Semiclassical complex angular momentum theory and Pade reconstruction for resonances, rainbows, and reaction thresholds

A semiclassical complex angular momentum theory, used to analyze atom-diatom reactive angular distributions, is applied to several well-known potential (one-particle) problems. Examples include resonance scattering, rainbow scattering, and the Eckart threshold model. Pade reconstruction of the corresponding matrix elements from the values at physical (integral) angular momenta and properties of the Pade approximants are discussed in detail.

Angular distribution for the elastic scattering of electrons from Ar+(3s^2 3p^5 ^2P) above the first inelastic threshold

The measured angular differential cross section (DCS) for the elastic scattering of electrons from Ar+(3s2 3p5 2P) at the collision energy of 16 eV is presented. By solving the Hartree-Fock equations, we calculate the corresponding theoretical DCS including the coupling between the orbital angular momenta and spin of the incident electron and those of the target ion and also relaxation effects. Since the collision energy is above one inelastic threshold for the transition 3s2 3p5 2P–3s 3p6 2S, we consider the effects on the DCS of inelastic absorption processes and elastic resonances. The measurements deviate significantly from the Rutherford cross section over the full angular range observed, especially in the region of a deep minimum centered at approximately 75°. Our theory and an uncoupled, unrelaxed method using a local, spherically symmetric potential by Manson [Phys. Rev. 182, 97 (1969)] both reproduce the overall shape of the measured DCS, although the coupled Hartree-Fock approach describes the depth of the minimum more accurately. The minimum is shallower in the present theory owing to our lower average value for the d-wave non-Coulomb phase shift s2, which is due to the high sensitivity of s2 to the different scattering potentials used in the two models. The present measurements and calculations therefore show the importance of including coupling and relaxation effects when accurately modeling electron-ion collisions. The phase shifts obtained by fitting to the measurements are compared with the values of Manson and the present method.

THEORY AND DESIGN OF A TUNABLE QUASI-LUMPED QUADRATURE COUPLER

In this article, we present the theory and a design methodology for a unable Quasi-Lumped Quadrature Coupler (QLQC). Because of its topology, the coupler is simply reconfigured by switching the bias of two varactor diodes via a very simple DC bias circuitry. No additional capacitors or inductors are required. A prototype at 3.5 GHz is etched on a 0.130-mm-thick layer substrate with a dielectric material of relative permittivity of 2.22. The simulated and measured scattering parameters are, presented. (c) 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 2219-2222 2009: Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24526

When some is actually all: Scalar inferences in face-threatening contexts

Accounts of the scalar inference from 'some X-ed' to 'not all X-ed' are central to the debate between contemporary theories of conversational pragmatics. An important contribution to this debate is to identify contexts that decrease the endorsement rate of the inference. We suggest that the inference is endorsed less often in face-threatening contexts, i.e., when X implies a loss of face for the listener. This claim is successfully tested in Experiment 1. Experiment 2 rules out a possible confound between face-threatening contexts and lower-bound contexts. Experiment 3 shows that whilst saying 'some X-ed' when one knew for a fact that all X-ed is always perceived as an underinformative utterance, it is also seen as a nice and polite thing to do when X threatens the face of the listener. These findings are considered from the perspective of Relevance Theory as well as that of the Generalized Conversational Inference approach. (C) 2009 Elsevier B.V. All rights reserved.

Convergence of partial-wave expansions for energies, scattering amplitudes and positron annihilation rates

We use many-body theory to find the asymptotic behaviour of second-order correlation corrections to the energies and positron annihilation rates in many- electron systems with respect to the angular momenta l of the single-particle orbitals included. The energy corrections decrease as 1/(l+1/2)4, in agreement with the result of Schwartz, whereas the positron annihilation rate has a slower 1/(l+1/2)2 convergence rate. We illustrate these results by numerical calculations of the energies of Ne and Kr and by examining results from extensive con?guration-interaction calculations of PsH binding and annihilation.

Comparing the implementation of two-dimensional numerical quadrature on GPU, FPGA and ClearSpeed systems to study electron scattering by atoms

The use of accelerators, with compute architectures different and distinct from the CPU, has become a new research frontier in high-performance computing over the past ?ve years. This paper is a case study on how the instruction-level parallelism offered by three accelerator technologies, FPGA, GPU and ClearSpeed, can be exploited in atomic physics. The algorithm studied is the evaluation of two electron integrals, using direct numerical quadrature, a task that arises in the study of intermediate energy electron scattering by hydrogen atoms. The results of our ‘productivity’ study show that while each accelerator is viable, there are considerable differences in the implementation strategies that must be followed on each.

