Resonances, scattering theory, and rigged Hilbert spaces

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,''in,'' and ''out'' eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ''out'' eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ''complete'' sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ''out'' eigenvectors. The free, ''in'' and ''out'' eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Influence of Solvent on Photoinduced Electron-Transfer Reaction: Time-Resolved Resonance Raman Study

Time-resolved resonance Raman spectroscopy (TR3) has been used to study the effect of solvent polarity on the mechanism and nature of intermediates formed in photoinduced electron-transfer reaction between triplet flouranil ((FL)-F-3) and tetramethylbenzene (TMB). Comparison of the TR3 spectra in polar, nonpolar, and medium polar media suggests that formation of radical anion due to electron-transfer reaction between (FL)-F-3 and TMB is favored in more polar solvents, whereas ketyl radical formation is more favored in less polar media. Compared to ketyl radical, the extent of radical anion formation is negligible in nonpolar solvents. Therefore, it is inferred that in nonpolar media ketyl radical is mainly generated by hydrogen-transfer reaction in the encounter complex between (FL)-F-3 and TMB. In solvents of medium polarity, the ion-pair decay leads to the formation of both ketyl radical and ketyl radical formed from the encounter between triplet state and the donor. Thus, competition between the formation of ketyl radical and ion pair is influenced by the solvent polarity. The nature of the ion pair in different solvent polarity has been investigated from the changes observed in the vibrational frequency of (fluoranil) FL part of the complex.

On Calculation Of Breakdown Voltages Of Mixtures Of Electron Attaching Gases

In this paper we report the analysis of dc breakdown tests on mixtures of CC12F2, SF6, C-C4F8, 2-C4F8, N2, C02, CF4, CHF3, and 1,1,1-CH3CF3 gases on the basis of the NKH formula Vmix=k(pd)aNbUC developed by us earlier for the binary mixtures of SF6 with air, N2, N20, and CO2. It is shown that while a and c have the values 0.915 and 0.850 respectively as earlier, k and b depend on the component gases. There is a good agreement between the calculated values on the basis of the formula and measured values reported in the literature.

Cr3+ electron paramagnetic resonance study of Sn(1-x)CrxO(2) (0.00 <= x <= 0.10)

This paper reports on the liquid-helium-temperature (5 K) electron paramagnetic resonance (EPR) spectra of Cr3+ ions in the nanoparticles of SnO2 synthesized at 600 degrees C with concentrations of 0%, 0.1%, 0.5%, 1%, 1.5%, 2.0%, 2.5%, 3.0%, 5.0%, and 10%. Each spectrum may be simulated as overlap of spectra due to four magnetically inequivalent Cr3+ centers characterized by different values of the spin-Hamiltonian parameters. Three of these centers belong to Cr3+ ions in orthorhombic sites, situated near oxygen vacancies, characterized by very large zero-field splitting parameters D and E, presumably due to the presence of nanoparticles in the samples. The fourth EPR spectrum belongs to the Cr3+ ions situated at sites with tetragonal symmetry, substituting for the Sn4+ ion, characterized by a very small value of D. In addition, there appears a ferromagnetic resonance line due to oxygen defects for samples with Cr3+ concentrations of <= 2.5%. Further, in samples with Cr3+ concentrations of >2.5%, there appears an intense and wide EPR line due to the interactions among the Cr3+ ions in the clusters formed due to rather excessive doping; the intensity and width of this line increase with increasing concentration. The Cr3+ EPR spectra observed in these nanopowders very different from those in bulk SnO2 crystals.

Molecularly adsorbed oxygen on metals: electron spectroscopic studies

Oxygen is shown to adsorb molecularly on gold as well as on Ag and Pt. UV and X-ray photoelectron spectroscopy and Auger electron spectroscopy have been employed to investigate electron states of molecularly adsorbed oxygen.

Highly Enhanced Thermopower in Two-Dimensional Electron Systems at Millikelvin Temperatures

We report experimental observation of an unexpectedly large thermopower in mesoscopic two-dimensional (2D) electron systems in GaAs/AlGaA heterostructures at sub-Kelvin temperatures and zero magnetic field. Unlike conventional nonmagnetic high-mobility 2D systems, the thermopower in our devices increases with decreasing temperature below 0.3 K, reaching values in excess of 100 mu V/K, thus exceeding the free electron estimate by more than 2 orders of magnitude. With support from a parallel study of the local density of states, we suggest such a phenomenon to be linked to intrinsic localized states and many-body spin correlations in the system.

Studies of Solids and Surfaces by Auger Electron Spectroscopy

Although the applications of Auger electron spectroscopy in surface analysis have by far outweighed its use as a tool to investigate electron states of solids and surfaces, there are a variety of situations where Auger spectroscopy provides unique information. Apart from the chemical shifts, Auger intensities are useful in determining the number of d-electron states in transition metal systems. Auger spectroscopy is a good probe to investigate the surface oxidation of metals. In addition to the intra-atomic Auger transitions, inter-atomic transitions observed in oxides and other systems reveal the nature of electron states of surfaces. Charge-transfer and hybridization effects in alloys are also usefully studied by Auger spectroscopy. Auger electron spectroscopy has not been a popular technique to investigate adsorption of molecules on surfaces, but the technique is useful to obtain fingerprints of surface species.

