Forward Scattering Cross Section Research Articles

Post-flight analysis of detailed size distributions of warm cloud droplets, as determined in situ by cloud and aerosol spectrometers

Abstract. Warm clouds, consisting of liquid cloud droplets, play an important role in modulating the amount of incoming solar radiation to Earth's surface and thus the climate. The size and number concentration of these cloud droplets control the reflectance of the cloud, the formation of precipitation and ultimately the lifetime of the cloud. Therefore, in situ observations of the number and diameter of cloud droplets are frequently performed with cloud and aerosol spectrometers, which determine the optical diameters of cloud particles (in the range of up to a few tens of micrometers) by measuring their forward-scattering cross sections in visible light and comparing these values with Mie theoretical computations. The use of such instruments must rely on a fast working scheme consisting of a limited pre-defined uneven grid of cross section values that corresponds to a theoretically derived uneven set of size intervals (bins). However, as more detailed structural analyses of warm clouds are needed to improve future climate projects, we present a new numerical post-flight methodology using recorded particle-by-particle sample files. The Mie formalism produces a complicated relationship between a particle's diameter and its forward-scattering cross section. This relationship cannot be expressed in an analytically closed form, and it should be numerically computed point by point, over a certain grid of diameter values. The optimal resolution required for constructing the diagram of this relationship is therefore analyzed. Cloud particle statistics are further assessed using a fine grid of particle diameters in order to capture the finest details of the cloud particle size distributions. The possibility and the usefulness of using coarser size grids, with either uneven or equal intervals, is also discussed. For coarse equidistant size grids, the general expressions of cloud microphysical parameters are calculated and the ensuing relative errors are discussed in detail. The proposed methodology is further applied to a subset of measured data, and it is shown that the overall uncertainties in computing various cloud parameters are mainly driven by the measurement errors of the forward-scattering cross section for each particle. Finally, the influence of the relatively large imprecision in the real and imaginary parts of the refractive index of cloud droplets on the size distributions and on the ensuing cloud parameters is analyzed. It is concluded that, in the presence of high atmospheric loads of hydrophilic and light-absorbing aerosols, such imprecisions may drastically affect the reliability of the cloud data obtained with cloud and aerosol spectrometers. Some complementary measurements for improving the quality of the cloud droplet size distributions obtained in post-flight analyses are suggested.

Understanding the effects of shape, material and location of incorporation of metal nanoparticles on the performance of plasmonic organic solar cells.

Truncated octahedral gold (Au) nanoparticles (NPs), Au nanocubes (NCs)-, and silver (Ag) NCs are used to study the effect of NPs shape, material and incorporation location on the performance of poly(3-hexylthiophene):[6,6]-phenyl-C71-butyric acid methyl ester (P3HT:PC71BM) based inverted bulk heterojunction (BHJ) organic solar cells (OSCs). Plasmonic OSCs (POSCs) with NPs incorporated as an interfacial layer between zinc oxide (ZnO) and active layer showed highest power conversion efficiency (PCE) and short circuit current density (Jsc) values for all kind of shapes and material compared to POSCs with NPs blended into the active layer. Near-field enhancement as well as enhanced forward scattering cross section is attributed for POSC performance improvement. Among the NPs with two shapes, POSCs with truncated octahedral Au NPs exceeded the photovoltaic performance compared to those of POSCs with Au and Ag NCs. Large number of antennas in truncated octahedral Au NPs compared to NC is reasoned to be the cause for this improvement. Even though Ag has better localised surface plasmon resoanance (LSPR) properties compared to Au, the POSCs with Ag NCs showed lower Jsc value and is due to reduced number of photons at the blue shifted LSPR wavelength of Ag NCs. The improvement in Jsc values of POSCs is confirmed by enhancement in absorption, external quantum efficiency (EQE), exciton generation and exciton dissociation probability measurements and is due to improved LSPR coupling of the NPs with the active layer. The surface enhanced Raman scattering (SERS) and photoluminescence (PL) studies confirm the absorption enhancement in the active layer by NP LSPR coupling and further confirm the enhancement in the photovoltaic performance of POSCs.

Assessment of deformation of human red blood cells in flow cytometry: measurement and simulation of bimodal forward scatter distributions.

