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NASA NTRS1984

Ultrasonic attenuation of a void-containing medium for very long wavelengths

Ultrasonic longitudinal through-thickness attenuation in an isotropic medium due to scattering by randomly distributed voids is considered analytically. The attenuation is evaluated on the assumption of no interaction between voids. The scattered power is assumed to be entirely lost, thus accounting for the ultrasonic attenuation. The scattered power due to the presence of a void is described in terms of the scattering cross section of the void. An exact solution exists for the scattering cross section of a spherical void. An approximate solution for the scattering cross section of an ellipsoidal void is developed based on the so-called Born approximation commonly used in quantum mechanics. This approximate solution is valid for k sub p a sub i much less than 1, where k sub p is the wave number of the incident longitudinal wave and a sub i is the largest dimension of the void. It is found that the shape of the void has negligible effect on the scattering cross section and that only the volume of the void is important. Thus, it is noted that in cases where k sub p a sub i is much less than 1, the exact scattering cross section of a spherical void having the same volume as an arbitrarily shaped void can be used for evaluating ultrasonic attenuation. Previously announced in STAR as N83-28466

Williams, J. H., Jr.↗

DOE OSTI2021

Spectroscopy of states in 136 Ba using the 138 Ba(p,t) reaction

Background: The 136 Ba isotope is the daughter nucleus in 136 Xe $ββ$ decay. It also lies in a shape transitional region of the nuclear chart, making it a suitable candidate to test a variety of nuclear models. Purpose: To obtain spectroscopic information on states in 136 Ba, which will allow a better understanding of its low-lying structure. These data may prove useful to constrain future 136 Xe → 136 Ba neutrinoless $ββ$ decay matrix element calculations. Methods: Here, a 138 Ba(p, t) reaction was used to populate states in 136 Ba up to approximately 4.6 MeV in excitation energy. The tritons were detected using a high-resolution Q3D magnetic spectrograph. A distorted wave Born approximation analysis was performed for the measured triton angular distributions. Results: 102 excited states in 136 Ba were observed, out of which 52 are reported for the first time. Definite spin-parity assignments are made for 26 newly observed states, while previously ambiguous assignments for ten other states are resolved. Together with other available data, the results are used to determine level densities in 136 Ba. These were compared with theory predictions, obtained using shell model calculations with Hamiltonians previously used for 136 Xe neutrinoless $ββ$ decay matrix element evaluations. Conclusions: The shell model predicted level densities agree reasonably well for the two Hamiltonians. However the results for theory and experiment are found to agree only at lower energies, diverging from one another for the higher lying states, with the discrepancy increasing with energy. This is presumably because of lower production cross sections for a majority of the higher-lying predicted states and the experimental limitations in resolving a large number of nearly degenerate states predicted by the theory.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Dispersive corrections in elastic electron-nucleus scattering: an investigation in the intermediate energy regime and their impact on the nuclear matter

Measurements of elastic electron scattering data within the past decade have highlighted two-photon exchange contributions as a necessary ingredient in theoretical calculations to precisely evaluate hydrogen elastic scattering cross sections. This correction can modify the cross section at the few percent level. In contrast, dispersive effects can cause significantly larger changes from the Born approximation. The purpose of this experiment is to extract the carbon-12 elastic cross section around the first diffraction minimum, where the Born term contributions to the cross section are small to maximize the sensitivity to dispersive effects. The analysis uses the LEDEX data from the high resolution Jefferson Lab Hall A spectrometers to extract the cross sections near the first diffraction minimum of 12 C at beam energies of 362 MeV and 685 MeV. The results are in very good agreement with previous world data, although with less precision. The average deviation from a static nuclear charge distribution expected from linear and quadratic fits indicate a 30.6% contribution of dispersive effects to the cross section at 1 GeV. The magnitude of the dispersive effects near the first diffraction minimum of 12 C has been confirmed to be large with a strong energy dependence and could account for a large fraction of the magnitude for the observed quenching of the longitudinal nuclear response. These effects could also be important for nuclei radii extracted from parity-violating asymmetries measured near a diffraction minimum.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1988

