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Attempt to determine what effect the anisotropy of the background medium will have on the scattering of electromagnetic waves from ionospheric irregularities. A Green's function is used to solve the scattered power using a certain bistatic geometry. Since the medium is anisotropic, cross-mode scattering in addition to self-mode scattering is possible. Several examples are given.
Remote sensing of brightness temperatures of a scattering medium composed of spherical scatterers beneath a homogeneous surface layer is studied by using Mie scattering functions. We illustrate the effects of a surface layer by plotting the brightness temperatures as functions of frequency and viewing angle for different layer thicknesses, dielectric constants, and fractional scattering volumes. It is found that the brightness temperature increases when the loss tangent of the surface layer is increased and when the fractional volume occupied by the scatterers is decreased. In the absence of a surface layer the brightness temperature is usually decreasing as a function of frequency. The presence of a homogeneous layer may cause the brightness temperature to increase with frequency. At all viewing angles the vertical polarization is brighter than the horizontal polarization.
The seismic codas, representing that part of the seismogram following the arrival of the surface waves or the direct S waves, characteristic of the earth and moon are compared with regard to the implications of coda characteristics for scattering and attenuation. Scattering models based on single S-S scatter theory, in which seismic energy in the coda is assumed to be S waves that have undergone only one scattering without conversion, and on diffusion theory, which assumed that energy in the coda has been scattered many times, are examined, and situations where the single-scattering and multiple-scattering theories are applicable are distinguished by the ratio of attenuation distance to the scattering mean free path. Values of the attenuation distance and the mean free path derived from coda studies for the earth and moon are compared, and it is found that for the frequency range 0.5-10 Hz, diffusion scattering is important in lunar codas, while at frequencies from 1 to 25 Hz single scattering is important in terrestrial codas. It is pointed out that attenuation acts to eliminate scattering paths much longer than the attenuation length. The observed differences between terrestrial and lunar codas are thus attributed to lesser attenuation and greater scattering on the moon.
In this document drafted by the Neutrino Scattering Theory Experiment Collaboration (NuSTEC), we provide input on the synergies between theoretical and experimental efforts that can provide critical input to the prediction accuracy needed for the forthcoming high-precision neutrino measurements. These efforts involve a wide range of energies and interaction processes, as well as target nuclei and interaction probes. The challenges discussed will be overcome only through the active support of integrated collaboration across strong and electroweak physics from both the nuclear and high energy physics communities.
Scattered electromagnetic waves from material bodies of different forms contain, in an intricate way, precise information on the intrinsic, geometrical and physical properties of the objects. Scattering theories, ever deepening, aim to provide dependable interpretation and prediction to the complicated interaction of electromagnetic radiation with matter. There are well-established multiple-scattering formulations based on classical electromagnetic theories. An example is the Generalized Multi-particle Mie-solution (GMM), which has recently been extended to a special version ̶ the GMM-PA approach, applicable to finite periodic arrays consisting of a huge number (e.g., >>106) of identical scattering centers [1]. The framework of the GMM-PA is nearly complete. When the size of the constituent unit scatterers becomes considerably small in comparison with incident wavelength, an appropriate array of such small element volumes may well be a satisfactory representation of a material entity having an arbitrary structure. X-ray diffraction is a powerful characterization tool used in a variety of scientific and technical fields, including material science. A diffraction pattern is nothing more than the spatial distribution of scattered intensity, determined by the distribution of scattering matter by way of its Fourier transform [1]. Since all linear dimensions entered into Maxwell's equations are normalized by wavelength, an analogy exists between optical and X-ray diffraction patterns. A large set of optical diffraction patterns experimentally obtained can be found in the literature [e.g., 2,3]. Theoretical results from the GMM-PA have been scrutinized using a large collection of publically accessible, experimentally obtained Fraunhofer diffraction patterns. As far as characteristic structures of the patterns are concerned, theoretical and experimental results are in uniform agreement; no exception has been found so far. Closely connected with the spatial distribution of scattered intensities are cross sections, such as for extinction, scattering, absorption, and radiation pressure, as a critical type of key quantity addressed in most theoretical and experimental studies of radiative scattering. Cross sections predicted from different scattering theories are supposed to be in general agreement. For objects of irregular shape, the GMM-PA solutions can be compared with the highly flexible Discrete Dipole Approximation (DDA) [4,5] when dividing a target to no more than ~106 unit cells. Also, there are different ways to calculate the cross sections in the GMM-PA, providing an additional means to examine the accuracy of the numerical solutions and to unveil potential issues concerning the theoretical formulations and numerical aspects. To solve multiple scattering by an assembly of material volumes through classical theories such as the GMM-PA, the radiative properties of the component scatterers, the complex refractive index in particular, must be provided as input parameters. When using a PA to characterize a material body, this involves the use of an adequate theoretical tool, an effective medium theory, to connect Maxwell's phenomenogical theory with the atomistic theory of matter. In the atomic theory, one regards matter as composed of interacting particles (atoms and molecules) embedded in the vacuum [6]. However, the radiative properties of atomic-scaled particles are known to be substantially different from bulk materials. Intensive research efforts in the fields of cluster science and nanoscience attempt to bridge the gap between bulk and atom and to understand the transition from classical to quantum physics. The GMM-PA calculations, which place virtually no restriction on the component-particle size, might help to gain certain insight into the transition.
Within the context of eikonal scattering theory, a generalized optical model potential approximation to the nucleus-nucleus multiple scattering series is used in an abrasion-ablation collision model to predict abrasion cross sections for relativistic projectile heavy ions. Unlike the optical limit of Glauber theory, which cannot be used for very light nuclei, the abrasion formalism is valid for any projectile target combination at any incident kinetic energy for which eikonal scattering theory can be utilized. Results are compared with experimental results and predictions from Glauber theory.