Electron energy loss spectroscopy (EELS) of H2O, H2S, H2Se and H2Te

Electronic excitation in H2O, H2S, H2Se and H2Te molecules has been studied by the EELS technique. Spectra of H2S and H2Se are remarkably similar with the 1b1-nd transition most intense. The intensity of the first transition 1b1-nsa1 decreases through H2O to H2Se and this transition is absent in H2Te. Transitions observed by EELS have been compared with optical absorption studies. A correlation diagram of the occupied and the excited states has been provided for these four molecules by making use of UVPES and EELS.

Electron-electron interactions in polyacetylene

Experimental evidence for strong electron-electron interactions in polyacetylene is presented. These include (i) observation of a dipole forbidden state below the optical gap, (ii) observation of negative spin densities at sites at which noninteracting models predict zero spin density (iii) vanishing optical gap, in the infinite chain limit, in the closely related symmetrical linear cyanine dyes. To correctly explain these features it is necessary to solve correlated model Hamiltonians. Using diagrammatic valence bond method model exact solutions of correlated models of finite-size systems can be obtained and various physical properties of the low-lying states can be computed. These properties, when extrapolated to the infinite chain limit explain many of the experimental features observed in polyacetylene.

An Electron-Microscopic Investigation Of Oxides Related To Beta-Alumina

High resolution electron microscopic (HREM) investigation of potassiumbeta-alumina and the related gallate and ferrite has revealed that whereas the aluminate and gallate are highly disordered, consisting of random sequence ofbeta andbetaPrime units, the ferrite is more ordered. The aluminate and gallate are sensitive to electron beam irradiation exhibiting beam-induced damage similar to sodiumbetaPrime-alumina. Significantly, the ferrite is beamstable, the difference in behaviour amongst these related oxides arising from the different mechanisms by which alkali metal nonstoichiometry is accommodated. Barium hexaaluminate and hexaferrite are both highly ordered; specimens prepared by the barium borate flux method exhibit a new radic3a×radic3a superstructure of the hexagonal magnetoplumbite cell.

A novel investigation of vapor-phase charge-transfer complexes of halogens with n-donors by electron energy loss spectroscopy

Complexes of I2 with diethyl ether and triethylamine and of Br, with diethyl ether have been investigated in the vapor phase for the first time by employing electron energy loss spectroscopy. Besides the CT bands, blue-shifted vacuum-UV bands of the halogens have been assigned; the amine-I, system appears to exhibit two CT bands,associated with two different excited states of the complex.

Electron-Energy Loss Spectroscopy (Eels) Of Organic-Molecules In Vapor-Phase - Design And Fabrication Of An Indigenous Eel Spectrometer

An indigenous electron energy loss spectrometer has been designed and fabricated for the study of free molecules. The spectrometer enables the recording of low-resolution electronic spectra of molecules inthe vapour phase with ready access to the vacuum ultraviolet region. Electron energy loss spectra of aliphatic alcohols and carbonyl compounds as wellas of benzene derivatives have been recorded with the indigenous spectrometer and the electronic transitions in these molecules discussed.

Characterization of Nanomaterials by Physical Methods

Much progress in nanoscience and nanotechnology has been made in the past few years thanks to the increased availability of sophisticated physical methods to characterize nanomaterials. These techniques include electron microscopy and scanning probe microscopies, in addition to standard techniques such as X-ray and neutron diffraction, X-ray scattering, and various spectroscopies. Characterization of nanomaterials includes the determination not only of size and shape, but also of the atomic and electronic structures and other important properties. In this article we describe some of the important methods employed for characterization of nanostructures, describing a few case studies for illustrative purposes. These case studies include characterizations of Au, ReO3, and GaN nanocrystals; ZnO, Ni, and Co nanowires; inorganic and carbon nanotubes; and two-dimensional graphene.

An electron microscopic study of quasicrystals in a quaternary alloy : Mg32(Al, Zn, Cu)49

The discovery of a solid exhibiting m 3 5 point group symmetry by Shechtman et. al. (l) in a rapidly solidified Al-14at%Mn alloy has activated intensive studies of a new class of solids, termed as quasicrystals (2). While the original discovery reported the existence of quasicrystals in AI-Mn. AI-Fe and AI-Cr alloys, subsequent work has revealed their existence in Mg-Zn-Al(3,4), Mg-A]-Cu(5), AI-Mn-Si(6) and Ti-Ni-V(7) alloys (Table l).

Insulating phase of a disordered system: Fermi glass versus electron glass

The authors examine the critical divergence of the low-frequency conductivity of the noninteracting Fermi glass and interacting electron glass models of the insulating phase of a disordered system as the metallic phase is approached. Results for the two are found to be rather different, which can be tested experimentally. In particular, for the electron glass, there exists a nonvanishing contribution to the dielectric constants from the low-frequency (hopping) conductivity even at low temperatures, which scales with the high-frequency (optical) contribution, and diverges with the same exponent at the insulator-metal transition.