Electromagnetic wave probing of Earth's environment

Polarimetric radar backscattering from anisotropic Earth terrain such as snow-covered ice fields and vegetation fields with row structures provides a challenging modeling problem from the electromagnetic wave point of view. Earth terrain covers are modeled as random media characterized by different dielectric constants and correlation functions. A three-layer model will be used to simulate a vegetation field or a snow-covered ice field with the top layer being snow or leaves, the middle layer being ice of trunks, and the bottom layer being sea water or ground. The volume scattering effects of snow-covered sea ice are studied with a three-layer random medium model for microwave remote sensing. The strong fluctuation theory and the bilocal approximation are applied to calculate the effective permittivities for snow and sea ice. The wave scattering theory in conjunction with the distorted Born approximation is then used to compute bistatic coefficients and backscattering cross sections. Theoretical results are illustrated by matching experimental data for dry snow-covered thick first-year sea ice at Point Barrow. The results derived can also be applied to the passive remote sensing by calculating the emissivity from the bistatic scattering coefficients.

Kong, Jin AU↗

NASA NTRS1983

Electromagnetic backscattering from a layer of vegetation - A discrete approach

Electromagnetic backscattering from a layer of vegetation over a flat lossy ground is studied. The vegetated region is composed of leaves which are modeled by lossy circular dielectric discs with prescribed orientation statistics. The mean field in the layer is computed by using the Foldy approximation and a two-variable technique which is valid for small fractional volume. Simple expressions are given for the skin depth of the mean wave. Following this, the distorted Born approximation is used to calculate the co-polarized and cross polarized backscattering coefficients. These are then computed as a function of angle of incidence for different layer depths and leaf configurations.

Lang, R. H.↗

NASA NTRS1981

Electromagnetic backscattering from a sparse distribution of lossy dielectric scatterers

Electromagnetic backscattering from a sparse distribution of lossy dielectric particles having random orientation and position is studied. The paper begins by using the Foldy approximation to find an equation for the mean field. From this equation, an effective permittivity for the scattering medium is obtained. The correlation of the scattered field is found by employing the distorted Born approximation, i.e., particles embedded in the effective medium are assumed to be single scatterers. The above method is then used to find the backscattering coefficients from a leaf canopy. The leaf canopy is modeled by a half space of dielectric discs that are small in comparison to a wavelength. Numerical results show that the depolarized cross section is a sensitive function of leaf inclination angle statistics.

Lang, R. H.↗

NASA NTRS1971

Analytic cross sections for 1 1S, to 1 1S to 2 1S, 1 1S to 2 1P transitions in helium by electron impact

The 1 1s yields 1 1s elastic and 1 1s yields 2 1s and 1 1s yields 2 excitation cross sections of Helium atoms by collision with a charged particle are obtained as analytic functions of incident velocity. The first order time dependent scattering theory is used. Numerical values of electron -He cross sections are obtained for incident energies in the range 30 eV to 800 eV and compared with earlier Born approximation calculations and with available experimental data. It is found that at 100 eV and above, the present results are in good agreement with the experimental results. They are also closer to the experimental results than the corresponding Born calculations.

Sukumar, C. V.↗

NASA NTRS2006

Direct Measurement of Wave Kernels in Time-Distance Helioseismology

Solar f-mode waves are surface-gravity waves which propagate horizontally in a thin layer near the photosphere with a dispersion relation approximately that of deep water waves. At the power maximum near 3 mHz, the wavelength of 5 Mm is large enough for various wave scattering properties to be observable. Gizon and Birch (2002,ApJ,571,966)h ave calculated kernels, in the Born approximation, for the sensitivity of wave travel times to local changes in damping rate and source strength. In this work, using isolated small magnetic features as approximate point-sourc'e scatterers, such a kernel has been measured. The observed kernel contains similar features to a theoretical damping kernel but not for a source kernel. A full understanding of the effect of small magnetic features on the waves will require more detailed modeling.

