Born Approximation Research Articles

TetraScatt model: Born approximation for the estimation of acoustic dispersion of fluid-like objects of arbitrary geometries

Abstract Modelling the acoustic scattering response due to penetrable objects of arbitrary shapes, such as those of many marine organisms, can be computationally intensive, often requiring high-performance computing equipment when considering a completely general situation. However, when the physical properties (sound speed and density) of the scatterer are similar to those of the surrounding medium, the Born approximation provides a computationally efficient way to calculate it. For simple geometrical shapes like spheres and spheroids, the acoustic scattering in the far-field evaluated through the Born approximation recipe results in a formula which has been historically employed to predict the response of weakly scattering organisms, such as zooplankton. Further, the Born approximation has been extended to bodies whose geometry can be described as a collection of non-circular rings centred on a smooth curve. In this work, we have developed a numerical approach to calculate the far-field backscattering by arbitrary 3D objects under the Born approximation. The object's geometry is represented by a volumetric mesh composed of tetrahedrons, and the computation is efficiently performed through analytical 3D integration, yielding a solution expressed in terms of elementary functions. The method's correctness has been successfully validated against benchmark solutions. Additionally, we present acoustic scattering results for species with complex shapes. To enable other researchers to use and validate the method, a computational package named tetrascatt was developed in the R programming language and published in the CRAN (Comprehensive R Archive Network).

Machine learning‐driven microwave imaging for soil moisture estimation near leaky pipe

AbstractCharacterizing soil moisture around drip irrigation pipes is crucial for precise and optimized farming. Machine learning (ML) approaches are particularly suitable for this task as they can reduce uncertainties caused by soil conditions and the drip pipe positions, using features extracted from relevant datasets. This letter addresses local moisture detection in the vicinity of dripping pipes using a portable microwave imaging system. The employed ML approach is fed with two dimensional images generated using back projection as a radar‐based algorithm and the Born approximation as an inverse scattering method, based on spatio‐temporal (collected data at various positions over the soil surface and at different time points.) measurements at various frequencies. The study investigates the performance of K‐nearest neighbour (KNN) and convolutional neural networks (CNN) algorithms for moisture classification based on these imaging techniques. We also explore the potential of KNN and CNN for moisture estimation around the plant roots and in the presence of pebbles. In general, CNN outperforms KNN in moisture content detection from microwave data, especially after applying imaging algorithms. A combination of CNN as the ML approach and the back projection algorithm to provide training data, yielded accuracy more than other models for moisture content estimation. Also, the practical results demonstrate that our method can detect soil moisture with an estimation error of less than 10%.

Time-lapse difference seismic inversion based on scattering theory

Time-lapse seismic monitoring technology is an effective tool for quantitatively estimating subsurface medium variations and plays a crucial role in resource and engineering explorations. Among existing time-lapse inversion methods, the difference inversion technique offers higher accuracy but requires linear inversion operators. During linearization, the background is often approximated as a homogeneous medium, resulting in the loss of effective information. Additionally, merely using reflection wave information is not conducive to improving inversion accuracy. However, the true structure of the subsurface is often complex and inhomogeneous, which can easily generate complex wavefields, such as scattering waves, thereby hindering the resolution of differences between time-lapse models. Therefore, incorporating more comprehensive wavefield information is essential for enhancing the accuracy of time-lapse seismic inversion. To address this issue, a wave-equation-based time-lapse difference inversion method is proposed to retrieve the production-induced property perturbation. In the proposed method, the forward operator is formulated through the scattering wave equation, the operator is linearized through the Born approximation, and the WKBJ method is used to approximate Green's function with high accuracy for the inhomogeneous background. In this study, time-lapse seismic parallel inversion and difference inversion are conducted using the proposed forward operator. Both numerical experiments and application of field seismic data indicate that the proposed time-lapse difference inversion method can realize a more accurate quantitative characterization of time-lapse variations.

