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Scattering Amplitude (scattering + amplitude)
Selected AbstractsScattering of charged tensor bosons in gauge and superstring theoriesFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-9 2010I. Antoniadis Abstract We calculate the leading-order scattering amplitude of one vector and two tensor gauge bosons in a recently proposed non-Abelian tensor gauge field theory and open superstring theory. The linear in momenta part of the superstring amplitude has identical Lorentz structure with the gauge theory, while its cubic in momenta part can be identified with an effective Lagrangian which is constructed using generalized non-Abelian field strength tensors. [source] Time asymmetric quantum theory , II.FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 6 2003Relativistic resonances from S -matrix poles Abstract Relativistic resonances and decaying states are described by representations of Poincaré transformations, similar to Wigner's definition of stable particles. To associate decaying state vectors to resonance poles of the S -matrix, the conventional Hilbert space assumption (or asymptotic completeness) is replaced by a new hypothesis that associates different dense Hardy subspaces to the in- and out-scattering states. Then one can separate the scattering amplitude into a background amplitude and one or several "relativistic Breit-Wigner" amplitudes, which represent the resonances per se. These Breit-Wigner amplitudes have a precisely defined lineshape and are associated to exponentially decaying Gamow vectors which furnish the irreducible representation spaces of causal Poincaré transformations into the forward light cone. [source] Model of a superconducting singular Fermi liquid with a first-order phase transitionPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 2 2004Ryszard Gonczarek Abstract Model of s -wave and d -wave superconductivity in a singular Fermi liquid with a divergent scattering amplitude for particles with the same quasi-momenta and opposite spins is formulated and presented with regard to a narrow, nearly half-filled conduction band. The ground state and other eigenstates for the superconducting phase are found. Thermodynamic functions are obtained by the use of the Bogolubov method. The gap equation along with the equation for the chemical potential is derived in a general form and solved in a self-consistent manner for s -wave pairing. Above a certain temperature there are two solutions of the gap equation, however only for the greater one the superconducting phase remains stable. It is shown that the system undergoes a first-order phase transition between the superconducting and the normal phase. The critical temperature and the heat of the transition are found. The temperature dependence of the entropy and the specific heat of the system is also presented. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] High-resolution study of dynamical diffraction phenomena accompanying the Renninger (222/113) case of three-beam diffraction in siliconACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2010A. Kazimirov X-ray optical schemes capable of producing a highly monochromatic beam with high angular collimation in both the vertical and horizontal planes have been evaluated and utilized to study high-resolution diffraction phenomena in the Renninger (222/113) case of three-beam diffraction in silicon. The effect of the total reflection of the incident beam into the nearly forbidden reflected beam was observed for the first time with the maximum 222 reflectivity at the 70% level. We have demonstrated that the width of the 222 reflection can be varied many times by tuning the azimuthal angle by only a few µrad in the vicinity of the three-beam diffraction region. This effect, predicted theoretically more than 20 years ago, is explained by the enhancement of the 222 scattering amplitude due to the virtual two-stage 000 113 222 process which depends on the azimuthal angle. [source] X-ray scattering amplitude of an atom in a permanent external electric fieldACTA CRYSTALLOGRAPHICA SECTION A, Issue 3 2003Vladimir G. Tsirelson Quantum-mechanical description of the X-ray scattering by the many-electron atom in a permanent external electric field is developed in terms of the perturbation theory. Explicit expression for the electric field induced addition to the atomic scattering factor is derived and calculations for some atoms are performed. It was found that the change of the X-ray structure factor due to an electric field is too small to be detected with existing experimental techniques. [source] Towards effective Lagrangians for adelic stringsFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 5-7 2009Article first published online: 20 MAR 200, B. Dragovich Abstract p-Adic strings are important objects of string theory, as well as of p-adic mathematical physics and nonlocal cosmology. By a concept of adelic string one can unify and simultaneously study various aspects of ordinary and p-adic strings. By this way, one can consider adelic strings as a very useful instrument in the further investigation of modern string theory. It is remarkable that for some scalar p-adic strings exist effective Lagrangians, which are based on real instead of p-adic numbers and describe not only four-point scattering amplitudes but also all higher ones at the tree level. In this work, starting from p-adic Lagrangians, we consider some approaches to construction of effective field Lagrangians for p-adic sector of adelic strings. It yields Lagrangians for nonlinear and nonlocal scalar field theory, where spacetime nonlocality is determined by an infinite number of derivatives contained in the operator-valued Riemann zeta function. Owing to the Riemann zeta function in the dynamics of these scalar field theories, obtained Lagrangians are also interesting in themselves. [source] On the absence of large-order divergences in superstring theoryFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 