Rayleigh Scattering Cross Section Research Articles

Study of The X-ray Coherent Scattering Cross Section of Copper

In this study the coherent scattering function ƒ(k) has been calculated for x-ray in Copper using the Wave function involving Slater’s roles approximation for the values 0 ≤ k ≤ 1.6 A0-1, The Rayleigh scattering cross section, has been calculated. The Rayleigh scattering cross section was found to be dominate at low energy, where the scattering cross section starting from very small energy and less than 1KeV, Also the increasing of angular distribution for Rayleigh scattering cross section is principle dependent on the value of atomic scattering factor f(k), and observed Rayleigh scattering decreasing at high energies, while it is more distinct at low energies, for this reason the Rayleigh scattering is very important at low energies, because the scattering angle is large.

Quantitative 2D thermometry in turbulent sooting non-premixed flames using filtered Rayleigh scattering.

This paper demonstrates the application of a thermometry method in turbulent sooting non-premixed flames using filtered Rayleigh scattering (FRS). Fuel tailoring is used to establish a specific C2H2-based fuel mixture such that temperature can be determined accurately by a single FRS measurement over the entirety of mixture fraction space, or equivalently, for all relevant thermo-chemical states. Evaluation is performed in a hierarchy of flows to establish measurement precision and accuracy. Initial assessments in a series of heated fuel mixtures; non-sooting, near-adiabatic flat flames; and laminar non-premixed sooting flames show accuracy of the approach over a full range of expected temperatures and high single-shot measurement precision (e.g., 65<SNR<80) for temperatures between 1900 and 2200 K. Subsequently, 2D temperature measurements are evaluated in a turbulent non-premixed sooting flame. For the current fuel mixture, the local mixture-averaged Rayleigh scattering cross section is nearly constant over all composition space, and thus traditional laser Rayleigh scattering (LRS) is used as a measurement standard in the absence of soot. The results show excellent agreement between the proposed FRS thermometry approach and LRS in non-sooting regions. In the presence of soot, the proposed FRS-based approach shows no signs of interference. In addition, 2D temperature imaging shows high SNR (60-74) over all temperature conditions. Thus, we believe the proposed methodology successfully provides a high-resolution 2D temperature method under turbulent sooting flame conditions.

Single femtosecond laser pulse excitation of individual cobalt nanoparticles

Laser-induced manipulation of magnetism at the nanoscale is a rapidly growing research topic with potential for applications in spintronics. In this work, we address the role of the scattering cross section, thermal effects, and laser fluence on the magnetic, structural, and chemical stability of individual magnetic nanoparticles excited by single femtosecond laser pulses. We find that the energy transfer from the fs laser pulse to the nanoparticles is limited by the Rayleigh scattering cross section, which in combination with the light absorption of the supporting substrate and protective layers determines the increase in the nanoparticle temperature. We investigate individual Co nanoparticles (8 to 20 nm in size) as a prototypical model system, using x-ray photoemission electron microscopy and scanning electron microscopy upon excitation with single femtosecond laser pulses of varying intensity and polarization. In agreement with calculations, we find no deterministic or stochastic reversal of the magnetization in the nanoparticles up to intensities where ultrafast demagnetization or all-optical switching is typically reported in thin films. Instead, at higher fluences, the laser pulse excitation leads to photo-chemical reactions of the nanoparticles with the protective layer, which results in an irreversible change in the magnetic properties. Based on our findings, we discuss the conditions required for achieving laser-induced switching in isolated nanomagnets.

Rayleigh scattering formalism for the tune-out wavelength: Application to the 2 3 S state of helium

SynopsisThe tune-out wavelength for an atom interacting with an incident laser beam is reformulated as a zero in the Rayleigh scattering cross section instead of the dynamic polarizability (or AC Stark shift). The two pictures are equivalent in lowest order, but not when higher-order retardation effects are taken into account. Detailed high-precision calculations in Hylleraas coordinates will be presented for the tune-out wavelength of helium at 413 nm near the 2 3 S – 33 P optical transition, including D-wave retardation corrections, and compared with recent high-precision measurements.

Quantitative planar temperature imaging in turbulent non-premixed flames using filtered Rayleigh scattering.