Light scattering by single cells is widely applied for flow cytometric differentiation of cells. However, even for human red blood cells (RBCs), which can be modeled as homogeneous dielectric particles, the potential of light scattering is not yet fully exploited. We developed a dedicated flow cytometer to simultaneously observe the forward scattering cross section (FSC) of RBCs for orthogonal laser beams with incident wave vectors and . At a wavelength , bimodal distributions are observed in two-dimensional dot plots of FSC( ) vs. FSC( ), which result from the RBCs' random orientation around the direction of flow, as well as from the distributions of their size and their optical properties. Typically, signals of RBCs were analyzed. We actively oriented the cells in the cytometer to prove that orientation is the main cause of bimodality. In addition, we studied the wavelength dependence of FSC( ) using and 632.8 nm, covering both weak and strong light absorption by the RBCs. Simulations of the light scattering by single RBCs were performed using the discrete dipole approximation (DDA) for a range of sizes, orientations and optical properties to obtain FSC distributions from RBC ensembles. Using the axisymmetric biconcave equilibrium shape of native RBCs, the experimentally observed distributions cannot be reproduced. If, however, an elongated shape model is employed that accounts for the stretching of the cell by hydrodynamic forces in the cytometer, the features of the strongly bimodal measured frequency distributions are reproduced by the simulation. Elongation ratios significantly greater than 1 in the range of 1.5 to 2.5 yield the best agreement between experiments and simulated data.

An effective field theory for forward scattering and factorization violation

Starting with QCD, we derive an effective field theory description for forward scattering and factorization violation as part of the soft-collinear effective field theory (SCET) for high energy scattering. These phenomena are mediated by long distance Glauber gluon exchanges, which are static in time, localized in the longitudinal distance, where $|t| \ll s$. In hard scattering, Glauber gluons can induce corrections which invalidate factorization. With SCET, Glauber exchange graphs can be calculated explicitly, and are distinct from graphs with soft, collinear, or ultrasoft gluons. We derive a complete basis of operators which describe the leading power effects of Glauber exchange. Key ingredients include regulating light-cone rapidity singularities and subtractions which prevent double counting. Our results include a novel all orders gauge invariant pure glue soft operator which appears between two collinear rapidity sectors. The 1-gluon Feynman rule for the soft operator coincides with the Lipatov vertex, but it also contributes to emissions with $\ge 2$ soft gluons. Our Glauber operator basis is derived using tree level and one-loop matching calculations from full QCD to SCET. The rapidity RGE yields gluon Reggeization at the amplitude level, and gives the BFKL equation for the soft and collinear functions in the forward scattering cross section. We derive an explicit rule for when eikonalization is valid, and provide a direct connection to the picture of multiple Wilson lines crossing a shockwave. In hard scattering operators Glauber subtractions for soft and collinear loop diagrams ensure that we are not sensitive to the directions for soft and collinear Wilson lines. Conversely, certain Glauber interactions can be absorbed into these soft and collinear Wilson lines by taking them to be in specific directions. We also discuss criteria for factorization violation.

Experimental verification of maritime target parameter evaluation in forward scatter maritime radar

Maritime security is related to national economic and political interests and is strategically important. One efficient way to accomplish maritime border protection is to use the netted forward scatter radar (FSR). FSR is a special type of bistatic radar that operates in a relatively narrow scattering area along the transmitter–receiver baseline, where the effect of the electromagnetic waves forward scattering on targets is dominant above other scattering mechanisms, and in this case, a forward scatter (FS) cross section may increase by orders of magnitude in comparison with the monostatic radar cross section (RCS). Considered in this study are the major problems of marine forward scattering radar detection and estimation of length of low-profile (small and slow) marine targets using a pre-processing approach. It is based on the assumption that the variation of the phase and amplitude in the Doppler signal signature is stronger inside the FS zone than in an outside region. Two variants of pre-processing algorithms are presented in the study, one for the envelope and the other for the phase. Both variants are based on the use the local variance filtering. The results obtained prove the sufficient improvement in a signal-to-clutter ratio (SCR). Estimation of the marine target length under the low SCR is designed using the assumption of known or previously estimated velocity. Presented results demonstrate high accuracy of length estimation. Considered steps of targets detection and target attributes evaluations are necessary for maritime targets classification. The designed algorithms are verified using a set of experimental records of signals from different marine targets obtained using marine FSR developed by the teams from University of Birmingham, UK and Sofia University, Bulgaria.