Duvall, T. L., Jr.↗

DOE OSTI2025

Microscopic calculations with noniterative finite amplitude methods and the application to neutron radiative captures and inelastic scatterings

We derive the fully self-consistent quasiparticle random-phase approximation (QRPA) equations with noniterative finite amplitude methods and calculate the transition strengths of giant resonances. Then, we apply the QRPA results to both neutron radiative capture calculations based on the statistical Hauser-Feshbach theory and inelastic scattering calculations based on distorted-wave Born approximation (DWBA). We compare the calculated results with available experimental data and demonstrate how our approach can reproduce giant resonances and various nuclear reactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1980

Modified radiative transfer theory for a two-layer random medium

Modified radiative transfer (MRT) equations appropriate for electromagnetic wave propagation in bounded random media are derived from the Bethe-Salpeter equation with the ladder approximation and the Dyson equation with the nonlinear approximation. The MRT equations are then solved with the first-order renormalization approximation to obtain analytical results for the backscattering cross sections of a two-layer random medium with arbitrary three-dimensional correlation functions. The coherent effects of the MRT theory are illustrated and comparisons are made with backscattering cross sections obtained with the first Born approximation to the wave equation.

Zuniga, M. A.↗

NASA NTRS1993

Polarimetric backscattering from sea ice

Polarimetric backscattering from sea ice is presented. Theoretical models for backscattering are first presented for various ice types. Then, theoretical results are compared with experimental data for new thin ice, first-year ice, and multi-year ice. Sea ice is modeled as a layer medium containing random scatterers and rough interfaces. For multi-year sea ice with snow cover, the sea ice layer is modeled as an ice background with embedded spheroidal air bubbles and the snow layer as air with ice grains. The hummocky topography on multi-year ice is characterized by a Gaussian distribution which has an averaging effect on backscattering coefficients. First-year sea ice is described by an ice medium hosting ellipsoidal brine inclusions. These inclusions are oriented preferentially in the vertical direction due to the columnar structure of first-year sea ice. Azimuthally, the orientation of the brine pockets are random corresponding to the random c-axes in sea ice, unless the axes are oriented by sea currents. For thin ice in newly opened leads, it has been observed that there exists a thin brine layer with very high salinity on the top surface of the new ice. This brine layer is depicted as a medium with high permittivity which can significantly affect electromagnetic scattering signatures from the lower thin ice layer, with a higher fractional volume of brine inclusions due to higher salinity as compared to thick first-year sea ice. The rough medium interfaces are described as Gaussian rough surfaces characterized by root-mean-square heights and surface correlation lengths. The contribution from rough surface, calculated under the Kirchhoff approximation or small perturbation method, is assumed to be independent from volume scattering. The total loss including absorption and scattering losses in the scattering media is represented by the imaginary part of effective permittivity obtained from the strong fluctuation theory. The polarimetric scattering coefficients for different ice types are then derived under the distorted Born approximation.

Nghiem, S. V.↗

NASA NTRS1981

Kinetic theory of relativistic plasmas

The thermalization of particle kinetic motion by binary collisions is considered for a plasma with a Boltzmann constant-temperature product approximately equal to 10 to 100 times the product of the electron mass with the square of the speed of light. At this temperature, the principal mechanism for relaxation of electron motion is via radiationless electron-electron collisions (Moller scattering). Ions are nonrelativistic, but are energetic enough so that their Coulomb scattering can be treated in the Born approximation. Relaxation times are computed and Boltzmann-equation Fokker-Planck operators are derived for the various binary-collision processes. The expression for the rate of kinetic energy exchange between electron and ion gases is derived for the case where the gases are at different temperatures.