The paper presents results demonstrating the application of filtered Rayleigh scattering (FRS) for quantitative temperature measurements within turbulent non-premixed jet flames. Through targeted fuel tailoring, i.e., the selection of a specific fuel mixture, temperature measurements are made under non-premixed fueling conditions with a single FRS measurement. For this to be feasible, the instantaneous measured FRS signal is uniquely proportional to the local temperature for all thermo-chemical states of the targeted fuel-oxidizer system. Simulated results using laminar, counterflow flame calculations show that for select CH4/H2/Ar fuel mixtures issuing into air, a unique relationship between the local FRS signal and temperature is achieved for all mixture fraction values over a full range of operating conditions from near-equilibrium to near-extinction flames. Furthermore, for the selected FRS-optimized fuel, the local mixture-averaged Rayleigh scattering cross section is nearly constant from fuel to oxidizer to products. Thus, traditional laser Rayleigh scattering (LRS) can be used to determine the temperature as a "standard" to which to compare and assess the FRS-based temperature results. Simultaneous LRS-FRS temperature measurements from Re=10,000, 20,000, and 30,000 turbulent non-premixed jet flames are presented that show good agreement between the two techniques in terms of instantaneous temperature fields and statistical quantities at various spatial locations within the flame. These results provide confidence that the current approach of FRS thermometry allows for accurate temperature measurements within the selected set of turbulent non-premixed flames.

Helium tune-out wavelength: Gauge invariance and retardation corrections

The problem of calculating the tune-out wavelength for an atom interacting with a plane electromagnetic wave is formulated as a zero in the Rayleigh scattering cross section, rather than a zero in the dynamic polarizability. Retardation (finite wavelength) corrections are discussed in the velocity gauge, and possible gauge transformations to a length form are investigated. For the special case of S-states, it is shown that a pure length form exists for the leading pxz retardation correction, even though one does not exist in general. The results of high-precision calculations in Hylleraas coordinates are presented for the tune-out wavelength of helium near the 23S − 33P transition at 413 nm.

Experimental assessment of the Tenti S6 model for combustion-relevant gases and filtered Rayleigh scattering applications

Accurate descriptions of Rayleigh–Brillouin scattering (RBS) spectra for gas-phase species are important in light scattering measurement techniques including filtered Rayleigh scattering (FRS). The current manuscript targets evaluation of the well-known Tenti S6 model for calculating the RBS spectra for combustion-relevant species over a broad range of temperatures with relevance towards FRS applications in reacting flows. In this work, testing of the Tenti S6 model was performed by comparing measured FRS signals to synthetic FRS signals generated through the combination of the Tenti S6 model and an experimentally verified I2 absorption model. First, temperature-dependent FRS signals were measured for a number of individual gases including Ar, N2, O2, CH4, H2, CO, and CO2 from 300 to 1400 K. Comparisons between the measurements and synthetic FRS signals show excellent agreement (< 4% average difference) over the full temperature range. For pure CO2, rotational Raman scattering effects must be taken into account when comparing measured and synthetic FRS signals. FRS measurements in binary mixtures were performed to assess the commonly used (but not verified) assumption that the total FRS signal from a mixture can be treated as the mole fraction-weighted average of the FRS signals from each component. Measured FRS signals in mixtures with large variations in both molecular weight and Rayleigh scattering cross section show a linear relationship with constituent mole fraction, indicating that this assumption is valid within the kinetic regime. Finally, FRS measurements were performed in near-adiabatic H2/air and CH4/air flames. Comparisons between measured and synthetic FRS signals show excellent agreement over a broad range of equivalence ratios ( $$\phi$$ ), which includes a temperature range of 1100 < T(K) < 2400 and large relative changes in species mole fractions. Overall, the results indicate that the predicted RBS lineshapes calculated using the Tenti S6 model are sufficiently accurate in the context of FRS measurements for the species and temperatures evaluated.

Calculation of Rayleigh Scattering (Coherent) Cross Section in Aluminum

Calculation of Rayleigh Scattering (Coherent) Cross Section in Aluminum

Measurement of large angle Rayleigh scattering cross sections for 39.5, 40.1 and 45.4 keV photons in elements with 26 ≤ Z ≤ 83

The present work reports Rayleigh scattering cross section measurements for the 39.5keV (Sm- Kα2), 40.1keV (Sm-Kα1) and 45.4keV (Sm-Kβ1,3) X-ray photons in 35 elements with 26 ≤ Z ≤ 83 at backward angle of 139°. The scattering measurements were performed in reflection mode geometrical set up involving a secondary photon source consisting of Samarium (62Sm) target excited by the 59.54keV γ-rays from the 241Am radioactive source. The scattered photons were detected using a low energy germanium (LEGe) detector. The product of detector efficiency, intensity of incident photons and other geometrical factors were determined by measuring the K X-ray yields from targets with 47 ≤ Z ≤ 59 and knowledge of the respective K X-ray fluorescence cross sections. The measured cross sections are compared with the theoretical cross sections based on the modified form factor (MF) formalisms and the second-order S-matrix approach. The experimental results demonstrate large deviations from the MF values for the elements with K shell binding energy (BK) in vicinity of the incident photon energy (Ein), which smooth out with inclusion of the anomalous scattering factors (ASFs). The S-matrix values, in general, agree with the measured cross sections for all the elements under investigation.

