Scattering Matrix Elements Research Articles

Scattering Matrix for Typical Urban Anthropogenic Origin Cement Dust and Discrimination of Representative Atmospheric Particulates

AbstractThe complete scattering matrix for cement dust was measured as a function of scattering angle from 5° to 160° at a wavelength of 532 nm, as a representative of mineral dust of anthropogenic origin in urban areas. Other related characteristics of cement dust, such as particle size distribution, chemical composition, refractive index, and micromorphology, were also analyzed. For this objective, a newly improved apparatus was built and calibrated using water droplets. Measurements of water droplets were in good agreement with Lorenz‐Mie calculations. To facilitate the direct applicability of measurements for cement dust in radiative transfer calculation, the synthetic scattering matrix was computed and defined over the full scattering angle range from 0° to 180°. The scattering matrices for cement dust and typical natural mineral dusts were found to be similar in trends and angular behaviors. Angular distributions of all matrix elements were confined to rather limited domains. To promote the application of light‐scattering matrix in atmospheric observation and remote sensing, discrimination methods for various atmospheric particulates (cement dust, soot, smolder smoke, and water droplets) based on the angular distributions of their scattering matrix elements are discussed. The ratio −F12/F11 proved to be the most effective discrimination method when a single matrix element is employed; aerosol identification can be achieved based on −F12/F11 values at 90° and 160°. Meanwhile, the combinations of −F12/F11 with F22/F11 (or (F11 − F22)/(F11 + F22)) or −F12/F11 with F44/F11 at 160° can be used when multiple matrix elements at the same scattering angle are selected.

Fully nonlocal inelastic scattering computations for spectroscopical transmission electron microscopy methods

The complex interplay of elastic and inelastic scattering amenable to different levels of approximation constitutes the major challenge for the computation and hence interpretation of TEM-based spectroscopical methods. The two major approaches to calculate inelastic scattering cross sections of fast electrons on crystals-Yoshioka-equations-based forward propagation and the reciprocal wave method-are founded in two conceptually differing schemes-a numerical forward integration of each inelastically scattered wave function, yielding the exit density matrix, and a computation of inelastic scattering matrix elements using elastically scattered initial and final states (double channeling). Here, we compare both approaches and show that the latter is computationally competitive to the former by exploiting analytical integration schemes over multiple excited states. Moreover, we show how to include full nonlocality of the inelastic scattering event, neglected in the forward propagation approaches, at no additional computing costs in the reciprocal wave method. Detailed simulations show in some cases significant errors due to the z-locality approximation and hence pitfalls in the interpretation of spectroscopical TEM results.

Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison.

The recently derived distributions for the scattering-matrix elements in quantum chaotic systems are not accessible in the majority of experiments, whereas the cross sections are. We analytically compute distributions for the off-diagonal cross sections in the Heidelberg approach, which is applicable to a wide range of quantum chaotic systems. Thus, eventually, we fully solve a problem that already arose more than half a century ago in compound-nucleus scattering. We compare our results with data from microwave and compound-nucleus experiments, particularly addressing the transition from isolated resonances towards the Ericson regime of strongly overlapping ones.

A new fully quantum-mechanical method used to calculate the collisional broadening coefficients and shift coefficients of Rb D1 lines perturbed by noble gases He and Ar**Project supported by the National Natural Science Foundation of China (Grants Nos. 11405077 and 11575073).

In this work, a new full quantum method is proposed to calculate the broadening and shift coefficients of the D1 line in neutral collision. Based on the variable phase approach and Baranger theory, this method calculates the scattering phase shift instead of scattering matrix elements in order to simplify the calculation. As an illustration, this method is used to calculate the broadening and shift coefficients of the absorption lines of alkali metal atom Rb, as it collides with buffer gas He and Ar, in a temperature range from 150 K to 800 K. With a comparison with other calculations and experiment measurements, the reasonable agreements in all cases demonstrate the validity and simplicity of this method.

