Linear-scaling algorithm for rapid computation of inelastic transitions in the presence of multiple electron scattering
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Results of calculations concerning the emission of bremsstrahlung by electrons in the upper atmosphere and the penetration of this radiation to atmospheric depths of 3 to 10 g/sq cm, where it can be measured by balloon-borne detectors. The calculations take into account the multiple scattering and slowing down of electrons, and the multiple Compton scattering and photoelectric absorption of bremsstrahlung photons. Numerical data have been generated for electron beams incident onto the atmosphere with energies between 20 keV and 2 MeV, assuming wide-area precipitation and an incident angular distribution isotropic over the downward hemisphere. The results relate the number and energy spectrum of the incident electrons to the bremsstrahlung flux spectrum at balloon heights. The interpretation of some observed bremsstrahlung flux spectra is attempted.
An approximate analytic solution is derived for the radiative transfer equation describing particulate surface light scattering, taking into account multiple scattering and mutual shadowing. Analytical expressions for the following quantities are found: bidirectional reflectance, radiance coefficient and factor, the normal, Bond, hemispherical, and physical albedos, integral phase function and phase integral, and limb-darkening profile. Scattering functions for mixtures can be calculated, as well as corrections for comparisons of experimental transmission or reflection spectra with observational planetary spectra. The theory should be useful for the interpretation of reflectance spectroscopy of laboratory surfaces and the photometry of solar system objects.
By treating the emission of optical phonons as a Markov process, a simple analytic method is developed for calculating the electronic ionization rate per unit length for dielectrics. The effects of scattering from acoustic and optical phonons are neglected. The treatment obtains universal functions in recursive form, the theory depending on only two dimensionless energy ratios. A comparison of the present work with other numerical approaches indicates that the effect of scattering becomes important only when the electric potential energy drop in a mean free path for optical-phonon emission is less than about 25% of the ionization potential. A comparison with Monte Carlo results is also given for Teflon.
Scattering from an inhomogeneous layer with irregular boundaries was calculated to model natural terrain such as a layer of vegetation or sea ice. The inhomogeneities were modeled by spherical or disc-shaped discrete scatterers which were small compared with the incident wavelength and were in the far field of one another. It was found that the cross-polarized scattering was dominated by multiple scattering effects and was sensitive to the orientations and distributions of the scatterers. This model has been applied to interpret measurements from vegetation, snow and sea ice. The scattering model was extended to handle disc-shaped scatterers which are comparable to the incident wavelength. The model was used to investigate the relative merits between active versus passive sensing of soil moisture over vegetated terrain. Results indicate that scattering mesurements are more sensitive to soil moisture changes than emission measurements. This is because while both types of measurements lose sensitivity to soil moisture because of the vegetation layer, the loss is greater for passive than active measurements.
Microwave modeling of vegetated terrain was investigated. The purpose was to: (1) use discrete scatter theory to model vegetation (crops and forested regions) in microwave region; (2) develop models for scatterers and ground; (3) multiple scattering analysis relate model parameters to average scattered power; and (4) develop inversion techniques to remotely determine model parameters.
An empirical model for scattering from a vegetation layer above an irregular ground surface is developed in terms of the first-order solution for like-polarized scattering and the second-order solution for cross-polarized scattering. The effects of multiple scattering within the layer and at the surface-volume boundary are compensated by using a correction factor based on the matrix doubling method. The major feature of this model is that all parameters in the model are physical parameters of the vegetation medium. There are no regression parameters. Comparisons of this empirical model with theoretical matrix-doubling method and radar measurements indicate good agreements in polarization, angular trends, and k sub a up to 4, where k is the wave number and a is the disk radius. The computational time is shortened by a factor of 8, relative to the theoretical model calculation.
We describe a Monte Carlo method for calculating polarization due to scattering in various geometries. We apply the method in this paper to the case of scattering in a spherical cloud illuminated by parallel rays. The polarization is largest in small optical depth blobs, where single scattering dominates. The polarization decreases as optical depth increases until a limit is reached where scattering occurs on the surface, and increasing optical depth has little effect on the results. For a given optical depth, decreasing the albedo leads to an increase of the degree of polarization of the scattered light because single scattering increases relative to multiple scattering. As the optical depth of the blob increases, the scattered flux becomes increasingly backward throwing. In the high albedo blobs, the maximum polarization becomes skewed towards the illuminated hemisphere at high optical depths. We discuss the applications to polarization in supergiants and R CrB stars, and scattering in a clumpy interstellar medium.
