Born Approximation Research Articles

Finite-Temperature Hole-Magnon Dynamics in an Antiferromagnet.

Employing the numerically accurate multiple Davydov Ansatz in combination with the thermo-field dynamics approach, we delve into the interplay of the finite-temperature dynamics of holes and magnons in an antiferromagnet, which allows for scrutinizing previous predictions from the self-consistent Born approximation while offering, for the first time, accurate finite-temperature computation of detailed magnon dynamics as a response and a facilitator to the hole motion. The study also uncovers a pronounced temperature dependence of the magnon and hole populations, pointing to the feasibility of potential thermal manipulation and control of hole dynamics. Our methodology can be applied not only to the calculation of steady-state angular-resolved photoemission spectra but also to the simulation of femtosecond terahertz pump-probe and other nonlinear signals for the characterization of antiferromagnetic materials.

Highly Ordered Monolayers of μm-Sized Polystyrene Spheres Studied by Grazing-Incidence Small-Angle X-ray Scattering, Simulations, and Geometrical Calculations.

Unraveling the two-dimensional (2D) structural ordering of colloidal particles assembled at a flat surface is essential for understanding and optimizing their physical properties. So far, grazing-incidence small-angle X-ray scattering (GISAXS) has been widely used to determine crystallographic information on 2D self-assembled structures of nanosize objects. However, solving the structure of 2D lattices consisting of micrometer (μm)-sized objects still remains a challenge using scattering methods. Here, a model 2D SCALMS (supported catalytically active liquid metal solution) template is fabricated from μm-sized polystyrene (PS) spheres that form a monolayer on top of the flat solid support. GISAXS patterns of the sample were collected for rotation angles around its surface normal in steps of 3°. For every rotation angle, different Bragg-type interference maxima along the out-of-plane (qz) direction were observed. On the basis of simulations of GISXAS patterns of single domains of ordered particle arrangements using the distorted wave Born approximation (DWBA) and validation against a simple geometrical scattering model, the interference maxima could nicely be interpreted to originate from a monolayer of the μm-sized spherical particles which are arranged in domains of hexagonal 2D paracrystalline order. This novel GISAXS evaluation technique serves as a proof of principle for determining the μm-size periodicity of 2D crystalline domains and demonstrates its potential to spatially resolve the relative orientations of such domains with respect to a reference direction.

The Born approximation in the three-dimensional Calderón problem Ⅱ: Numerical reconstruction in the radial case

In this work we illustrate a number of properties of the Born approximation in the three-dimensional Calderón inverse conductivity problem by numerical experiments. The results are based on an explicit representation formula for the Born approximation recently introduced by the authors. We focus on the particular case of radial conductivities in the ball $ B_R \subset \mathbb{R}^3 $ of radius $ R $, in which the linearization of the Calderón problem is equivalent to a Hausdorff moment problem. We give numerical evidences that the Born approximation is well defined for $ L^{\infty} $ conductivities, and present a novel numerical algorithm to reconstruct a radial conductivity from the Born approximation under a suitable smallness assumption. We also show that the Born approximation has depth-dependent uniqueness and approximation capabilities depending on the distance (depth) to the boundary $ \partial B_R $. We then investigate how increasing the radius $ R $ affects the quality of the Born approximation, and the existence of a scattering limit as $ R\to \infty $. Similar properties are also illustrated in the inverse boundary problem for the Schrödinger operator $ -\Delta +q $, and strong recovery of singularity results are observed in this case.