JaSTA-2: Second version of the Java Superposition T-matrix Application

JaSTA-2: Second version of the Java Superposition T-matrix Application

Three-wave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian.

Large amplitude waves in magnetized plasmas, generated either by external pumps or internal instabilities, can scatter via three-wave interactions. While three-wave scattering is well known in collimated geometry, what happens when waves propagate at angles with one another in magnetized plasmas remains largely unknown, mainly due to the analytical difficulty of this problem. In this paper, we overcome this analytical difficulty and find a convenient formula for three-wave coupling coefficient in cold, uniform, magnetized, and collisionless plasmas in the most general geometry. This is achieved by systematically solving the fluid-Maxwell model to second order using a multiscale perturbative expansion. The general formula for the coupling coefficient becomes transparent when we reformulate it as the scattering matrix element of a quantized Lagrangian. Using the quantized Lagrangian, it is possible to bypass the perturbative solution and directly obtain the nonlinear coupling coefficient from the linear response of the plasma. To illustrate how to evaluate the cold coupling coefficient, we give a set of examples where the participating waves are either quasitransverse or quasilongitudinal. In these examples, we determine the angular dependence of three-wave scattering, and demonstrate that backscattering is not necessarily the strongest scattering channel in magnetized plasmas, in contrast to what happens in unmagnetized plasmas. Our approach gives a more complete picture, beyond the simple collimated geometry, of how injected waves can decay in magnetic confinement devices, as well as how lasers can be scattered in magnetized plasma targets.

Excited helium under high pressures in the bulk and in nanobubbles

We systematically investigate the effects of intense pressures on the excitation energies of helium trapped in bubbles in order to deepen our understanding of the fundamental physics of atoms in extreme conditions. The excitation energy of a confined helium atom is known to differ from that of a free atom being greater in both the bulk liquid or solid or a bubble confined in a metallic matrix state. We compare calculations for the energy shift with both laboratory experiments for bulk systems and results derived from scanning transmission electron microscope (STEM) studies of helium nanobubbles embedded in different matrices. We find excellent agreement between our calculations and the latest extensive measurements in the bulk. However, we find significant discrepancies when we compare with results deduced using the ‘standard’ approach for analysing STEM data. Here, we show the scattering matrix element determining the intensity of this excitation in a STEM experiment is significantly affected by the same environmental factors that shift the excitation energy. Consequently, there is a serious theoretical inconsistency in the way the STEM results are calculated, in that the ‘standard’ approach depends on a supposedly known scattering cross section, whereas we show here that this cross section is itself dependent on the environment. Correcting for this inconsistency does not, in itself, improve agreement.

Lattice thermal transport in La3Cu3X4 compounds (X=P,As,Sb,Bi) : Interplay of anharmonicity and scattering phase space

Thermal conductivities of $\mathrm{L}{\mathrm{a}}_{3}\mathrm{C}{\mathrm{u}}_{3}{X}_{4}(X=\mathrm{P},\phantom{\rule{0.28em}{0ex}}\mathrm{As},\phantom{\rule{0.28em}{0ex}}\mathrm{Sb},\phantom{\rule{0.28em}{0ex}}\mathrm{Bi})$ compounds are examined using first-principles density functional theory and Boltzmann transport methods. We observe a trend of increasing lattice thermal conductivity (${\ensuremath{\kappa}}_{l}$) with increasing atomic mass, challenging our expectations, as lighter mass systems typically have larger sound speeds and weaker intrinsic scattering. In particular, we find that $\mathrm{L}{\mathrm{a}}_{3}\mathrm{C}{\mathrm{u}}_{3}{\mathrm{P}}_{4}$ has the lowest ${\ensuremath{\kappa}}_{l}$, despite having larger sound speed and the most restricted available phase space for phonon-phonon scattering, an important criterion for estimating and comparing ${\ensuremath{\kappa}}_{l}$ among like systems. The origin of this unusual behavior lies in the strength of the individual anharmonic phonon scattering matrix elements, which are much larger in $\mathrm{L}{\mathrm{a}}_{3}\mathrm{C}{\mathrm{u}}_{3}{\mathrm{P}}_{4}$ than in the heavier $\mathrm{L}{\mathrm{a}}_{3}\mathrm{C}{\mathrm{u}}_{3}\mathrm{B}{\mathrm{i}}_{4}$ system. Our finding provides insights into the interplay of harmonic and anharmonic properties of complex, low-thermal-conductivity compounds, of potential use for thermoelectric and thermal barrier coating applications.