Transition of dimuonium through foil

This paper presents a study of the passage of dimuonium through the foil of ordinary matter. First, we provide an overview of how dimuonium is planned to be produced for such a type of experiment and how it is expected to interact with the ordinary atoms—predominantly electromagnetically via the screened Coulomb potential of the atomic nuclei. Then, we describe the transport equations that represent the evolution of dimuonium states during the passage and their solution methods. Finally, for three different foils (beryllium, aluminium, and lead), we present the results of this study. To estimate the impact of uncertainties in the potential of a target atom, we study 15 different approximations of the atomic potential and show that the corresponding atomic-potential-model-dependent error in the yields of the low-lying states of dimuonium is quite small within the framework of the applied Born approximation. The convergence of the results after truncation of the infinite system of transport equations to the finite number of quantum states of dimuonium is also studied, and good convergence for the yields of low-lying states is demonstrated. Published by the American Physical Society 2024

Theoretical study of differential cross sections for the ionization of helium by fast proton impact

Abstract We present the angular distribution of the ejected electron for single ionization of He by fast proton impact. A four-body formalism of the three-Coulomb wave is applied to calculate the triple differential cross sections at several impact energies in the scattering, perpendicular and azimuthal planes. Moreover, the three-body formalism of three-Coulomb, two-Coulomb and first Born approximation models has also been used to study the many-body effect on electron emission and the validity of the models. In the three-Coulomb wave model, the final state wave function incorporates distortion due to the three-body mutual Coulombic interaction. In this formalism, we use an uncorrelated and correlated Born initial state, which consists of a plane wave for the incoming projectile times a two-electron bound state wavefunction of the helium atom representing the 1s2(1S) state. But, in the case of the three-body formalism, the initial state wavefunction consists of a long-range Coulomb distortion for the incoming projectile and one active electron of the He atom described by the Roothaan–Hartree–Fock wavefunction. The structure with a single or two peaks with unequal intensity is observed in the angular distributions of the triple differential cross sections for the different kinematic conditions. In addition, the influence of static electron correlations is investigated using different bound state wavefunctions for the ground state of the He target. In the four-body formalism, the present computations are very fast by reducing a nine-dimensional integral to a two-dimensional real integral. Despite the simplicity and speed of the proposed quadrature, the comparison shows that the obtained results are in reasonable agreement with the experiment and are compatible with those of other theories.

Singlet Polaron Theory of Low-Energy Optical Excitations in NiPS_{3}.

We develop a theory that explains the low-energy optical excitations near 1.5eV observed by optical experiments in NiPS_{3}. Using abinitio methods, we construct a two-band Hubbard model for two effective Ni orbitals. The dominant effective hopping corresponds to third-nearest neighbors. This model exhibits triplet-singlet excitations of energy near 2 times the Hund exchange. We derive an effective model for the movement of two singlets in an antiferromagnetic background, that we solve using a generalized self-consistent Born approximation, disentangling the nature of these novel excitations, which move coherently as "singlet polarons".

Nodal spectral functions stabilized by non-Hermitian topology of quasiparticles

In quantum materials, basic observables such as spectral functions and susceptibilities are determined by Green's functions and their complex quasiparticle spectrum rather than by bare electrons. Even in closed many-body systems, this makes a description in terms of effective non-Hermitian (NH) Bloch Hamiltonians natural and intuitive. Here, we discuss how the abundance and stability of nodal phases is drastically affected by NH topology. While previous work has mostly considered complex degeneracies known as exceptional points as the NH counterpart of nodal points, we propose to relax this assumption by only requiring a crossing of the real part of the complex quasiparticle spectra, which entails a band crossing in the spectral function, i.e., a nodal spectral function. Interestingly, such real crossings are topologically protected by the braiding properties of the complex Bloch bands, and thus generically occur already in one-dimensional systems without symmetry or fine tuning. We propose and study a microscopic lattice model in which a sublattice-dependent interaction stabilizes nodal spectral functions. Besides the gapless spectrum, we identify nonreciprocal charge transport properties after a local potential quench as a key signature of nontrivial band braiding. Finally, in the limit of zero interaction on one of the sublattices, we find a perfectly ballistic unidirectional mode in a nonintegrable environment, reminiscent of a chiral edge state known from quantum Hall phases. Our analysis is corroborated by numerical simulations both in the framework of exact diagonalization and within the conserving second Born approximation. Published by the American Physical Society 2024

