Resonance studies using the contour deformation method in the complex momentum plane

A contour deformation method (CDM) in the complex momentum plane has been successfully extended and implemented to probe resonances in atomic and molecular systems. Specifically, solution of the Schrödinger equation is performed in momentum space with momentum deformed on a contour in the complex plane. The bound, resonant, and complex continuum states could be directly revealed from the eigenvalues of the Schrödinger equation in the complex momentum plane. The calculations of shape resonances in electron scattering with Na⁺ in Debye plasmas (one channel), and in the charge transfer process ${\mathrm{H}}^{?}(1s^2)+\mathrm{Li}(1s^{2}2s)$ ($1^2{\Sigma }^{+}$) $\to \mathrm{H}(1s)+{\mathrm{Li}}^{?}(1s^{2}2s^2)$ ($2^2{\Sigma }^{+}$) (coupled channels) are given as illustrative examples. It is shown that calculated results from CDM agree very well with those extracted from the eigenphase sum of scattering theories. The effectiveness of CDM is also demonstrated by comparing its results with those obtained by the complex rotation scaling and exterior complex scaling methods. The convergence of CDM results can be obtained by increasing the momentum integration region and the number of integration points. The studied examples demonstrate that CDM could be a powerful tool for studies of resonances in complex atomic and molecular systems.     

Square well/barrier resonances in the potentiodynamic plane

The complex wave number plane equips us with an elegant mathematical construct which can be used to display and classify the different types of states which arise from solution of the time-independent Schrödinger equation for a quantum mechanical potential. The complex wave number plane is also useful for tracking the trajectories of these solutions as the potential is perturbed in some way, often resulting in profound dynamical structure. In this work we propose an alternative coordinate system, which we call the potentiodynamic plane, which has the useful property that the trajectories stay bounded, and apply this to the square well/barrier potential to reveal some new insights.     

Phononic Casimir corrections for Graphene resonator

By calculating a Casimir energy for the acoustic phonons of Graphene, we find some temperature-dependent corrections for the pretension of a Graphene sheet suspended on a trench. We obtain values of the order of few mN/m for these corrections in fully as well as doubly clamped Graphene on a narrow trench with one nanometer width, at room temperature. These values are considerable compared to the experimental values, and can increase the fundamental resonance frequency of the Graphene. The values of these corrections increase by increasing the temperature, and so they can be utilized for tuning the Graphene pretension.     

F*空间上点态半有界和非无界线性算子族的共鸣定理

证明每个F~*空间(即满足第一可数公理的Hausdorff拓扑向量空间)可借助于它的"标准生成伪范数族"来表征.利用标准生成伪范数族P,在F~*空间中引入P-有界集、P-半有界集和P-无界集的概念,建立点态半有界和非无界线性算子族的共鸣定理.作为其推论,得到了Menger概率赋范空间中点态概率半有界和非概率无界线性算子族的共鸣定理,改进并推广了某些已有的结果.     

Resonance strategies for the belting style: Results of a single female subject study

This study explores resonance strategies used for the belting style and associated vocal fold vibratory patterns, for the vowels /e/, /a/, /i/, and /u/ on G4 and B4-flat. Acoustic spectra of belted vowels and their unoptimized, "speech-like" equivalents were compared. Vocal fold vibratory patterns were quantified using electroglottography. Results show that /a/ is inherently suitable for belting and requires no adjustment. For /e/, F2-H5 tuning was observed. For /i/, F1 was detuned from H1, enhancing also H2. For /u/, both F1 and F2 were raised to accomplish F2-H3 tuning. These results show that the loud, bright sound of the belting style is achieved by the implementation of resonance strategies that enhance higher harmonics. Electroglottography revealed that resonance strategies also result in raising the closed quotient (CQ) above 52%, an apparent threshold value for belting.     

Electronic and Resonance Raman Spectra of the μ-tris(Bipyrazine)ruthenium(II)-Hexaquis{ruthenium(II)EDTA} Supramolecular Complex

Abstract

Resonance Raman and electronic spectra of the μ-tris(bipyrazine)ruthenium(II)-hexaquis{ruthenium(II)EDTA} supramolecular complex are reported in this paper. Excitation in the 457–676 nm range leads to the selective enhancement of the Ru-bipyrazine vibrational peaks according to distinct patterns, supporting the assignment of the absorption bands at 670 and 490 nm as charge-transfer (MLCT) transitions from the [Ru^IIEDTA] d_π orbitals to the π₁? and π₂? LUMO levels of the bipyrazine ligand. A vibronic coupling mechanism involving the two excited states is suggested for the excitation at 490 nm. The occurrence of MLCT transitions in the [Ru(bpz)₃]²⁺ central unity, around 440 nm, is supported by the Raman and fluorescence excitation profiles.     

Electronic and Resonance Raman Spectra of the Hexanuclear Cluster [Ru30(02CCH3)6 {(pyrazine)Ru(NH3)5}3 6+

Abstract

The trinuclear [Ru³0(00CCH³)⁶, (pyrazine)³] cluster reacts with pentaammineruthenium(II) ions, yielding a hexanuclear pyrazine bridged complex. The hexanuclear cluster exhibits a broad absorption band around 1000 nm and a strong band at 533 nm, ascribed to metal-metal and metal-pyrazine charge transfer transitions, respectively. Excitation at the visible band leads to the enhancement of the totally symmetric vibrational modes of pyrazine at 1605, 1230, 1085 and 700 cm?¹, and of a vibrational peak at 335 cm?¹, ascribed to the Ru(peripheral)-N(pyrazine) stretching mode. The spectroscopic data are consistent with a weak coupling between the central and peripheral ruthenium ions.     

Magnetic resonance investigations of LaCl 3 :Ce 3+ scintillators

In undoped and Ce 3+ -doped LaCl 3 EPR has been detected in the X-ray luminescence (XL-EPR) in K-band (25 v GHz) at 1.5 v K. Two excited triplet states with different EPR parameters and spectral shapes could be separated, both triplet states have been attributed to "out-of-plane" self-trapped excitons (STE) in LaCl 3 . No EPR signals of V K centres (self-trapped holes) could be detected in undoped or Ce 3+ -doped LaCl 3 after X-irradiation at low temperatures. X-irradiation of undoped LaCl 3 creates also an EPR spectrum which can be tentatively attributed to F-type defects. The scintillation mechanism is discussed.     

Photoinduced oxygen-vacancy related centers in PbWO 4 : Electron spin resonance and thermally stimulated luminescence study

Using electron spin resonance (ESR) and thermally stimulated luminescence (TSL) three different electron traps based on regular W sites perturbed by oxygen vacancies have been identified in PbWO 4 . Analysis of ESR spectra parameters ( g -factor values and principal axes orientations) has shown that revealed centers are (WO 3 ) m vacancy containing complex anions associated with a defect in Pb sublattice: (WO 3 ) m m A Pb complexes. One of the centers (W 1 ) is thermally stable up to 350-370 v K, while the other two (W 2 and W 3 ) only to 270-290 v K. Above these temperatures trapped electrons become free and recombine with localized holes, giving rise to TSL glow peaks at T\approx 323\,\hbox{K} and 365\,\hbox{K} . Using the initial rise method the 323\,\hbox{K} TSL peak-shape was fitted allowing the first order recombination kinetic that gives trap parameters E = 0.88\,\hbox{eV} and s\simeq 5\ast 10^{12}1/\hbox{s} .