Graviton-photon scattering

We use the feature that the gravitational Compton scattering amplitude factorizes in terms of Abelian QED amplitudes to evaluate various gravitational Compton processes. We examine both the QED and gravitational Compton scattering from a massive spin-1 system by the use of helicity amplitude methods. In the case of gravitational Compton scattering we show how the massless limit can be used to evaluate the cross section for graviton-photon scattering and discuss the difference between photon interactions and the zero mass spin-1 limit. We show that the forward scattering cross section for graviton photoproduction has a very peculiar behavior, differing from the standard Thomson and Rutherford cross sections for a Coulomb-like potential.

Breaking trade-offs between translucency and diffusion in particle-doped films

Particle-doped thin films that are translucent and diffusive have applications in cosmetics, coatings, and display technologies, but finding material combinations that produce these effects simultaneously is challenging: formulations tend to be either transparent or opaque. Using a combination of Mie scattering calculations and spectral transmission measurements on monodisperse colloidal suspensions, we demonstrate that the two characteristic optical properties of the films, total transmittance and haze, scale with the effective backscattering and forward scattering cross sections, both of which are properties of single particles. These scalings enable an efficient computational search for combinations of particle sizes, concentrations, and refractive indices that break the trade-off between translucency and diffusion. The optimum particle sizes and concentrations obey power-law dependences on the refractive index difference, a result of the interference condition for resonances in the scattering cross sections. The power laws serve as design equations for formulating particle-doped thin films.

R-matrix calculations of differential and integral cross sections for low-energy electron collisions with ethanol

Electron collisions with C2H5OH are studied up to impact energies of 10 eV using several theoretical models. Calculated differential cross sections suggest that the extrapolation to low angles used to extend experimental data and hence give integral cross sections significantly underestimates the large, dipole-driven forward scattering cross section. An improved set of values for the rotationally-unresolved elastic cross section is proposed; the corresponding rotationally resolved cross sections are also presented. Static exchange plus polarisation calculations find a very broad shape resonance in each of the 2A′ and 2A′′ symmetries in the 7 eV collision region however no resonance at lower energies, in qualitative agreement with the interpretation of some but not all dissociative electron attachment measurements.

Pion double charge exchange in a composite-meson model

The pion double charge exchange amplitude is evaluated in a composite-meson model based on the four-quark interaction. The model assumes that the mesons are two-quark systems and can interact with each other only through quark loops. To evaluate the meson exchange current contribution, the form factors of the two-pion decay modes of the $\ensuremath{\rho},\ensuremath{\sigma}$, and ${f}_{0}$ mesons have been used in the calculations. The contribution of the four-quark box diagram has been taken into account as well as a contact diagram. The contributions of the $\ensuremath{\rho},\ensuremath{\sigma}$, and ${f}_{0}$ mesons increase the forward scattering cross section, which depends weakly on the energy.

Scattering of Electromagnetic Radiation by a Perfect Electromagnetic Conductor Sphere

An analytic theory for the electromagnetic scattering from a perfect electromagnetic conductor (PEMC) sphere is developed. The PEMC is characterized by a single parameter M, where M = 0 reduces to the perfect magnetic conductor (PMC) case and the limit M → ∞ corresponds to the perfect electric conductor (PEC) case. The theory allows for the occurrence of cross-polarized fields in the scattered wave, a feature which does not exist in the standard Mie scattering theory. The application of the theory to the calculation of the scattering cross section is presented. As an example we evaluate the relative contributions of the co-polarized and the cross-polarized fields to the backward and forward scattering cross sections.

Saturn's Rings I: Optical Depth Profiles from the 28 Sgr Occultation

We present optical depth profiles for Saturn's rings at wavelengths of 0.9, 2.1, 3.3, and 3.9 μm, obtained from the occultation of the star 28 Sgr on 3 July 1989 when the rings were near their maximum opening angle. The radial resolution of the data is ∼18 km, as set by the angular diameter of the star. Very few, if any, structural changes are observed in the rings since the Voyager encounters in 1980/1981. Azimuthal variations in optical depth are restricted to the outermost part of the B Ring and to several previously known noncircular features. The mean optical depth in the heretofore unprobed central part of the B Ring is found to be 2.3±0.15 at 3.9 μm. Quantitative comparisons of the optical depths with those measured by the Voyager PPS stellar occultation experiment at 0.27 μm do reveal systematic differences between the major ring regions. In the C Ring, we find τ 28 Sgr/τ PPS≃1.4, while in the B Ring and outer A Ring τ 28 Sgr/τ PPS≃1.0. Only in the inner A Ring is τ 28 Sgr<τ PPS. In agreement with previous studies at microwave and optical wavelengths, we conclude that there is very little evidence in the 28 Sgr data for a significant population of micrometer-sized particles anywhere in the main rings. Most of the observed variation in τ 28 Sgr/τ PPS can instead be attributed to variations in the particle size distribution in the rings in the centimeter to meter size range, which controls the angular width of the rings' forward-scattering cross section. This in turn controls the effective extinction efficiency for Earth-based occultation experiments, and thus the measured optical depth. In a companion paper we use these data to derive power-law models of the size distribution in each major ring region.