Rayleigh scattering cross-section measurements of nitrogen, argon, oxygen and air

Knowledge about Rayleigh scattering cross sections is relevant to predictions about radiative transfer in the atmosphere, and needed to calibrate the reflectivity of mirrors that are used in high-finesse optical cavities to measure atmospheric trace gases and aerosols. In this work we have measured the absolute Rayleigh scattering cross-section of nitrogen at 405.8 and 532.2nm using cavity ring-down spectroscopy (CRDS). Further, multi-spectral measurements of the scattering cross-sections of argon, oxygen and air are presented relative to that of nitrogen from 350 to 660nm using Broadband Cavity Enhanced Spectroscopy (BBCES). The reported measurements agree with refractive index based theory within 0.2±0.4%, and have an absolute accuracy of better than 1.3%. Our measurements expand the spectral range over which Rayleigh scattering cross section measurements of argon, oxygen and air are available at near-ultraviolet wavelengths. The expressions used to represent the Rayleigh scattering cross-section in the literature are evaluated to assess how uncertainties affect quantities measured by cavity enhanced absorption spectroscopic (CEAS) techniques. We conclude that Rayleigh scattering cross sections calculated from theory provide accurate data within very low error bounds, and are suited well to calibrate CEAS measurements of atmospheric trace gases and aerosols.

Near-infrared Rayleigh scattering of SF6

Cavity ring-down measurements have been performed on sulphur hexafluoride, in order to determine the extinction in the pressure range from 0 to 20 bar at 20°C (293 K), by using a tunable continuous wave distributed feedback diode laser emitting around 1180 nm. The cavity loss rate has been found to have both a linear dependence and a quadratic dependence on the gas density. While the linear component has been identified with the Rayleigh scattering, the quadratic component is likely due to collision-induced processes. The Rayleigh scattering cross section at 1180 nm has been determined as (1.25 ± 0.18) × 10−27 cm2 and has been compared with Rayleigh scattering cross sections measured in the deep-ultraviolet and visible spectral region.

Broadband transparency with a graded anisotropic metal–dielectric sphere

By applying Rayleigh scattering theory, we explore the scattering of electromagnetic waves by a non-magnetic graded anisotropic sphere in quasi-static conditions. The electric permittivity tensor of the sphere is radially anisotropic, with different radial and tangential components characterized by the lossless graded Drude model. The Rayleigh scattering cross section (RSCS) and the electric polarization of the sphere, as well as the distribution of electric field in the sphere, are calculated both analytically and numerically. The results not only indicate a broadband electromagnetic transparency caused by the graded anisotropic constitutive profile, but also reveal the physical mechanisms behind this phenomenon. In addition, by comparing the results for graded and non-graded isotropic spheres, it is demonstrated that the graded anisotropic sphere leads to a better broadband electromagnetic transparency.

Consistency of a causal theory of radiative reaction with the optical theorem

The Abraham-Lorentz-Dirac equation for a point electron, while suffering from runaway solutions and an acausal response to external forces, is compatible with the optical theorem. We show that a theory of radiative reaction that allows for a finite charge distribution is not only causal and free of runaway solutions, but is also consistent with the optical theorem and the standard formula for the Rayleigh scattering cross section.

Calculation of the total Rayleigh scattering cross sections of photons in the energy range of 30–50 keV for Nb and Mo elements

The total Rayleigh scattering cross sections are calculated in the energy range of 30–50 keV using the modified relativistic form factors (MRFF), non-relativistic form factors (NFF), and relativistic form factors (RFF). Numerical calculations are made for energies above the K-threshold comparisons, for medium- Z elements (Nb and Mo), primarily at small momentum transfers. The integration range is divided into intervals using a modified formula to take into account the smaller scattering angles. The calculated cross sections based on MRFF, NFF, and RFF are presented and compared with the tabulated theoretical values. It is found that the values calculated using the NFF and RFF are smaller than the tabulated values with a ratio of 3–7%. It is also observed that the smallest total Rayleigh scattering cross section values are obtained using the MRFF.

Excitonic Rayleigh scattering spectra of metallic single-walled carbon nanotubes

We have performed microscopic calculations of the Rayleigh scattering cross section for arbitrary metallic single-walled carbon nanotubes. The focus of our investigations lies on excitonic effects and their influence on the characteristic features in a Rayleigh scattering spectrum. Our approach is based on density-matrix theory including tight-binding energies, the carrier-light coupling as well as the carrier-carrier interaction. Due to the refractive-index contribution to the scattering cross section, we observe characteristic features in Rayleigh spectra, such as a strong deviation from the Lorentz peak shape and the larger oscillator strength of the lower-lying transition ${M}_{ii}^{\ensuremath{-}}$ in the double-peaked structure, independently of the chiral angle and the diameter of the investigated nanotubes. We observe excitonic binding energies in the range of 60--80 meV for metallic nanotubes with diameters of 1.5--2.5 nm. The overlap of the excitonic transition with the close-by continuum has a significant influence on the peak shape and a minor influence on the peak intensity ratios. The presented results are in good agreement with recent experimental data.