Green Scalar Function Method for Analyzing Dielectric Media

In this work we present a formalism based on scalar Green’s functions to deal with electromagnetic scattering problems. Although the formulations of the Mie theory and Born approximations in terms of electromagnetic scattering are well known and relevant, they have certain disadvantages: complexity, computational time, few symmetries, etc. Therefore, the study with scalar Green’s functions allows dealing with these problems with greater simplicity and efficiency. However, the information provided by the vector formulation is sacrificed. Nevertheless, different cases of electromagnetic scattering of dielectric media with different dimensions, geometries and refractive indices will be presented. Thus, we will be able to verify the capacity of this scalar method in predicting light-scattering problems.

Coulomb excitation of hydrogen atoms by vortex ion beams

Abstract Coulomb excitation of hydrogen atoms by vortex protons is theoretically investigated within the framework of the non--relativistic first--Born approximation and the density matrix approach. Special attention is paid to the magnetic sublevel population of excited atoms and, consequently, to the angular distribution of the fluorescence radiation. We argue that both these properties are sensitive to the projection of the orbital angular momentum (OAM), carried by the projectile ions. In order to illustrate the OAM--effect, detailed calculations have been performed for the $1s \to 2p$ excitation and the subsequent $2p \to 1s$ radiative decay of a hydrogen target, interacting with incident Laguerre--Gaussian vortex protons. The calculation results suggest that Coulomb excitation can be employed for the diagnostics of vortex ion beam at accelerator and storage ring facilities.

Iterative processing of the noise coherence matrix to determine the acoustic properties of the water area

Abstract An expression is given for the coherence matrix of the acoustic field produced by random sources in an inhomogeneous medium in the Born approximation. An iterative algorithm is proposed to determine the wave number inside the inhomogeneity based on this expression. The reconstruction results are analyzed for the cases of precise input data, data with interference, and incomplete data.

Source-independent Q-compensated viscoacoustic least-squares reverse time migration

The strong viscosity of the subsurface introduces amplitude absorption and phase-velocity dispersion. Incorrect compensation of the inherent attenuation (the strength of the seismic attenuation can be quantified by the inverse of the quality factor Q, which is defined as [Formula: see text] times the ratio of the stored energy to the lost energy in a single cycle of deformation) can significantly affect imaging quality. Although Q-least-squares reverse time migration ( Q-LSRTM) allows for the compensation of attenuation effects during the iterations, the traditional [Formula: see text]-norm minimization, which is highly sensitive to the source wavelet, poses a challenge in accurately estimating the source wavelet from the field data. Thus, we develop a source-independent Q-LSRTM, in which a convolutional objective function is introduced to replace the [Formula: see text]-norm constraint to mitigate the source wavelet effect. According to the Born approximation, we first linearize the constant-order decoupled fractional Laplacian viscoacoustic wave equation to derive the demigration operator and then construct the corresponding adjoint equation and gradient based on the convolutional objective function, iteratively estimating the reflectivity images. Our method relaxes the sensitivity to the wavelet compared with the conventional [Formula: see text]-norm scheme due to the convolutional objective function, which has the ability to construct the same new source for simulated and observed data. Numerical tests on a layered model, the Marmousi model, and field data demonstrate that our source-independent Q-LSRTM enables us to obtain high-quality reflectivity images even when using incorrect source wavelets.

Phase retrieval and phaseless inverse scattering with background information

Abstract We consider the problem of finding a compactly supported potential in the multidimensional Schrödinger equation from its differential scattering cross section (squared modulus of the scattering amplitude) at fixed energy. In the Born approximation this problem simplifies to
the phase retrieval problem of reconstructing the potential from the absolute value of its Fourier transform on a ball. To compensate for the missing phase information we use the method of a priori known background scatterers. In particular, we propose an iterative scheme for finding the potential from measurements of a single differential scattering cross section corresponding to the sum of the unknown potential and a known background potential, which is sufficiently disjoint. If this condition is relaxed, then we give similar results for finding the potential from additional monochromatic measurements of the differential scattering cross section of the unknown potential
without the background potential. The performance of the proposed algorithms is demonstrated in numerical examples. In the present work we significantly advance theoretically and numerically studies of [Agaltsov, Hohage, Novikov, Inverse Problems 35, 24001, 2019] and [Novikov, Sivkin, Inverse Problems, 37(5), 2021].