Rayleigh-Mie approximation for line-of-sight propagation through rain at 5-90 GHz

An earlier heuristic model of attenuation and phase changes through a layer of oblate spheroids is replaced by a new, simpler, model with much greater accuracy. The model is meant to cover propagation through rain at 5-90 GHz frequencies and at rain rates from 5-150 mm/hr. Accurate predictions of co and crosspolar attenuation, of co and crosspolar discrimination, and of the various phase changes associated with each polarization of the incident wave are now possible by means of calculations requiring no more than simple numerical extensions of Mie calculations superposed upon the Rayleigh forward-scattering cross sections. Some degree of canting-angle variations is included. Comparison of calculations by this approximation to a variety of empirical or simulated rain statistics available in the literature is presented.

Theoretical description of possible detection of swimbladdered fish in forward scatter

This paper presents a possible theory for acoustic detection of swimbladder fish in forward scatter. A major application of this theory lies in counting fish in rivers. First, the calculation of the forward scattering cross section of gas-filled fish swimbladders with various shapes is presented. Then useful formulas for fish detection in the forward scatter are derived. It is shown that in a nonturbulent medium the fish moving speed may be calculated from the signal amplitude auto-correlation function, which may also be used to estimate the size of fish if the fish speed can be determined by other means. In a turbulent medium, the signal correlation functions are calculated incorporating both sound scattering from fish and turbulence and it is shown that the scattering from the fish may have distinctive features compared to that from the turbulence. An explicit example shows to what degree the fish is countable. Application to an actual measurement is also briefly discussed.

Absolute cross section for D( 4He, D) 4He forward scattering

The D( 4He, D) 4He differential cross section for forward scattering of deuterons by helium ions has been measured, with an estimated precision of ± 5%, in the range 1–3 MeV at the scattering angles of 20°, 25°, 30°, 35° and 40°. Deuterated polystyrene (C 8D 8) n films spun on Si wafers were used for the measurements, enabling the forward scattering cross section to be determined directly with reference to the 4He backscattering cross section of carbon (which was, in turn, referenced to the Rutherford cross section for 4He on Cu). The D( 4He, D) 4He cross section exhibits a resonance at 2.135 ± 0.01 MeV, with ∼ 60 keV FWHM, the amplitude of which is strongly dependent on scattering angle. For the rest of the energy range, the cross section is featureless, and can be fitted well by a simple polynomial.

Energy distribution of energetic O+ precipitation into the atmosphere

Measurements of ring current ion densities by the Active Magnetospheric Particle Tracer Explorers CCE satellite suggest that a large flux of energetic (tens of keV) O+ precipitates in the mid‐latitude atmosphere during major geomagnetic storms. The mass spectrometer (&gt;30 keV) on board the NOAA 6 satellite measured an ion flux of 30 ergs cm−2 s−1 at 52° invariant latitude during a very large geomagnetic storm. To calculate atmospheric response to precipitation of the energetic O+ fluxes, we have revised an O+ transport model to include energies up to 200 keV. The model's sensitivity to the estimated cross sections and model atmospheres for various monoenergetic O+ fluxes are presented in this paper. Calculation of the atmospheric response to O+ precipitation shows that (1) most of the incident energy is immediately transformed into atmospheric heating, (2) the total number of escape particles is smaller than the total number of incident particles, in contrast to the results of previous models, and (3) the peak heating and ionization altitudes vary from 104 to 300 km depending on the incident energy. The results are most sensitive to the estimated differential scattering cross sections at large scattering angles. The use of forward scattering cross sections at both extremes of the possible range results in very different energy allocations and altitudes of peak ionization and heating (a difference of as much as 80 km). The MSIS‐86 model atmosphere with extreme parametric values caused little change in the energy allocation, but the large variation in the model atomic oxygen density (F10.7 index = 70 and 210) alters the peak heating and ionization altitude for low‐energy incident O+ (a few keV) by 50 km.