Optical extinction change of magnetic nanoparticle suspension under pulsed magnetic field

We investigated the optical extinction change of γ-Fe2O3 magnetic nanoparticle suspension induced by a pulsed magnetic field. The Extinction decrease accompanied by a pulsed magnetic field showed clear relationship with the magnetization of magnetic nanoparticle. However, there observed a different response to the magnetic field between increasing and decreasing of the magnetic field. This indicated that the extinction change followed the time variation of magnetic field with some time constant. The time constant was estimated to be 4.5 μs, but it was different from either of rotational Brownian relaxation (0.23 μs) and Neel relaxation (10 ns) of individual particle. It was thought that the optical density decrease might be attributed to the decrease of Rayleigh scattering cross section by the rotation of the magnetic nanoparticle aggregates.

Deep-UV Rayleigh scattering of N2, CH4 and SF6

Rayleigh scattering room temperature cross-section values of N2, CH4 and SF6 have been obtained between 198 and 270 nm by combining cavity ring-down spectroscopy (CRDS) and pressure ramp measurements. The experimental data have been fitted to a functional representation, describing the ∼1/λ4 like behaviour of the Rayleigh scattering cross section over a wide wavelength range. The resulting values are compared with numerical predictions, based on refractive indices and molecular anisotropy data available in the literature. From this, values of molecular volume polarizability αvol and depolarization ratios are derived. It is found that the optical extinction for all three gases is governed by Rayleigh scattering for wavelengths down to 200 nm. No absorption onsets in the specified deep-UV region have been observed.

Spatial resolution effects on the measurement of scalar variance and scalar gradient in turbulent nonpremixed jet flames

The effect of spatial averaging is important for scalar gradient measurements in turbulent nonpremixed flames, especially when the local dissipation length scale is small. Line imaging of Raman, Rayleigh and CO-LIF is used to investigate the effects of experimental resolution on the scalar variance and radial gradient in the near field of turbulent nonpremixed CH4/H2/N2 jet flames at Reynolds numbers of 15,200 and 22,800 (DLR-A and B) and in piloted CH4/air jet flames at Reynolds numbers of 13,400, 22,400 and 33,600 (Sandia flames C/D/E). The finite spatial resolution effects are studied by applying the Box filter with varying filter widths. The resulting resolution curves for both scalar variance and mean squared-gradient follow nearly the same trends as theoretical curves calculated from the model turbulence kinetic energy spectrum of Pope. The observed collapse of resolution curves of mean squared-gradient for nearly all studied cases implies the shape of the dissipation spectrum is approximately universal. Fluid transport properties are shown to have no effect on the dissipation resolution curve, which implies that the dissipation length scale inferred from the square gradient is equivalent to the length scale for the scalar dissipation rate, which includes the diffusion coefficient. With the Box filter, the required spatial resolution to resolve 98% of the mean dissipation rate is about one−two times of the dissipation cutoff length scale (analogous to the Batchelor scale in turbulent isothermal flows). The effects of resolution on the variances of mixture fraction, temperature, and the inverted Rayleigh signal are also compared. The ratio of the filtered variance to the true variance is shown to depend nearly linearly on the probe resolution. The inverted Rayleigh scattering signal can be used to study the resolution effect on temperature variance even when the Rayleigh scattering cross section is not constant. The experimental results also indicate that these laboratory scale turbulent jet flames have small effective Reynolds numbers, such that there is some direct interaction of the large (energy containing) and small (dissipative) scalar length scales, especially for the near field case at x/d = 7.5 of the piloted Sandia flames C/D/E.

Theoretical approach to Rayleigh and absorption spectra of semiconducting carbon nanotubes

AbstractA microscopic calculation of the Rayleigh scattering cross section and the absorption coefficient for arbitrary single‐walled carbon nanotubes is presented. The approach is based on the density matrix formalism combined with the tight‐binding band structure. Both Rayleigh and absorption spectra show a characteristic intensity ratio behavior, which can be explained by an interplay of the optical matrix element and the joint density of states. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Verification of the Rayleigh scattering cross section

A simple experiment is described for the direct determination of the wavelength dependence of the Rayleigh scattering cross section using the classic example of the blue sky. Suggestions for inclusion into an undergraduate lab are discussed.