Neutron-proton pairing in the unstable N=Z nuclei of the f-shell through two-nucleon transfer reactions

Pair transfer is a unique tool to study pairing correlations in nuclei. Neutron-proton pairing is investigated in the N=Z nuclei of the f-shell, through the reaction (p,3He) in inverse kinematics, that allows to populate at the same time the lowest J=0+, T=1 (isovector pairing) state and J=1+, T=0 (isoscalar pairing) state. Radioactive beams of 56Ni and 52Fe produced by fragmentation at the GANIL/LISE facility combined with particle and gamma-ray detection make it possible to carry out this study from 48Cr (mid-shell nucleus) to 56Ni (doubly-magic nucleus). The cross-sections were extracted and compared with second-order distorted-wave born approximation (DWBA) calculations performed with neutron-proton amplitudes obtained from shell model calculations with GXPF1 interaction. Very low cross-sections for the J=1+,T=0 state (isoscalar channel) were observed. The cross-section for 56Ni is one of order of magnitude lower than for 40Ca showing a strong reduction of the isoscalar channel in the f-shell as compared to the sd-shell. On the other hand, the increase of the cross-section towards the middle of the shell for the isovector channel points towards a possible superfluid phase.

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One of the most important areas of plasma physics is the physics of elementary processes, that is, the physics of processes occurring during collisions of molecules, atoms, ions, electrons and photons. The composition of plasma, its thermodynamic, transport, optical and other properties are determined by the processes occurring in the plasma system, as well as their speeds. For this reason, by analyzing collision processes, it is possible to investigate certain properties of the plasma. Traditionally, the study of elementary processes within a specific model begins with the study of the scattering cross section, when the first estimates are made using simple methods. These methods include the Born method, which can and should be applied in practice.In this work, studies were carried out of the influence of collective effects in plasma on the states and energies of hydrogen atoms and hydrogen-like ions, as well as on excitation processes. Quantum mechanics methods were used in the research process, including the variational method and the perturbation theory, especially the Born approximation for inelastic scattering processes. As a result of the work, data were obtained based on the Born approximation for the process of excitation of a hydrogen atom by electron impact. The Born approximation shows better results in the case of high-energy collisions. The results obtained during the study have scientific and experimental significance, since they make it possible to determine the velocity coefficients through the calculation of scattering cross sections. These coefficients, in turn, are necessary to solve the kinetic equation used to describe the sedimentation (concentration) of particles in the plasma.

Generalized oscillator strengths and integral cross sections of krypton studied by high-energy electron scattering

Absolute generalized oscillator strengths of the valence-shell excitations of krypton have been determined with an incident electron energy of 1500 eV and an energy resolution of about 80 meV. By employing the relative flow technique with a dilute target, the pressure effect is excluded and the accuracy of the measured generalized oscillator strengths is improved. By comparing the present generalized oscillator strengths with the previous experimental and theoretical results, it is found that the first Born approximation is not reached at the squared momentum transfer larger than 1 a.u.. The optical oscillator strengths have been obtained by extrapolating the measured generalized oscillator strengths to zero squared momentum transfer, which cross-checks the previous electron impact and photoabsorption results. With the aid of the BE-scaling method, the integral cross sections of krypton have been determined from the excitation threshold to 5000 eV. The present oscillator strengths and integral cross sections supplement the fundamental database of the electron scattering of krypton and provide a benchmark for the theoretical methods.

Inverse Scattering Under the Born Approximation Using an Object T-Matrix and Full Bistatic Spherical Sampling Geometry

Inverse Scattering Under the Born Approximation Using an Object T-Matrix and Full Bistatic Spherical Sampling Geometry

Influence of 2-D Transceiver Array Aperture Size and Polarization on 3-D Microwave Imaging of Subsurface Objects Under Born Approximation

Influence of 2-D Transceiver Array Aperture Size and Polarization on 3-D Microwave Imaging of Subsurface Objects Under Born Approximation

Influence of ab initio derived site-dependent hopping parameters on electronic transport in graphene nanoribbons.