Scattering by a thin multicoated perfectly conducting spherical shell with a circular aperture

An analytic solution is presented for the problem of an infinitely thin perfectly conducting spherical shell with a circular aperture of arbitrary angle cut into the shell, filled with a dielectric, and coated by different thicknesses of spherical dielectric layers. The fields in all regions are expanded in terms of spherical wave functions and the boundary conditions of the continuity of the tangential fields at the dielectric–dielectric and dielectric–free-space boundaries are applied to express the expansion coefficients of the first dielectric layer in terms of the scattering coefficients. To approximate the modal expansion coefficients, the least-square error method is applied to the equations resulting from matching the fields through the aperture. Different numerical results for the simple case of a single coating layer are obtained in the form of amplitude patterns for the aperture and scattered fields versus angle as well as the backward- and forward-scattering cross sections for different loadings as functions of cavity size.

(d,3He) reactions for the formation of deeply bound pionic atoms.

We have studied theoretically the proton pick-up ({ital d},{sup 3}He) reactions leading to deeply bound pionic atoms. The forward scattering cross sections for an incident energy {ital T}{sub {ital d}}=600 MeV have been calculated using the effective number approach for the {sup 208}Pb target nucleus. It was found that the pionic 2{ital p} state has the maximum cross section among all calculated states. We conclude that ({ital d},{sup 3}He) reactions produce pionic atoms in a detectable manner.

Electromagnetic scattering by an arbitrary configuration of dielectric spheres

An analytic solution is obtained for the problem of plane electromagnetic-wave scattering by an arbitrary configuration of N dielectric spheres. The multipole expansion method is employed, and the boundary condition is imposed using the translational addition theorem for vector spherical wave functions. A system of simultaneous linear equations is given in matrix form for the scattering coefficients. An approximate solution, which has been developed and employed by the authors for the scattering by N conducting spheres, is extended to the dielectric spheres case. Plots for the normalized backscattering, bistatic, and forward-scattering cross sections are presented over wide ranges of permittivity, size, and electrical separations between the neighbouring spheres. The results show a reduction in the normalized backscattering and bistatic cross sections for certain choices of permittivity relative to conducting arrays of spheres of the same dimensions and separations.

Photon scattering from 12C and 208Pb in the Δ-region

The photon-scattering cross sections at 115° for 12C and 208Pb have been measured using bremsstrahlung energies E of 150, 200, 250, 300, 350 and 400 MeV. Scattered photons having energies in the range 0.9 E to E were accepted by the detector. The measured cross sections are much larger than the prediction of a simple model relating the scattering cross section at a large angle to the forward-scattering cross section and the form factor for elastic electron scattering. This discrepancy is discussed in terms of collective effects, inelastic scattering, or exchange-current distributions.

Interference between Rayleigh, Delbruck, and nuclear resonance scattering processes

The forward scattering cross section at $\ensuremath{\theta}=1\ifmmode^\circ\else\textdegree\fi{} \mathrm{and} 1.7\ifmmode^\circ\else\textdegree\fi{}$ of $E=4\ensuremath{-}10$ MeV monoenergetic photons from Pb and Bi targets has been measured. The photon beam was obtained from the $\mathrm{Fe}(\mathrm{n}, \ensuremath{\gamma})$ reaction. The elastic cross section at such angles, being dominated by Rayleigh and Delbruck scattering processes, was measured relative to the Compton cross section. The fact that one of the $\ensuremath{\gamma}$ lines of the $\mathrm{Fe}(\mathrm{n}, \ensuremath{\gamma})$ reaction happens to overlap the 7.28 MeV level in $^{208}\mathrm{Pb}$, yielding a strong nuclear resonance fluorescence signal, enabled us to observe, for the first time, an interference effect with the Rayleigh and Delbruck scattering processes. A theoretical expression of the nuclear resonance scattering amplitude for the specific case of the random photoexcitation process is derived. The interference effect of this latter process with Rayleigh and Delbruck scattering is calculated and an excellent agreement with measured values is obtained.NUCLEAR REACTIONS Pb, $^{208}\mathrm{Pb}$, $^{209}\mathrm{Bi}(\ensuremath{\gamma}, \ensuremath{\gamma})$, $E=4.2\ensuremath{-}9.3$ MeV, measured $\ensuremath{\sigma}(\ensuremath{\theta})$, Delbruck and Rayleigh scattering, nuclear resonance fluorescence, interference effects.