

A simple class ofU(N) Racah coefficients and their application

Using permutation group techniques, a general expression is derived for the special class ofU(N) Racah coefficients for which the representations [f ¹] and [f ³] in the recoupling matrix for [f ¹]×[f ²]×[f ³][f] are either both totally antisymmetric or both totally symmetric. For the totally antisymmetric case further specialization gives a simple expression for aU(N) Racah coefficient which is needed in taking the average of the product of operators over the states of an irreducible representation ofU(N), where this result can be useful in the study of identical fermion systems by spectral distribution methods.Supported by the US National Science Foundation.     

Lattice site occupation and precipitate dissolution of implanted and irradiated Al(Rh) and Al(Ir)

Abstract

The apparent substitutional fraction, f_s , of Rh and Ir implanted into Al single crystals at 293 K with peak concentrations of 0.17±0.01 at.% is 0.57 ± 0.02 and 0.47±0.02, respectively. Upon annealing to 593 K f_s decreases and the critical angles of the impurities narrow due to partially coherent precipitate formation. Irradiation with 300 keV Ar ions at 77 K with deposited energy densities up to 20 dpa leads to precipitate dissolution accompanied by an increase of f_s up to 0.70±0.02 for Al(Rh) and 0.82±0.02 for Al(Ir). The relatively high f_s values do not decrease during annealing from 77 K to 293 K, indicating that vacancy trapping is not a dominant process. Precipitate formation seems therefore to limit the maximum obtainable f_s values during implantation at 293 K for these systems.     

Time Reversal and Tomographic Representation for Signal Processing in Living Systems

The tomographic representation for signal processing opens new opportunities for studies of living system signals. Some signals can be described by functions of time f(t), which are approximately connected with each other by reversing of time. In this case, there is a possibility to observe transformation of tomograms for such functions. We obtain the correspondence of tomograms for functions f(t) and f(?t) in the vicinity of the frequency scale and illustrate by the examples of electric impedance of rat femoral artery pulsing in two different modes. We show that the use of a reference signal for signal processing of living systems provides new opportunities for employing both – their standard Fourier transforms and tomograms – to obtain new additional and useful information.