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All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Multiple scattering in reflection nebulae. IV - The multiplicity of scattering

The characteristics of higher order scattering in plane-parallel reflection nebulae of finite optical thickness have been examined. Measured both by the mean number of scatterings and the effective multiplicity, the importance of multiple scattering in such systems varies strongly with position as well as direction, and the effects cannot be taken into account by simple corrections only. It is found that the amount of higher order scattering is relatively insensitive to the shape of the phase function over a wide range of asymmetries, while the dependence of multiplicity on particle albedo, optical thickness of the nebula, and other geometrical factors is as expected. Pronounced asymmetries in the surface brightness distribution of strongly tilted plane-parallel nebulae are explained by different radial variations of the effective multiplicity along opposite radii on the projected nebular face.

Witt, A. N.↗
NASA NTRS1978

Scattering of light from particulate surfaces. I - A laboratory assessment of multiple-scattering effects

In planetary applications it is sometimes important to know the degree to which multiple scattering is influencing the photometric properties of a surface. An investigation is conducted concerning the point at which the single-scattering approximation used in the theory developed by Hapke (1963) and Irvine (1966) breaks down. It is shown that the Hapke-Irvine photometric function provides an adequate representation of the scattering properties of particulate surfaces whose geometric albedos (or normal reflectances) do not exceed 0.3. An experiment is conducted to estimate the normal reflectance below which the Hapke-Irvine equation considered provides an adequate representation of the scattering properties of a particulate surface. The investigation makes use of a set of samples which were prepared by mixing magnesium oxide and charcoal powders. The samples have a range in normal reflectance from 0.04 to 1.04.

Veverka, J.↗
NASA NTRS1980

Retrieval of aerosol size distributions from scattering and extinction measurements in the presence of multiple scattering

A fast technique, based on approximation to atmospheric radiative transfer in the solar aureole, is presented for the retrieval of aerosol size distribution from multispectral measurements of both scattered sky radiance and extinction by aerosol media. In this approximation, it is assumed that for a relatively clear day, the sky radiance is due to single scattering by molecules and aerosols, and to multiple scattering by molecules alone. The accuracy of this approximation is discussed in connection with the inversion of scattered radiation data. Results for aerosol size distributions retrieved from multispectral solar extinction measurements by the nonlinear least squares method are discussed, and the retrievals are found to be accurate when checked against ground truth measurements.

Deepak, A.↗
NASA NTRS1984

Strong fluctuation theory for electromagnetic wave scattering by a layer of random discrete scatterers

The strong fluctuation theory is applied to the study of electromagnetic wave scattering from a layer of random discrete scatterers. The singularity of the dyadic Green's function is taken into account in the calculation of the effective permittivity functions. The correlation functions for the random medium with different scatterer constituents and size distributions are derived. Applying the dyadic Green's function for a two-layer medium and using the bilocal and distorted Born approximations, the first and the second moments of the fields are then calculated. Both the backscattering and bistatic scattering coefficients are obtained, and the former is shown to match favorably with experimental data obtained from snow fields.

Jin, Y. Q.↗
NASA NTRS1989

A covariant multiple scattering series for elastic projectile-target scattering

A covariant formulation of the multiple scattering series for the optical potential is presented. The case of a scalar nucleon interacting with a spin zero isospin zero A-body target through meson exchange, is considered. It is shown that a covariant equation for the projectile-target t-matrix can be obtained which sums the ladder and crossed ladder diagrams efficiently. From this equation, a multiple scattering series for the optical potential is derived, and it is shown that in the impulse approximation, the two-body t-matrix associated with the first order optical potential is the one in which one particle is kept on mass-shell. The meaning of various terms in the multiple scattering series is given. The construction of the first-order optical potential for elastic scattering calculations is described.

Gross, Franz↗
NASA NTRS1991

Scattering of electromagnetic waves from a half-space of randomly distributed discrete scatterers and polarized backscattering ratio law

The effective-medium approximation is applied to investigate scattering from a half-space of randomly and densely distributed discrete scatterers. Starting from vector wave equations, an approximation, called effective-medium Born approximation, a particular way, treating Green's functions, and special coordinates, of which the origin is set at the field point, are used to calculate the bistatic- and back-scatterings. An analytic solution of backscattering with closed form is obtained and it shows a depolarization effect. The theoretical results are in good agreement with the experimental measurements in the cases of snow, multi- and first-year sea-ice. The root product ratio of polarization to depolarization in backscattering is equal to 8; this result constitutes a law about polarized scattering phenomena in the nature.

Zhu, P. Y.↗
NASA NTRS1996

Ring Effect Studies: Rayleigh Scattering, including Molecular Parameters for Rotational Raman Scattering, and the Faunhofer Spectrum

Improved parameters for the description of Rayleigh scattering in air and for the detailed rotational Raman scattering component for scattering by O2 and N2 are presented for the wavelength range 200-1000 nm. These parameters enable more accurate calculations of bulk molecular scattering and of the 'Ring effect' for a variety of atmospheric radiative transfer and constituent retrieval applications. A solar reference spectrum with accurate absolute vacuum wavelength calibration, suitable for convolution with the rotational Raman spectrum for Ring effect calculations, has been produced and is briefly described. The solar-rotational Raman convolved product is available for fitting of atmospheric spectra.