Inverse source problem for discrete Helmholtz equation

Abstract We consider multi-frequency inverse source problem for the discrete Helmholtz operator on the square lattice Z d , d ⩾ 1 . We consider this problem for the cases with and without phase information. We prove uniqueness results and present examples of non-uniqueness for this problem for the case of compactly supported source function, and a Lipshitz stability estimate for the phased case is established. Relations with inverse scattering problem for the discrete Schrödinger operators in the Born approximation are also provided.

Study of the electromagnetic form factors of the nucleons in the timelike region

The electromagnetic form factors GE and GM of the proton and neutron in the timelike region are extracted in a study of the processes e+e− → p¯p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{p}p $$\\end{document} and e+e− → n¯n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{n}n $$\\end{document}. The reaction amplitude is evaluated within the distorted wave Born approximation, with the interaction of the antinucleon-nucleon N¯N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\left(\\overline{N}N\\right) $$\\end{document} pair taken into account. The latter is constructed within SU(3) chiral effective field theory up to next-to-leading order. An excellent description of the e+e− → N¯N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{N}N $$\\end{document} data in the energy region from the N¯N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{N}N $$\\end{document} threshold up to center-of-mass energies Ecm = 2.2 GeV is achieved. Results for the electromagnetic form factors GE, GM, GE/GM, and the subtracted effective form factors, Gosc, are provided. These can be helpful for further studies of the properties of the nucleons.

Modification of the electronic oscillation spectrum in metallic clusters, caused by the presence of a large spatial scale of inhomogeneity

This work presents a theoretical analysis of the oscillations of a system of degenerate electrons in metallic submicron clusters, taking into account the presence of a large-scale spatial inhomogeneity caused by quantum shell effects. The analysis was carried out in a model formulation in which the large-scale effect was taken into account by the presence of an effective external field acting on the electrons. Two approaches to the description of electron dynamics were considered: kinetic and hydrodynamic. The results obtained within these approaches are in good qualitative and quantitative agreement with each other and demonstrate that for certain cluster sizes, a spectrum of oscillations of the electronic system appears with frequencies differing by the value Δω ∼ ω0/R20 and localized in the vicinity of plasmon frequency ω0 (R0, radius of cluster). The impact of the large-scale effect on the processes of light and electron scattering by metal clusters is estimated. It is shown that maxima appear in the absorption spectrum of the electromagnetic waves, and they turn out to be shifted from the plasmon frequency by value Δω ∼ ω0/R20. Within the framework of the Born approximation, it is shown that a maximum at kR0 ∼ 4π appears in the cross section of elastic scattering of electrons on a metal cluster. The results obtained are important from the point of view of interpreting experiments on plasmonic structures, in particular, on metal films.

Ray-tracing versus Born approximation in full-sky weak lensing simulations of the MillenniumTNG project

ABSTRACT Weak gravitational lensing is a powerful tool for precision tests of cosmology. As the expected deflection angles are small, predictions based on non-linear N-body simulations are commonly computed with the Born approximation. Here, we examine this assumption using DORIAN, a newly developed full-sky ray-tracing scheme applied to high-resolution mass-shell outputs of the two largest simulations in the MillenniumTNG suite, each with a 3000 Mpc box containing almost 1.1 trillion cold dark matter particles in addition to 16.7 billion particles representing massive neutrinos. We examine simple two-point statistics like the angular power spectrum of the convergence field, as well as statistics sensitive to higher order correlations such as peak and minimum statistics, void statistics, and Minkowski functionals of the convergence maps. Overall, we find only small differences between the Born approximation and a full ray-tracing treatment. While these are negligibly small at power-spectrum level, some higher order statistics show more sizeable effects; ray-tracing is necessary to achieve per cent level precision. At the resolution reached here, full-sky maps with 0.8 billion pixels and an angular resolution of 0.43 arcmin, we find that interpolation accuracy can introduce appreciable errors in ray-tracing results. We therefore implemented an interpolation method based on non-uniform fast Fourier transforms (NUFFT) along with more traditional methods. Bilinear interpolation introduces significant smoothing, while nearest grid point sampling agrees well with NUFFT, at least for our fiducial source redshift, $z_s=1.0$, and for the 1 arcmin smoothing we use for higher order statistics.