Graphene Nano Ribbons (GNRs) have been studied extensively due to their potential applications in electrical transport, optical devices, etc. The Tight Binding (TB) model is a common method used to theoretically study the properties of GNRs. However, the hopping parameters of two-dimensional graphene (2DG) are often used as the hopping parameters of the TB model of GNRs, which may lead to inaccuracies in the prediction of GNRs. In this work, we calculated the site-dependent hopping parameters from density functional theory and construction of Wannier orbitals for use in a realistic TB model. It has been found that due to the edge effect, the hopping parameters of edge C atoms are markedly different from the bulk part, which is prominently observed in narrow GNRs. Compared to graphene, the change of hopping parameter of edge C atoms of zigzag GNRs (ZGNRs) and armchair GNRs (AGNRs) is as high as 0.11 and 0.08 eV, respectively. Moreover, we investigated the impact of the calculated site-dependent (SD) hopping parameters on the electronic transport properties of GNRs in the absence and presence of the perpendicular electric field and dilute charged impurities using the Green function approach, Landauer-Büttiker formalism and self-consistent Born approximation. We find an electron-hole asymmetry in the electronic structure and transport properties of ZGNRs with SD hopping parameters. Furthermore, AGNRs with SD hopping energies show a band gap regardless of their width, while AGNRs with 2DG hopping parameters exhibit metallic or semiconductor phases depending on their width. In addition, electric field-induced 4-ZGNR with SD hopping parameters undergoes a metallic to n-doped semiconducting phase transition whereas for 4-ZGNR with 2DG hopping parameters and 8-AGNRs with 2DG or SD hopping parameters, the application of an electric field opens the band gap in both conduction and valence bands simultaneously. Our findings provide evidence for the electron-hole symmetry breaking in ZGNR with SD hopping parameters and make ZGNRs a suitable candidate in valleytronic devices.

A Physics-Based Deep Learning to Extend Born Approximation Validity to Strong Scatterers

A Physics-Based Deep Learning to Extend Born Approximation Validity to Strong Scatterers

Real-time tracking of moving objects from scattering matrix in real-world microwave imaging

<abstract><p>The problem of the real-time microwave imaging of small, moving objects from a scattering matrix without diagonal elements, whose elements are measured scattering parameters, is considered herein. An imaging algorithm based on a Kirchhoff migration operated at single frequency is designed, and its mathematical structure is investigated by establishing a relationship with an infinite series of Bessel functions of integer order and antenna configuration. This is based on the application of the Born approximation to the scattering parameters of small objects. The structure explains the reason for the detection of moving objects via a designed imaging function and supplies some of its properties. To demonstrate the strengths and weaknesses of the proposed algorithm, various simulations with real-data are conducted.</p></abstract>

Electron impact single ionization TDCS of H2O at 81 eV for coplanar asymmetric emission of electrons

We report the results of triple differential cross section (TDCS) for the electron impact single ionization of water molecules at incident electron energy 81 eV for coplanar asymmetric emission of electrons. The TDCS results have been obtained in distorted wave second Born approximation using orientation averaged molecular orbital (OAMO) approximation. The TDCS results have been calculated for the ionization of 1b1 and 3a1 molecular orbital of water molecules for the coplanar asymmetric emission of electrons. The obtained theoretical TDCSs are compared with the available measurements as well as with the first Born results. The second Born results are found to be significant by improving agreement with the measurements particularly in the binary peak region.

Positron and Electron Impact Elastic Scattering by Atomic Beryllium

Theoretical results for positron and electron elastic scattering from beryllium atom at incident energies ranging from the first inelastic threshold to 200 eVare presented. Elastic, total, momentum transfer, and differential cross sections are computed using both the first order distorted wave Born approximation andthe optical potential approaches utilizing a complex potential. We have shown that our data agree fairly well with the available data and provided the details of thePhysics in case of discrepancies. This study demonstrates the importance of accurate atomic elastic scattering cross sections.

Description of elastic scattering for 7Li-induced reactions on 1p-shell nuclei* *Supported by the National Natural Science Foundation of China (11405099, 11575291, 12065003), the Natural Science Foundation of Shanxi Province, China (202103021224309, 201901D111317). This work is also a part of IAEA Coordinated Research Projects (CRPs) on Recommended Input Parameter Library (RIPL) for Fission Cross Section Calculations (20464)

The experimental data of elastic scattering angular distributions for 9Be, 10B, 11B, 12C, 13C, 15N, and 16O targets from 4.5 to 131.8 MeV and 7Li target from 8.0 to 42.0 MeV are fitted to realize the global phenomenological optical potentials (GPOPs) for the 7Li-induced reactions on 1p-shell nuclei. Thus, the 7Li elastic scattering from the 1p-shell nuclei can be systematically described using the established GPOPs. The elastic scattering angular distributions are also reanalyzed using a microscopic method within the framework of the new version of double folding São Paulo potential (SPP2). To better describe the elastic scattering at backward angles, the contribution of elastic transfer is further estimated by the distorted wave Born approximation (DWBA) method. Based on the obtained GPOPs, the inelastic scattering angular distributions are also obtained through the coupled channels (CC) method for the different excited states.

