Resonances and Gamow States in Non-Local Potentials

For a large class of non-local, non separable potentials with non-compact support, the solution of the radial integrodifferential equation may be reduced to the solution of a homogeneous linear integral equation of Fredholm type with a quadratically integrable kernel. In this way we derive expansions of the wave functions and the Green's function of the Schrödinger equation with a non-local potential in terms of bound states, resonant states and a continuum of scattering functions with complex wave number. The rules of normalization, orthogonality and completeness satisfied by the eigenstates of the Schrödinger equation belonging to complex eigenvalues with Im E_n < 0, (Gamow or resonant states) are also derived. Finally, by means of a realistic example, it is shown how to use these expansions to exhibit the resonant behaviour of the differential cross section. Explicit expressions for the transition amplitudes and the partial widths in terms of expectation values of operators computed with Gamow functions are given.     

Structural manipulation of pyrochlores: Thermal evolution of metastable Gd2(Ti1−yZry)2O7 powders prepared by mechanical milling

The structural and microstructural characteristics of metastable Gd₂(Ti_1−yZr_y)₂O₇ powders prepared by mechanical milling have been studied by a combination of XRD and Raman spectroscopy. Irrespective of their Zr content, as-prepared powder phases present an anion-deficient fluorite-type of structure as opposed to the pyrochlore equilibrium configuration obtained for the same solid solution by other synthetic routes. These fluorites are stable versus thermal activation, at least up to temperatures of 800 °C. For the Ti-rich compositions, thermal treatments at higher temperatures facilitate the rearrangement of the cation and anion substructures and the relaxation of mechanochemically induced defects whereas for compositions with high Zr content, the fluorite crystal structure is retained even at temperatures as high as 1200 °C. Interestingly enough, transient pyrochlores showing a very unusual cation distribution were observed during the thermally induced defect-recovery process.     

Corrosion products on steel 20 in aerated hydrazine solutions: Mössbauer study

Composition of corrosion layers on steel 20 in aerated solutions with hydrazine concentrations less than 11 ppm was studied at 50, 60, and 80°C in dynamic conditions by transmission Mössbauer spectroscopy and X-ray diffraction as supplementary technique. Corrosion rates were determined by gravimetric method. A comparison with corrosion in water at 80°C was made. The observed layers have not any protective character. For 0.1 m/s linear velocity, they are composed by nonstoichiometric magnetite, (Fe_3?x O₄,x=0.02–0.04) with lepidocrocite (γ-FeOOH) as secondary phase at 50°C. Haematite (α-Fe₂O₃) is observed at 60 and 80°C with a 19 nm particle size. It becomes smaller for higher velocity (0.7 m/s).     

Banach-stone theorems and separating maps

LetC(X,E) andC(Y,F) denote the spaces of continuous functions on the Tihonov spacesX andY, taking values in the Banach spacesE andF, respectively. A linear mapH:C(X,E)→C(Y,F) isseparating iff(x)g(x)=0 for allx inX impliesHf(y)Hg(y)=0 for ally inY. Some automatic continuity properties and Banach-Stone type theorems (i.e., asserting that isometries must be of a certain form) for separating mapsH between spaces of real- and complex-valued functions have already been developed. The extension of such results to spaces of vector-valued functions is the general subject of this paper. We prove in Theorem 4.1, for example, for compactX andY, that a linear isometryH betweenC(X,E) andC(Y,F) is a “Banach-Stone” map if and only ifH is “biseparating (i.e,H andH ⁻¹ are separating). The Banach-Stone theorems of Jerison and Lau for vector-valued functions are then deduced in Corollaries 4.3 and 4.4 for the cases whenE andF or their topological duals, respectively, are strictly convex. Research supported by the Fundació Caixa Castelló, MI/25.043/92     

Birefringent filter with amplitude beats

In this work, we show a very simple birefringent filter useful to modulate a broadband light spectrum. We first show the generation of various oscillating spectra using two identical multiple-order waveplates. In particular a sinusoidal broadband spectrum with a rapid oscillation is obtained. This spectrum is amplitude modulated by adding another waveplate to the system. This waveplate has a small phase shift, and with the proper orientation generates amplitude beats on the broadband spectrum. Finally, we show how this system can be voltage controlled by means of a ferroelectric liquid crystal modulator. We experimentally demonstrate this behavior with the aid of a portable spectrophotometer, and we provide a theoretical explanation on the basis of the Jones matrix formalism.     

Site segregation in size-mismatched nanoalloys: Application to Cu-Ag

In order to determine the energetic driving forces for surface segregation in bimetallic clusters, we use a combined approach coupling numerical simulations within an N-body interatomic potential and a lattice-gas model. This approach, which has been used successfully to study both the superficial segregation in semi-infinite alloys and the intergranular segregation, allows us to determine the relative contributions of the three elementary driving forces for the different sites of the cluster surface (vertices, edges and facets) in both dilute limits for the Cu-Ag system. We show that the segregation hierarchy based on broken-bond arguments (preferential segregation to the vertex sites, less to edge sites, and least to facet sites) is not at all universal. In particular, unusual hierarchies are predicted when the sizes of the constituents are strongly different. Furthermore, we compare the segregation driving forces for cubo-octahedral and icosahedral clusters. They are similar for the vertex sites and edge sites, whereas they differ significantly for the sites of the triangular facets. The segregation of the species with the largest atomic radius (Ag) is indeed largely enhanced in the icosahedral structure due to dilations of the orthoradial distances.