GAUSSIAN PULSE SCATTERING BY NONLINEAR THUE-MORSE QUASIPERIODIC MULTILAYERS

The pulse mixing and scattering by finite nonlinear Thue-Morse quasi-periodic dielectric multilayered structure illuminated by two Gaussian pulses with different centre frequencies and lengths are investigated. The three-wave mixing technique is applied to study the nonlinear processes. The properties of the scattered waveforms and the effects of the structure and the incident pulses' parameters on the mixing process are discussed.

Positron scattering and annihilation in hydrogenlike ions

Diagrammatic many-body theory is used to calculate the scattering phase shifts, normalized annihilation rates Zeff, and annihilation ? spectra for positron collisions with the hydrogenlike ions He+, Li2+, B4+, and F8+. Short-range electron-positron correlations and longer-range positron-ion correlations are accounted for by evaluating nonlocal corrections to the annihilation vertex and the exact positron self-energy. The numerical calculation of the many-body theory diagrams is performed using B-spline basis sets. To elucidate the role of the positron-ion repulsion, the annihilation rate is also estimated analytically in the Coulomb-Born approximation. It is found that the energy dependence and magnitude of Zeff are governed by the Gamow factor that characterizes the suppression of the positron wave function near the ion. For all of the H-like ions, the correlation enhancement of the annihilation rate is found to be predominantly due to corrections to the annihilation vertex, while the corrections to the positron wave function play only a minor role. Results of the calculations for s-, p-, and d-wave incident positrons of energies up to the positronium-formation threshold are presented. Where comparison is possible, our values are in excellent agreement with the results obtained using other, e.g., variational, methods. The annihilation-vertex enhancement factors obtained in the present calculations are found to scale approximately as 1+(1.6+0.46l)/Zi, where Zi is the net charge of the ion and l is the positron orbital angular momentum. Our results for positron annihilation in H-like ions provide insights into the problem of positron annihilation with core electrons in atoms and condensed matter systems, which have similar binding energies.

Positron scattering and annihilation on noble-gas atoms

Positron scattering and annihilation on noble-gas atoms is studied ab initio using many-body theory methods for positron energies below the positronium formation threshold. We show that in this energy range, the many-body theory yields accurate numerical results and provides a near-complete understanding of the positron–noble-gas atom system. It accounts for positron-atom and electron-positron correlations, including the polarization of the atom by the positron and the nonperturbative effect of virtual positronium formation. These correlations have a large influence on the scattering dynamics and result in a strong enhancement of the annihilation rates compared to the independent-particle mean-field description. Computed elastic scattering cross sections are found to be in good agreement with recent experimental results and Kohn variational and convergent close-coupling calculations. The calculated values of the annihilation rate parameter Zeff (effective number of electrons participating in annihilation) rise steeply along the sequence of noble-gas atoms due to the increasing strength of the correlation effects, and agree well with experimental data.

Measurement of The Dynamic Response of Compressed Hydrogen by Inelastic X-Ray Scattering

Measurement of the dynamic properties of hydrogen and helium under extreme pressures is a key to understanding the physics of planetary interiors. The inelastic scattering signal from statically compressed hydrogen inside diamond anvil cells at 2.8 GPa and 6.4 GPa was measured at the Diamond Light Source synchrotron facility in the UK. The first direct measurement of the local field correction to the Coulomb interactions in degenerate plasmas was obtained from spectral shifts in the scattering data and compared to predictions by the Utsumi-Ichimaru theory for degenerate electron liquids.

New pairing scheme to overhaul BCS theory

In a superconductor pair occupancy probabilities are doubly defined with conflicting values when normal and umklapp scattering coexist with the same destination momentum. To resolve this issue a new pairing scheme is introduced to assert normal–umklapp frustration under such circumstances. Superconductivity then arises solely from residual umklapp scattering to destination momenta not reached by normal scattering. Consequent Tc calculations from first principles for niobium, tantalum, lead and aluminum turn out to be accurate within a few percent. A new perspective is revealed to support Matthias׳ rule. New light is also shed relevant to the future study of metallic hydrogen.