Application of the spectral element method to the solution of the multichannel Schrödinger equation.

We apply the spectral element method to the determination of scattering and bound states of the multichannel Schrödinger equation. In our approach, the reaction coordinate is discretized on a grid of points whereas the internal coordinates are described by either purely diabatic or locally diabatic (diabatic-by-sector) bases. Bound levels and scattering matrix elements are determined with spectral accuracy using relatively small number of points. The scattering problem is cast as a linear system solved using state-of-the-art sparse matrix non-iterative packages. Boundary conditions can be imposed so as to compute a single column of the matrix solution. A comparison with log-derivative propagators customarily used in molecular physics is performed. The same discretization scheme can also be applied to bound levels that are computed using direct scalable sparse-matrix solvers.

Improved surface-roughness scattering and mobility models for multi-gate FETs with arbitrary cross-section and biasing scheme

We present a new model for surface roughness (SR) scattering in n-type multi-gate FETs (MuGFETs) and gate-all-around nanowire FETs with fairly arbitrary cross-sections, its implementation in a complete device simulator, and the validation against experimental electron mobility data. The model describes the SR scattering matrix elements as non-linear transformations of interface fluctuations, which strongly influences the root mean square value of the roughness required to reproduce experimental mobility data. Mobility simulations are performed via the deterministic solution of the Boltzmann transport equation for a 1D-electron gas and including the most relevant scattering mechanisms for electronic transport, such as acoustic, polar, and non-polar optical phonon scattering, Coulomb scattering, and SR scattering. Simulation results show the importance of accounting for arbitrary cross-sections and biasing conditions when compared to experimental data. We also discuss how mobility is affected by the shape of the cross-section as well as by its area in gate-all-around and tri-gate MuGFETs.

Theoretical Cross Sections of the Inelastic Fine Structure Transition M(2P1/2) + Ng ↔ M(2P3/2) + Ng for M = K, Rb, and Cs and Ng = He, Ne, and Ar.

Scattering matrix elements of the inelastic fine structure transition M(2P1/2) + Ng ↔ M(2P3/2) + Ng are computed using the channel packet method (CPM) for alkali-metal atoms M = K, Rb, and Cs, as they collide with noble-gas atoms Ng = He, Ne, and Ar. The calculations are performed within the block Born-Oppenheimer approximation where excited state VA2Π1/2(R), VA2Π3/2(R), and VB2Σ1/2(R) adiabatic potential energy surfaces are used together with a Hund's case (c) basis to construct a 6 × 6 diabatic representation of the electronic Hamiltonian. Matrix elements of the angular kinetic energy of the nuclei incorporate Coriolis coupling and, together with the diabatic representation of the electronic Hamiltonian, yield a 6 × 6 effective potential energy matrix. This matrix is diagonal in the asymptotic limit of large internuclear separation with eigenvalues that correlate to the 2Pj alkali atomic energy levels. Scattering matrix elements are computed using the CPM by preparing reactant and product wave packets on the effective potential energy surfaces that correspond to the excited 2Pj alkali states of interest. The reactant wave packet is then propagated forward in time using the split operator method together with a unitary transformation between the adiabatic and diabatic representations. The Fourier transformation of the correlation function between the evolving reactant wave packet and stationary product wave packet yields state-to-state scattering matrix elements as a function of energy for a particular choice of total angular momentum J. Calculations are performed for energies that range from 0.0 to 0.01 hartree and values of J that start with a minimum of J = 0.5 for all M + Ng pairs up to a maximum that ranges from J = 450.5 for KAr to J = 100.5 for CsAr. A sum over J together with an average over energy is used to compute thermally averaged cross sections for a temperature range of T = 0-400 K.