A Novel Analysis of Super-Resolution for Born-Iterative-Type Algorithms in Microwave Medical Sensing and Imaging.

Microwave medical sensing and imaging (MMSI) is a highly active research field. In MMSI, electromagnetic inverse scattering (EIS) is a commonly used technique that infers the internal characteristics of the diseased area by measuring the scattered field. It is worth noting that the image formed by EIS often exhibits the super-resolution phenomenon, which has attracted much research interest over the past decade. A classical perspective is that multiple scattering leads to super-resolution, but this is subject to debate. This paper aims to analyze the super-resolution behavior for Born-iterative-type algorithms for the following three aspects. Firstly, the resolution defined by the traditional Rayleigh criterion can only be applied to point scatterers. It does not suit general scatterers. By using the Sparrow criterion and the generalized spread function, the super-resolution condition can be derived for general scatterers even under the Born approximation (BA) condition. Secondly, an iterative algorithm results in larger coefficients in the high-frequency regime of the optical transfer function compared to non-iterative BA. Due to the anti-apodization effect, the spread function of the iterative method becomes steeper, which leads to a better resolution following the definition of the Sparrow criterion mentioned above. Thirdly, the solution from the previous iteration, as the prior knowledge for the next iteration, will cause changes in the total field, which provides additional information outside the Ewald sphere and thereby gives rise to super-resolution. Comprehensive numerical examples are used to verify these viewpoints.

Nonlinear least-squares reverse time migration of prismatic waves for delineating steeply dipping structures

Prismatic reflections in seismic data carry abundant information about subsurface steeply dipping structures, such as salt flanks or near-vertical faults, playing an important role in delineating these structures when effectively used. Conventional linear least-squares reverse time migration (L-LSRTM) fails to use prismatic waves due to the first-order Born approximation, resulting in a blurry image of steep interfaces. We develop a nonlinear LSRTM (NL-LSRTM) method to take advantage of prismatic waves for the detailed characterization of subsurface steeply dipping structures. Compared with current least-squares migration methods of prismatic waves, our NL-LSRTM is nonlinear and thus avoids the challenging extraction of prismatic waves or the prior knowledge of L-LSRTM results. The gradient of NL-LSRTM consists of the primary and prismatic imaging terms, which can accurately project observed primary and prismatic waves into the image domain for the simultaneous depiction of near-horizontal and near-vertical structures. However, we find that the full Hessian-based Newton normal equation has two similar terms, which prompts us to make further comparison between the Newton normal equation and our NL-LSRTM. We determine that the Newton normal equation is problematic when applied to the migration problem because the primary reflections in the seismic records will be incorrectly projected into the image along the prismatic wavepath, resulting in an artifact-contaminated image. In contrast, the nonlinear data-fitting process included in the NL-LSRTM contributes to balancing the amplitudes of primary and prismatic imaging results, thus making NL-LSRTM produce superior images compared with the Newton normal equation. Several numerical tests validate the applicability and robustness of NL-LSRTM for the delineation of steeply dipping structures and illustrate that the imaging results are much better than the conventional L-LSRTM.