Quantitative simulations of carrier transport in physical systems that are of the size of a few nanometers require the use of quantum mechanical models at a very fundamental level.
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This paper describes an analytical theory to calculate the emittance growth rates due to intrabeam scattering in focusing systems with arbitrary x-y coupling. The presented results are based on calculations of average emittance growth rates for an initially Gaussian distribution.
The present measurements are carried out to investigate the multiple scattering of 662 keV gamma photons emerging from targets of binary alloys (brass and soldering material). The scattered photons are detected by 51 mm × 51 mm NaI(Tl) scintillation detector whose response unscrambling converting the observed pulse–height distribution to a true photon energy spectrum, is obtained with the help of 10 × 10 inverse response matrix. The numbers of multiply scattered events, having same energy as in the singly scattered distribution, first increases with target thickness and then saturate. The application of response function of scintillation detector does not result in any change of measured saturation thickness. Monte Carlo calculation supports the present experimental results.
This presentation provides an evaluation workflow scheme for the project. It also discusses nuclear data libraries, including an overview of worldwide nuclear data libraries and current funding agencies. The presentation also discusses the theoretical framework commonly used in the evaluated work, including the R-matrix theory (≈ up to a few keVs for heavy nuclei) as well as pre-equilibrium (PE) and Hauser-Feshbach (HF) theory (⪆1 MeV for medium/heavy nuclei). Inclusion of experimental effects are also discussed. Examples of evaluated work, including theory, experiments, and applications are discussed, specifically n+ 28,29,30 Si evaluation (direct capture component), n+ 53 Cr evaluation (strong multiple scattering effects), n+ 239 Pu(n,γf) reaction (fluctuations in neutron multiplicities), and α+ 17,18 O evaluations (emerging neutron spectra).
Monte Carlo (MC) numerical simulation is carried out for the intensity of multiply backscattered radiation as a function of the source–receiver distance for the Henyey–Greenstein (HG) and Rayleigh–Gans (RG) anisotropic scattering models. It is found that, in spite of the standard diffusive regime assumption on the universality of the description of scattering in terms of the extinction coefficient and the transport length, the multiple scattering intensity depends on the form of the phase function and on the degree of anisotropy even for systems with identical extinction coefficients and transport lengths. In this case, the results obtained by the RG phase function are more sensitive to the scattering ansisotropy than those obtained by the HG function.
All orders of scattering are analyzed for two artifical canopies. The SHL canopy consists of Small Horizontal Leaves that are much smaller than the leaf-to-leaf spacing. The IHL canopy consists of Infinite Horizontal Layers, where each leaf is of infinite extent (a horizontal plane). Hemispheric leaf reflectances and transmittances independent of the direction of illumination lead to exact solutions for these models. Sunlight that penetrates to a given leaf area index level is much stronger in an SHL canopy than that in IHL; but the difference becomes muted when leaf transmittance is large. Multiple scattering enhances the hemispheric canopy reflectance more strongly in SHL than it does in IHL. The enhancement depends linearly on leaf transmittance in SHL and on the transmittance squared in IHL. Comparison with measured reflectances indicates that IHL model grossly underestimates multiple scattering in soybean canopies.
Inversion of electromagnetic (EM) signals reflected from or transmitted through a medium, or emitted by it due to internal sources can be used to investigate the optical and physical properties of a variety of scattering/absorbing/emitting materials. Such media encompass planetary atmospheres and surfaces (including water/snow/ice), and plant canopies. In many situations the signals emerging from such media can be described by a linear transport equation which in the case of EM radiation is the radiative transfer equation (RTE). Solutions of the RTE can be used as a forward model to solve the inverse problem to determine the medium state parameters giving rise to the emergent (reflected/transmitted/emitted) EM signals. A novel method is developed to determine layer-by-layer contributions to the emergent signals from such stratified, multilayered media based on the solution of the pertinent RTE. As a specific example of how this approach may be applied, the radiation reflected from a multilayered atmosphere is used to solve the problem relevant for EM probing by a space-based lidar system. The solutions agree with those obtained using the standard lidar approach for situations in which single scattering prevails, but this novel approach also yields reliable results for optically thick, multiple scattering aerosol and cloud layers that cannot be provided by the traditional lidar approach.