SCATTERING MATRIX FOR THE INTERACTION BETWEEN SOLAR ACOUSTIC WAVES AND SUNSPOTS. I. MEASUREMENTS

ABSTRACT Assessing the interaction between solar acoustic waves and sunspots is a scattering problem. The scattering matrix elements are the most commonly used measured quantities to describe scattering problems. We use the wavefunctions of scattered waves of NOAAs 11084 and 11092 measured in the previous study to compute the scattering matrix elements, with plane waves as the basis. The measured scattered wavefunction is from the incident wave of radial order n to the wave of another radial order n′, for . For a time-independent sunspot, there is no mode mixing between different frequencies. An incident mode is scattered into various modes with different wavenumbers but the same frequency. Working in the frequency domain, we have the individual incident plane-wave mode, which is scattered into various plane-wave modes with the same frequency. This allows us to compute the scattering matrix element between two plane-wave modes for each frequency. Each scattering matrix element is a complex number, representing the transition from the incident mode to another mode. The amplitudes of diagonal elements are larger than those of the off-diagonal elements. The amplitude and phase of the off-diagonal elements are detectable only for and , where is the change in the transverse component of the wavenumber and Δk = 0.035 rad Mm−1.

Light Meson Decay with Gaussian Confinement in a JKJ Decay Model

A form to describe hadron strong decays is in terms of quark and gluon degrees of freedom in microscopic decay models. Initially we assume that strong decays are driven by the same inter-quark Hamiltonian which determines the spectrum, and that it incorporates gaussian confinement. An [Formula: see text] decay matrix element of the JKJ Hamiltonian involves a pair-production current matrix elements times a scattering matrix element. Diagrammatically this corresponds to an interaction between an initial line and produced pair. In this work we apply the model to the light meson sector and calculate the decay rate, comparing with the experimental values.

Physically Based Evaluation of Effect of Buried Oxide on Surface Roughness Scattering Limited Hole Mobility in Ultrathin GeOI MOSFETs

This paper presents a numerical simulation study investigating the effect of buried oxide on surface roughness scattering limited hole mobility ( $\mu _{\mathsf {SR}}$ ) in ultrathin germanium-on-insulator (GeOI) MOSFETs, for the first time. The simulation considers wave function penetration at channel/oxide interface and nonlinear dependence of scattering matrix element on surface fluctuation. Three types of buried oxide materials are compared (GeO2, SiO2, and Si3N4). The $\mu _{\mathsf {SR}}$ increases in the order of SiO2 $\mu _{\mathsf {SR}}$ on buried oxide material is due to surface fluctuation scattering from backside Ge/buried oxide interface. Our simulation results show that Si3N4 and GeO2 are beneficial as buried oxide for mobility enhancement in GeOI MOSFETs, compared with conventional SiO2 as buried oxide. Our findings provide an insight into further improving mobility characteristic.

On the use of the generalized SPRT method in the equivalent hard sphere approximation for nuclear data evaluation

A consistent description of the neutron cross sections from thermal energy up to the MeV region is challenging. One of the first steps consists in optimizing the optical model parameters using average resonance parameters, such as the neutron strength functions. They can be derived from a statistical analysis of the resolved resonance parameters, or calculated with the generalized form of the SPRT method by using scattering matrix elements provided by optical model calculations. One of the difficulties is to establish the contributions of the direct and compound nucleus reactions. This problem was solved by using a slightly modified average R-Matrix formula with an equivalent hard sphere radius deduced from the phase shift originating from the potential. The performances of the proposed formalism are illustrated with results obtained for the 238 U+n nuclear systems.