Thermalization of radiation-induced electrons in wide-bandgap materials: A first-principles approach

The present study is concerned with simulating the thermalization of high-energy charge carriers (electrons and/or electron–hole pairs), generated by ionizing radiation, in diamond and β-Ga2O3. Computational tools developed by the nuclear/particle physics and electronic device communities allow for accurate simulation of charge-carrier transport and thermalization in the high-energy (exceeding ∼100 eV) and low-energy (below ∼10 eV) regimes, respectively. Between these energy regimes, there is an intermediate energy range of about 10–100 eV, which we call the “10–100 eV gap,” in which the energy-loss processes are historically not well studied or understood. To close this “gap,” we use a first-principles approach (density functional theory) to calculate the band structure of diamond and β-Ga2O3 up to ∼100 eV along with the phonon dispersion, carrier-phonon matrix elements, and dynamic dielectric function. Additionally, using the first-order perturbation theory (Fermi's golden rule/first Born approximation), we calculate the carrier-phonon scattering rates and the carrier energy-loss rates (impact ionization and plasmon scattering). With these data, we simulate the thermalization of 100-eV electrons and the generated electron–hole pairs by solving the semiclassical Boltzmann transport equation using Monte Carlo techniques. We find that electron thermalization is complete within ∼0.4 and ∼1.0 ps for diamond and β-Ga2O3, respectively, while holes thermalize within ∼0.5 ps for both. We also calculate electron–hole pair creation energies of 12.87 and 11.24 eV, respectively.

Electron impact triple differential cross sections of Xe atoms for coplanar to perpendicular plane single ionisation at 60 eV, 80 eV and 100 eV above ionisation

The evolution of the triple differential cross section (TDCS) for the electron impact ionisation of xenon atoms is reported for the variation of momentum of the projectile electron from a coplanar geometry to a perpendicular plane through intermediate angles with the detection plane. The TDCSs have been calculated for the Xe atoms at 60 eV, 80 eV and 100 eV above the ionisation potential. We have calculated the TDCS using distorted wave Born approximation, utilising both the first and second Born terms. Effects of target polarisation and post-collision interaction have also been included in the complete description of the collision dynamics. The TDCS results are compared with recent measurements by Patel et al (2022 Phys. Rev. A 105 032818) showing a dependence between the TDCS and the scattering geometry and kinematics of the collision. Second-order effects have been found significant, particularly in the description of perpendicular plane ionisation at a low energy and the effect of target polarisation has been found important in describing the coplanar ionisation of the xenon target. With an overall good agreement with the recent measurements, there are points of disagreement which are the motivation for further theoretical effort in the near future, as the present attempt is the first of its kind to analyse these measurements.

The effect of the stagnant layer on the photon mean-free-path length in concentrated suspensions of nanoparticles

We analyze the possibility of evaluation of the thickness and refractive index of the stagnant layer in concentrated suspensions of nanoparticles through the transport characteristics of scattered light photons. The analysis is based on a physically-transparent generalization of the concept of the single scattering intensity off systems in which the number of particles within regions with linear sizes of order of the wavelength in the medium greatly exceeds unity. This generalization is carried out within the notion of compact groups of particles, makes it possible to go beyond the traditional Born approximation, and take into account many-particle effects contributed from those ranges of integration variables in the terms of the iteration series for the scattered field where the internal propagators have delta-function-type behavior. As a result, the evaluation of the photon transport characteristics becomes possible without a detailed modeling of many-particle scattering and correlation processes in the system. 
 The photon mean-free-path length is investigated theoretically as a function of the stagnant refractive index and that of the layer thickness to show a noticeable effect of both parameters on it. As the layer refractive index is increased at a fixed layer thickness, the mean-free-path length decreases because the suspension optical density increases. As a function of the layer thickness, the photon mean-free-path length reveals different types of behavior, depending on the relation between the refractive indices of the stagnant layer and base liquid. If the former is smaller than the latter, this behavior is increasing; in the opposite case, it is decreasing. An experimentally observed increase of the photon mean-free-path length with the particle concentration is usually explained as a manifestation of higher correlation effects. Our theory reveals that the presence of the stagnant layer make the situation more complicated, for both factors may either enhance or diminish each other. To resolve the issue, new specially-designed experiments are required to be set up.

The Investigation of the 8Li(α, n)11B Cross Section at Low Energy by a Distorted Wave Born Approximation Model

The Investigation of the 8Li(α, n)11B Cross Section at Low Energy by a Distorted Wave Born Approximation Model