It is shown through the use of transformation theory that unique semiclassical atomic scattering states which obey the asymptotic conditions of formal scattering theory can be derived by transforming 'nontraveling' atomic states, ie., states whose coordinate variables are referred to a stationary origin, to frames at rest with respect to the incoming or outgoing particles. An overview of the problem of properly defining such scattering states is presented. The operator which carries out the necessary transformation from inertial to noninertial frames is derived and its properties are discussed. The relation of this transformation operator to the 'translation factor' discussed in the literature is presented. The application of this operator to transform the time-dependent Schroedinger equation from an inertial to a noninertial frame is presented and shown to introduce new terms in the resulting equation. The implications of these new terms to scattering problems are discussed.
Impact expansions and interference patterns in atomic scattering theory for cases of forward scattering, backscatter, inversion problem and screened Coulomb potential approximation
Many applications of electromagnetic scattering involve particles immersed in an absorbing rather than lossless medium, thereby making the conventional scattering theory potentially inapplicable. To analyze this issue quantitatively, we employ the FORTRAN program developed recently on the basis of the first-principles electromagnetic theory to study far-field scattering by spherical particles embedded in an absorbing infinite host medium. We further examine the phenomenon of negative extinction identified recently for monodisperse spheres and uncover additional evidence in favor of its interference origin. We identify the main effects of increasing the width of the size distribution on the ensemble-averaged extinction efficiency factor and show that negative extinction can be eradicated by averaging over a very narrow size distribution. We also analyze, for the first time, the effects of absorption inside the host medium and ensemble averaging on the phase function and other elements of the Stokes scattering matrix. It is shown in particular that increasing absorption significantly suppresses the interference structure and can result in a dramatic expansion of the areas of positive polarization. Furthermore, the phase functions computed for larger effective size parameters can develop a very deep minimum at side-scattering angles bracketed by a strong diffraction peak in the forward direction and a pronounced backscattering maximum.
Theory of Thomson scattering from weakly ionized plasma extended to include effects of unequal electron and ion temperatures, constant magnetic field, and electron drift
A theory is described in which the moon is regarded as a "quasi-smooth" scatterer at radar frequencies. A scattered pulse is then composed of a number of individual returns each of which is provided by a single scattering area. In this manner it is possible to account for all the major features of the pulse, and the evidence in favor of the theory is presented. From a study of the measured power received at different frequencies, it is shown that the scattering area nearest to the earth is the source of a specular return, and it is then possible to obtain information about the material of which the area is composed. The electromagnetic constants are derived and their significance discussed.
A theory of electron-molecule scattering is developed which is a synthesis of close-coupling and adiabatic-nuclei theories. Specifically, the theory is close-coupling with respect to vibrational degrees of freedom and adiabatic-nuclei with respect to rotation. It can be applied to any number of partial waves required; the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations is given which indicates those partial waves and energy domains requiring the various approximations. The theory allows all cross sections (pure rotational, vibrational, simultaneous vibration-rotation, differential, and total) to be calculated, and explicit formulas for all these cross sections are given. The theory is applied to low-energy e-N2 scattering. The fixed-nuclei results are such that the criterion shows clearly that vibrational close coupling is necessary, but only for the Pi sub g partial wave. It is found that the close-coupling calculation for this wave gives rise to the substructure as well as the gross structure of the 2.4-eV resonance and that vibrational excitation cross sections are about twice as large as previously inferred.
Light scattering theory applied to particle arrays to explain scattering in highly reflecting paint coatings
The microwave brightness temperature for snow fields was studied assuming that the snow cover consists of closely packed scattering spheres which do not interact coherently. The Mie scattering theory was used to compute the volume scattering albedo. It is shown that in the wavelength range from 0.8 to 2.8 cm, most of the micro-radiation emanates from a layer 10 meters or less in thickness. It is concluded that it is possible to determine snow accumulation rates as well as near-surface temperature.
A numerical method was developed using geometrical optics to predict far-field optical scattering from particles that are symmetric about the optic axis. The diffractive component of scattering is calculated and combined with the reflective and refractive components to give the total scattering pattern. The phase terms of the scattered light are calculated as well. Verification of the method was achieved by assuming a spherical particle and comparing the results to Mie scattering theory. Agreement with the Mie theory was excellent in the forward-scattering direction. However, small-amplitude oscillations near the rainbow regions were not observed using the numerical method. Numerical data from spheroidal particles and hemispherical particles are also presented. The use of hemispherical particles as a calibration standard for intensity-type optical particle-sizing instruments is discussed.
A theory of electron-molecule scattering was developed which was a synthesis of close coupling and adiabatic-nuclei theories. The theory is shown to be a close coupling theory with respect to vibrational degrees of freedom but is a adiabatic-nuclei theory with respect to rotation. It can be applied to any number of partial waves required, and the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations and not on experiment can be given as to which partial waves and energy domains require the various approximations. The theory allows all cross sections (i.e., pure rotational, vibrational, simultaneous vibration-rotation, differential and total) to be calculated. Explicit formulae for all the cross sections are presented.
Spherically symmetrical classical scattering theory shows dependence on phase shift through appearance in quantal formulas for scattering amplitude and total cross section
The extinction paradox is a contradiction between geometrical optics results which predict that at high frequencies the scattering cross section of an object should equal its geometrical cross section and rigorous scattering theory which shows that at high frequencies the scattering cross section approaches twice the geometrical cross section of the object. Confusion about the reason for this paradox persists today even though the nature of the paradox was correctly identified many years ago by Brillouin. The resolution of the paradox is restated and illustrated with an example, and then the implications to the interpretation of scattering cross sections are identified.