Quantum jumps, superpositions, and the continuous evolution of quantum states

The apparent dichotomy between quantum jumps on the one hand, and continuous time evolution according to wave equations on the other hand, provided a challenge to Bohr's proposal of quantum jumps in atoms. Furthermore, Schrödinger's time-dependent equation also seemed to require a modification of the explanation for the origin of line spectra due to the apparent possibility of superpositions of energy eigenstates for different energy levels. Indeed, Schrödinger himself proposed a quantum beat mechanism for the generation of discrete line spectra from superpositions of eigenstates with different energies.However, these issues between old quantum theory and Schrödinger's wave mechanics were correctly resolved only after the development and full implementation of photon quantization. The second quantized scattering matrix formalism reconciles quantum jumps with continuous time evolution through the identification of quantum jumps with transitions between different sectors of Fock space. The continuous evolution of quantum states is then recognized as a sum over continually evolving jump amplitudes between different sectors in Fock space.In today's terminology, this suggests that linear combinations of scattering matrix elements are epistemic sums over ontic states. Insights from the resolution of the dichotomy between quantum jumps and continuous time evolution therefore hold important lessons for modern research both on interpretations of quantum mechanics and on the foundations of quantum computing. They demonstrate that discussions of interpretations of quantum theory necessarily need to take into account field quantization. They also demonstrate the limitations of the role of wave equations in quantum theory, and caution us that superpositions of quantum states for the formation of qubits may be more limited than usually expected.

Negative partial density of states in mesoscopic systems

Since the experimental observation of quantum mechanical scattering phase shift in mesoscopic systems, several aspects of it have not yet been understood. The experimental observations have also accentuated many theoretical problems related to Friedel sum rule and negativity of partial density of states. We address these problems using the concepts of Argand diagram and Burgers circuit. We can prove the possibility of negative partial density of states in mesoscopic systems. Such a conclusive and general evidence cannot be given in one, two or three dimensions. We can show a general connection between phase drops and exactness of semi classical Friedel sum rule. We also show Argand diagram for a scattering matrix element can be of few classes based on their topology and all observations can be classified accordingly.

Comparative analysis of proton and pion scattering on the isotopes 6,8Не within Glauber theory

The differential cross sections for p6,8He and p6,8He scattering at the RIKEN andGSI energies (0.073 and 0.7 GeV per nucleon) were calculated on the basis of Glauber theory. Pion and proton interaction with a nucleus is determined by the multiple-scattering series (Glauber operator), so that various collision multiplicities and their contributions to the summed cross section can be taken into account. The use of the α-n-n wave function for 6He and the wave function on the basis of the large-scale shell model (LSSM) for 8He makes it possible to calculate analytically scattering matrix elements.

Light scattering by irregular particles much larger than the wavelength with wavelength-scale surface roughness.

We simulate light scattering by random irregular particles that have dimensions much larger than the wavelength of incident light at the size parameter of X=200 using the discontinuous Galerkin time domain method. A comparison of the DGTD solution for smoothly faceted particles with that obtained with a geometric optics model shows good agreement for the scattering angle curves of intensity and polarization. If a wavelength-scale surface roughness is introduced, diffuse scattering at rough interface results in smooth and featureless curves for all scattering matrix elements which is consistent with the laboratory measurements of real samples.

An Improved Surface Roughness Scattering Model for Bulk, Thin-Body, and Quantum-Well MOSFETs

This paper reports about the implementation in a multisubband Monte Carlo device simulator of a comprehensive surface roughness scattering model, based on a nonlinear relation between the scattering matrix elements and the fluctuations Δ(r) of the interface position. The model is first extended by including carrier screening effects and accounting for scattering at multiple interfaces, and it is then used for the analysis of relevant experimental data sets. We show that the new model can reproduce fairly well the silicon universal mobility curves as well as mobility data for ultrathin-body InGaAs MOSFETs using Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rms</sub> values consistent with atomic force microscopy (AFM) and TEM measurements. Our simulation results and some experimental data also indicate that mobility in InGaAs MOSFETs is reduced with decreasing well thickness, T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W</sub> , with a weaker dependence compared with the T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> behavior observed in Si devices.