Chance, K. V.↗
DOE OSTI2025

The role of intermediate ΔΔ states in nucleon–nucleon scattering in the large-Nc and unitary limits, and ΔΔ and ΩΩ scattering

We explore potential explanations for why using large-Nc (Nc is the number of colors) scaling to determine the relative size of few-nucleon low-energy operators agrees with experiment even when dynamical Δ’s are not explicitly included. Given that the large-Nc analysis is predicated on the nucleons and Δ’s being degenerate, this is a curious result. We show that for purely S-wave interactions the relationships dictated by large-Nc scaling are unaffected whether the Δ is included or not. In the case of higher partial waves that do not mix with S-waves, the impact of the Δ is perturbative, which makes the agreement with naive (Δ-less) large-Nc ordering unsurprising. For higher partial waves that mix with S-waves, the nucleon and Δ would need to decouple to get agreement with naive large-Nc ordering. We find all NN, ΔN, and ΔΔ low energy coefficients for leading-order baryon–baryon scattering in Δ-full pionless effective field theory in terms of the two independent parameters dictated by the SU(2F) spin-flavor symmetry that arises in the Nc → ∞ limit. Because of recent lattice quantum chromodynamics results and experimental interest, we extend our analysis to the three-flavor case to study ΩΩ scattering. We show that in the unitary limit (where scattering lengths become infinite) one of the two SU(2F) parameters is driven to zero, resulting in enhanced symmetries, which agree with those found in spin-1/2 entanglement studies.

Richardson, Thomas R↗
DOE OSTI2025

Self-Consistent Relativistic Electron Scattering using the Sherlock Scattering Model for X-ray Diagnostics

We present on a new, self-consistent, arbitrary-temperature Romberg integration scheme for modeling electron scattering in materials in a LANL Lagrangian Shock Hydro (LSH) code. Electron beam-target interactions are fundamental to a wide range of scientific and technological applications. When high-energy electron beams hit their target, they may scatter, deposit energy, or ionize the source. These processes govern the behavior and outcomes in nanotechnology manufacturing, electron microscopy, and modern X-ray diagnostics. Simulating these interactions is essential for interpreting experimental results, predicting material responses, and designing efficient tools and experiments. At Los Alamos, this is done using a LSH code, which is a multi-dimension, multi-material, massively parallel, multi-physics code used to simulate applications from asteroid impacts to electron beam interactions. By effectively and efficiently modeling the way that electrons scatter from the beam we can bolster these simulations and more accurately predict experimental outcomes. The model currently implemented in the LSH of interest is based on work by Papp and does not self-consistently preserve momentum in the slightly relativistic regime; here we adopt a model proposed by Braams and Karney and implement a Romberg integration scheme to compute the diffusion tensor. In this paper we will provide background on the Braams-Karney diffusion tensor as well as the Romberg integration scheme we employed to numerically solve for it. We will show that our integration scheme is accurate in solving for the set of scalar potentials used to re-express the diffusion tensor in differential form, and in solving for the diffusion coefficients in the larger LSH code. By using this diffusion tensor rather than the existing Papp one, and numerically integrating it with a Romberg method, we produce much more accurate, self-consistent results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1976

Scattering in the atmosphere of Venus. Line profiles and phase curves for Rayleigh scattering

Spectral line profiles, curves of growth, and curves for the equivalent width of a line as a function of Venus phase angle are computed for a Rayleigh scattering cloud and compared with those for a cloud of isotropic scatterers. The results are similar for the two kinds of scattering, with the exception for the curves of equivalent width as a function of Venus phase angle. These latter curves exhibit the inverse phase effect and rule out the possibility that the scale height of the clouds can be much less than half the scale height of the gas.

Young, L. D. G.↗
NASA NTRS1976

Scattering in the atmosphere of Venus. I - Line profiles and curves of growth for isotropic scattering

Line profiles and curves of growth were computed for both reflected and transmitted radiation for typical lines in CO2 bands (in the photographic infrared) which occur in the spectrum of Venus. In the model, the pressure variation with altitude was considered, and the base of the cloud deck was set at the 2 bar level. The temperature was held constant at 250 K, and a Voigt profile was used for the line shape. It was also assumed that the scale height of the cloud particles was equal to the scale height of the gas. The calculations were made for four values of the scattering optical thickness (0.1, 1.0, and 100) using a continuum single-scattering albedo of 0.9975 (which gives a Bond albedo of 0.896 for a scattering optical thickness of 100, the value observed for Venus at these wavelengths). Curves of growth are also presented for reflected radiation which has been averaged over the visible disk for three values of the Venus phase angle (0, 86, and 166 deg).