1 2003S. Davis The genus-dependence of multi-loop superstring amplitudes is estimated at large orders in perturbation theory using the super-Schottky group parameterization of supermoduli space. Restriction of the integration region to a subset of supermoduli space and a single fundamental domain of the super-modular group suggests an exponential dependence on the genus. Upper bounds for these estimates are obtained for arbitrary N-point superstring scattering amplitudes and are shown to be consistent with exact results obtained for special type II string amplitudes for orbifold or Calabi-Yau compactifications. The genus-dependence is then obtained by considering the effect of the remaining contribution to the superstring amplitudes after the coefficients of the formally divergent parts of the integrals vanish as a result of a sum over spin structures. The introduction of supersymmetry therefore leads to the elimination of large-order divergences in string perturbation theory, a result which is based only on the supersymmetric generalization of the Polyakov measure and not the gauge group of the string model. [source] X-ray extinction changes due to dislocationsJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 6 2007M. Masimov A correct interpretation of the diffraction phenomenon in crystals with low dislocation content, for which the kinematical scattering theory does not yield any reasonable results, was carried out by X-ray extinction treatments. Different approaches to investigating the dislocation-induced X-ray extinction changes are reviewed and the applicability of the statistical dynamical theory to analysis of the substructure characteristics of crystals is discussed. A relationship between the scattering amplitudes and the dislocation density in crystals is established by using pair correlation functions. A procedure for determination of the substructure characteristics by means of measurements of the integrated intensities is proposed. The tests illustrate satisfactory agreement of the investigated approaches with experimental data. [source] Computer-assisted analysis of TEM diffraction contrast images of (In,Ga)N/GaN nanostructuresPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 12 2008P. Manolaki Abstract III-nitride semiconductor nanostructures are subject of intense studies with respect to their optoelectronic, structural and chemical properties. Important parameters for the wavelength of the emitted light are the chemical composition and the dimensionality of the nanostructures. Transmission electron microscopy is used to determine these characteristics at a nanometer scale. In this work, the information provided by diffraction contrast images of (In,Ga)N/GaN quantum wells (QWs) is studied. Experimental dark-field images alternatively using the 0001 and the 0002 reflection show a different contrast regime. In order to understand the contrast, one has to calculate the intensity Ig of the individual diffracted beam g. The intensity of the 0002 beam is a function of the sum of the atomic scattering amplitudes of the group III and the group V element. Consequently, the 0002 reflection is strain sensitive. According to the kinematical theory the 0001 reflection is forbidden. However, it is excited in the experiment. Therefore, dynamical effects have to be taken into account. The corresponding intensity is calculated by the Howie-Whelan equations. It turns out that the intensity of the 0001 beam strongly depends on the In content of (In,Ga)N. A good agreement of intensity profiles of 0001 dark-field images compared to the theory is found. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Structure determination without Fourier inversion.ACTA CRYSTALLOGRAPHICA SECTION A, Issue 6 2009The parameter-space concept for solving crystal structures from reflection amplitudes (without employing or searching for their phases) is described on a theoretically oriented basis. Emphasis is placed on the principles of the method, on selecting one of three types of parameter spaces discussed in this paper, and in particular on the structure model employed (equal-atom point model, however usually reduced to one-dimensional projections) and on the system of `isosurfaces' representing experimental `geometrical structure amplitudes' in an orthonormal parameter space of as many dimensions as unknown atomic coordinates. The symmetry of the parameter space as well as of the imprinted isosurfaces and its effect on solution methods is discussed. For point atoms scattering with different phases or signs (as is possible in the case of X-ray resonant or of neutron scattering) it is demonstrated that the `landscape' of these isosurfaces remains invariant save certain shifts of origin known beforehand (under the condition that all atomic scattering amplitudes have been reduced to 1 thus meeting the requirement of the structure model above). Partly referring to earlier publications on the subject, measures are briefly described which permit circumventing an analytical solution of the system of structure-amplitude equations and lead to either a unique (unequivocal) approximate structure solution (offering rather high spatial resolution) or to all possible solutions permitted by the experimental data used (thus including also all potential `false minima'). A simple connection to Patterson vectors is given, also a first hint on data errors. References are given for practical details of various solution techniques already tested and for reconstruction of three-dimensional structures from their projections by `point tomography'. We would feel foolish if we tried to aim at any kind of `competition' to existing methods. Having mentioned `pros and cons' of our concept, some ideas about potential applications are nevertheless offered which are mainly based on its inherent resolution power though demanding rather few reflection data (use of optimal intensity contrast included) and possibly providing a result proven to be unique. [source] | |||||||||||||