Gould, R. J.↗

DOE OSTI2021

Electronic scattering off a magnetic hopfion

We study scattering of itinerant electrons off a magnetic hopfion in a three-dimensional metallic magnet described by a magnetization vector S(r). A hopfion is a confined topological soliton of S(r) characterized by an emergent magnetic field Bγ(r)≡ε αβγ S∙(∇ α S×∇ β S)/4≠0 with vanishing average value [B(r)]=0. We evaluate the scattering amplitude in the opposite limits of large and small hopfion radius R using the eikonal and Born approximations, respectively. In both limits, we find that the scattering cross section contains a skew-scattering component giving rise to the Hall effect within a hopfion plane. That conclusion contests the popular notion that the Hall effect in noncollinear magnetic structures necessarily implies [B(r)]≠0. In the limit of small hopfion radius pR<<1, we expand the Born series in powers of momentum p and identify different expansion terms corresponding to the hopfion anisotropy, toroidal moment, and skew scattering.

36 MATERIALS SCIENCE↗

NASA NTRS1981

Radiative transfer theory for active remote sensing of a layer of small ellipsoidal scatterers

The radiative transfer theory is applied within the Rayleigh approximation to calculate the backscattering cross section of a layer of randomly positioned and oriented small ellipsoids. The orientation of the ellipsoids is characterized by a probability density function of the Eulerian angles of rotation. The radiative transfer equations are solved by an iterative approach to first order in albedo. In the half space limit the results are identical to those obtained via the approach of Foldy's and distorted Born approximation. Numerical results of the theory are illustrated using parameters encountered in active remote sensing of vegetation layers. A distinctive characteristic is the strong depolarization shown by vertically aligned leaves.

Tsang, L.↗

NASA NTRS1997

Coherent Effects in Microwave Backscattering Models for Forrest Canopies

In modeling forest canopies, several scattering mechanisms are taken into account: (1) volume scattering; (2) surface-volume interaction; and (3) surface scattering from forest floor. Depending on the structural and dielectric characteristics of forest canopies, the relative contribution of each mechanism in the total backscatter signal of an imaging radar can vary. In this paper, two commonly used first-order discrete scattering models, distorted born approximation (DBA) and radiative transfer (RT) are used to simulate the backscattered power received by polarimetric radars at P-, L-, and C-bands over coniferous and deciduous forests. The difference between the two models resides on the coherent effect in the surface-volume interaction terms. To demonstrate this point, the models are first compared based on their underlying theoretical assumptions and then according to simulation results over coniferous and deciduous forests. It is shown that by using the same scattering functions for various components of trees (i.e., leaf, branch, stem), the radiative transfer and distorted Born models are equivalent, except in low frequencies, where surface-volume interaction terms may become important, and the coherent contribution may be significant. In this case, the difference between the two models can reach up to 3 dB in both co-polarized and cross-polarized channels, which can influence the performance of retrieval algorithms.

Saatchi, Sasan S.↗

DOE OSTI2024

coh3

CoH3 (CoH ver.3) is an optical model, exciton pre-equilibrium, and Hauser-Feshbach statistical model code, which calculates nuclear reaction cross sections for medium to heavy targets in the keV to MeV energy region. This program is written in standard C++, divided into approximately 200 source and header files. CoH solves the Schroedinger equation for optical potentials defined in the code, and calculates differential elastic scattering, reaction, and total cross sections, for neutron, proton, deuteron, triton, 3He, and alpha-particle. Deformed optical potentials are solved with the coupled-channels method, in which the ground state rotational band members, or vibrational phonon states are coupled. The optical model gives particle transmission coefficients that are fed into the statistical model calculations. CoH includes the pre-equilibrium model (exciton model), the direct/semidirect capture model, and the multi-stage Hauser-Feshbach statistical decay with width fluctuation correction based on the Gaussian orthogonal ensemble. For weakly coupled levels, the DWBA (distorted wave Born approximation) method is used to calculate the direct inelastic scattering process to the excited states.