Young, L. D. G.↗
NASA NTRS1977

Scattering in the atmosphere of Venus. III - Line profiles and phase curves for Rayleigh scattering

Spectral line profiles, curves of growth, and curves for the equivalent width of a line as a function of Venus phase angle have been computed for a Rayleigh scattering cloud and compared with those for a cloud of isotropic scatterers. The results are very similar for the two kinds of scattering, with the exception of the curves of equivalent width as a function of Venus phase angle. These latter curves exhibit the 'inverse phase effect' and rule out a scale height of the clouds much less than half the scale height of the gas. The optical depth of the clouds is approximately 100.

Young, L. D. G.↗
NASA NTRS1979

Inverse multiple scattering problems. III - Inadequacy of certain limb darkening and phase curves for retrieving atmospheric information and limitations of approximate scattering models

The paper considers three complementary inverse multiple scattering problems relating to a uniquely defined atmospheric scattering model. Consideration is given to the appropriateness, for data inversion purposes, of intensities observed in diffuse reflection under a variety of experimental conditions; the uniqueness of the inverse solution is investigated. It is found that light curves representing monotonic variations, such as limb darkening curves and phase curves for a planetary (e.g., Venus) disk center are unsuitable for inferring atmospheric and scattering parameters.

Fymat, A. L.↗
NASA NTRS1985

Elastic scattering of alpha particles and the phase of the nucleon-nucleon scattering amplitude

Glauber theory can describe elastic scattering of alpha particles by He-4, He-3, H-2, and H-1 at 7 GeV/c if the phase of the nucleon-nucleon elastic-scattering amplitude varies with momentum transfer. The phase variation leads to diffraction patterns differing markedly from those typical of constant-phase calculations and greatly affects the magnitudes of the intensities. These changes are mainly due to changes in the interference between amplitudes for different orders of multiple scattering and to a decrease in their moduli.

Franco, V.↗
NASA NTRS1986

Scattering from nonspherical Chebyshev particles. I - Cross sections, single-scattering albedo, asymmetry factor, and backscattered fraction

Using the extended boundary condition method, scattering calculations from randomly oriented rotationally symmetric nonspherical particles were made, the size parameters (1-25) and the refractive indicies (1.5 0.02i) of which were chosen to relate to the transfer of solar and IR radiation in an aerosol atmosphere. Comparison of computations for 23 Chebyshev shapes to corresponding size-averaged spherical results revealed that nonsphericity increased absorption for size parameters larger than around 10 and decreased the asymmetry factor, and correspondingly increased the backscattered fraction, in the size ranges 8-15. The scattering efficiency was somewhat larger for nonspherical particles, while the single-scattering albedo tended to be smaller, and concavity was shown to almost always enhance spherical-nonspherical differences.

Mugnai, A.↗
NASA NTRS1988

Scattering from nonspherical Chebyshev particles. II - Means of angular scattering patterns

The calculated angular scattering properties of over 250 randomly oriented nonspherical Chebyshev particles are examined for the effect of three factors: size; concavity vs convexity; and amount of deformation from a sphere. Both shape and size averaging are performed to reveal general features of the angular scattering not discernible for particular shapes and sizes. Comparisons with a comparably extensive experimental study published by Zerull in 1976 reveal remarkable qualitative similarities, even though Zerull used greatly different shapes from ours. This augurs well for the eventual development of a general theory of nonspherical scattering, although such a theory must account for concavity in addition to the amount of deviation from a sphere; and it cannot be entirely deterministic, as the third paper in this series will argue.

Wiscombe, Warren J.↗
NASA NTRS1988

Light scattering by an arbitrary particle - The scattering-order formulation of the coupled-dipole method

The field scattered by an arbitrary particle modeled as an array of coupled dipoles can be expressed as an infinite series in terms of scattering orders. The fields of a given scattering order can be calculated from those of the previous order. When the series converge, the approximate method agrees well with the exact theory for a sphere. The maximum size of the dipolar array that can be used with the method as well as the number of terms required for convergence depends on the relative refractive index and the shape of the particle.

Singham, Shermila Brito↗
NASA NTRS1993

Calibration of the forward-scattering spectrometer probe - Modeling scattering from a multimode laser beam

Scattering calculations using a detailed model of the multimode laser beam in the forward-scattering spectrometer probe (FSSP) were carried out using a recently developed extension to Mie scattering theory. From this model, new calibration curves for the FSSP were calculated. The difference between the old calibration curves and the new ones is small for droplet diameters less than 10 microns, but the difference increases to approximately 10 percent at diameters of 50 microns. When using glass beads to calibrate the FSSP, calibration errors can be minimized by using glass beads of many different diameters, over the entire range of the FSSP. If the FSSP is calibrated using one-diameter glass beads, then the new formalism is necessary to extrapolate the calibration over the entire range.

Hovenac, Edward A.↗