Kawano, Toshihiko↗

NASA NTRS1977

Vibrational and rotational transitions in low-energy electron-diatomic-molecule collisions. I - Close-coupling theory in the moving body-fixed frame. II - Hybrid theory and close-coupling theory: An /l subscript z-prime/-conserving close-coupling approximation

A detailed vibrational-rotational (V-R) close-coupling formulation of electron-diatomic-molecule scattering is developed in which the target molecular axis is chosen to be the z-axis and the resulting coupled differential equation is solved in the moving body-fixed frame throughout the entire interaction region. The coupled differential equation and asymptotic boundary conditions in the body-fixed frame are given for each parity, and procedures are outlined for evaluating V-R transition cross sections on the basis of the body-fixed transition and reactance matrix elements. Conditions are discussed for obtaining identical results from the space-fixed and body-fixed formulations in the case where a finite truncated basis set is used. The hybrid theory of Chandra and Temkin (1976) is then reformulated, relevant expressions and formulas for the simultaneous V-R transitions of the hybrid theory are obtained in the same forms as those of the V-R close-coupling theory, and distorted-wave Born-approximation expressions for the cross sections of the hybrid theory are presented. A close-coupling approximation that conserves the internuclear axis component of the incident electronic angular momentum (l subscript z-prime) is derived from the V-R close-coupling formulation in the moving body-fixed frame.

Choi, B. H.↗

NASA NTRS1991

Remote sensing of earth terrain

In remote sensing, the encountered geophysical media such as agricultural canopy, forest, snow, or ice are inhomogeneous and contain scatters in a random manner. Furthermore, weather conditions such as fog, mist, or snow cover can intervene the electromagnetic observation of the remotely sensed media. In the modelling of such media accounting for the weather effects, a multi-layer random medium model has been developed. The scattering effects of the random media are described by three-dimensional correlation functions with variances and correlation lengths corresponding to the fluctuation strengths and the physical geometry of the inhomogeneities, respectively. With proper consideration of the dyadic Green's function and its singularities, the strong fluctuation theory is used to calculate the effective permittivities which account for the modification of the wave speed and attenuation in the presence of the scatters. The distorted Born approximation is then applied to obtain the correlations of the scattered fields. From the correlation of the scattered field, calculated is the complete set of scattering coefficients for polarimetric radar observation or brightness temperature in passive radiometer applications. In the remote sensing of terrestrial ecosystems, the development of microwave remote sensing technology and the potential of SAR to measure vegetation structure and biomass have increased effort to conduct experimental and theoretical researches on the interactions between microwave and vegetation canopies. The overall objective is to develop inversion algorithms to retrieve biophysical parameters from radar data. In this perspective, theoretical models and experimental data are methodically interconnected in the following manner: Due to the complexity of the interactions involved, all theoretical models have limited domains of validity; the proposed solution is to use theoretical models, which is validated by experiments, to establish the region in which the radar response is most sensitive to the parameters of interest; theoretically simulated data will be used to generate simple invertible models over the region. For applications to the remote sensing of sea ice, the developed theoretical models need to be tested with experimental measurements. With measured ground truth such as ice thickness, temperature, salinity, and structure, input parameters to the theoretical models can be obtained to calculate the polarimetric scattering coefficients for radars or brightness temperature for radiometers and then compare theoretical results with experimental data. Validated models will play an important role in the interpretation and classification of ice in monitoring global ice cover from space borne remote sensors in the future. We present an inversion algorithm based on a recently developed inversion method referred to as the Renormalized Source-Type Integral Equation approach. The objective of this method is to overcome some of the limitations and difficulties of the iterative Born technique. It recasts the inversion, which is nonlinear in nature, in terms of the solution of a set of linear equations; however, the final inversion equation is still nonlinear. The derived inversion equation is an exact equation which sums up the iterative Neuman (or Born) series in a closed form and, thus, is a valid representation even in the case when the Born series diverges; hence, the name Renormalized Source-Type Integral Equation Approach.

Yueh, Herng-Aung↗