Influence of initial correlations on evolution over time of an open quantum system

A novel approach to accounting for the influence of initial system–bath correlations on the dynamics of an open quantum system, based on the conventional projection operator technique, is suggested. To avoid the difficulties of treating the initial correlations, the conventional Nakajima–Zwanzig inhomogeneous generalized master equations (GMEs) for a system’s reduced statistical operator and correlation function are exactly converted into the homogeneous GMEs (HGMEs), which take into account the initial correlations in the kernel governing the evolution of these HGMEs. In the second order (Born) approximation in the system–bath interaction, the obtained HGMEs are local in time and valid at all timescales. They are further specialized for a realistic equilibrium Gibbs initial (at t=t0) system+bath state (for a system reduced statistical operator an external force at t>t0 is applied) and then for a bath of oscillators (Boson field). As an example, the evolution of a selected quantum oscillator (a localized mode) interacting with a Boson field (Fano-like model) is considered at different timescales. It is shown explicitly how the initial correlations influence the oscillator evolution process. In particular, it is shown that the equilibrium system’s correlation function acquires at the large timescale the additional constant phase factor conditioned by survived initial system–bath correlations.

Study of one-step and two-step neutron transfer in the reaction 6Li + 9Be* *Supported by the Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan (AP19677087) and by the Russian Science Foundation (24-22-00117)

This paper presents the results of experiments conducted to measure the cross-sections for elastic scattering and nucleon transfer channels in the 6Li+9Be reaction at an incident energy of 68 MeV: 9Be(6Li,6Li)9Be, 9Be(6Li,7Li)8Be, 9Be(6Li,7Li)8Be2+, 9Be(6Li,8Li)7Be, and 9Be(6Li,7Be)8Li. The objective of the study is to elucidate the manifestation of the cluster structure of 9Be. Theoretical analysis of the contributions of the one-step and two-step neutron transfer mechanisms is performed using the distorted wave Born approximation method with the Fresco code. Good agreement between the calculations and the experimental data is obtained for the channels of elastic scattering 9Be(6Li,6Li)9Be, neutron 9Be(6Li,7Li)8Be, and proton transfer 9Be(6Li,7Be)8Li, as well as for the transfer of two neutrons 9Be(6Li,8Li)7Be. The dineutron cluster transfer mechanism makes a dominant contribution to the 9Be(6Li,8Li)7Be reaction channel at forward angles.

Can Nth order Born approximation be exact?

Abstract For the scattering of scalar waves in two and three dimensions and electromagnetic waves in three dimensions, we identify a condition on the scattering interaction under which the N-th order Born approximation gives the exact solution of the scattering problem for some N ≥ 1.

Exciton interacting with a moiré lattice: Polarons, strings, and optical probing of spin correlations

The ability to create and stack different atomically thin transition metal dichacogenide (TMD) layers on top of each other has opened up a rich playground for exploring new and interesting two-dimensional (2D) quantum phases. As a consequence of this remarkable development, there is presently a need for new sensors to probe these 2D layers, since conventional techniques for bulk materials such as x-ray and neutron scattering are inefficient. Here, we develop a general theory for how an exciton in a TMD monolayer couples to spin and charge correlations in an adjacent moiré lattice created by a TMD bilayer. Virtual tunneling of charge carriers, assumed for concreteness to be holes, between the moiré lattice and the monolayer combined with the presence of bound hole-exciton states, i.e., trions, give rise to an effective interaction between the moiré holes and the exciton. In addition to the Umklapp scattering, we show that this interaction is spin-dependent and therefore couples the exciton to the spin correlations of the moiré holes, which may be in- as well as out-of-plane. We then use our theory to examine two specific examples where the moiré holes form in-plane ferromagnetic or antiferromagnetic order. In both cases, the exciton creates spin waves in the moiré lattice, which we analyze by using a self-consistent Born approximation that includes such processes to infinite order. We show that the competition between magnetic order and exciton motion leads to the formation of a well-defined quasiparticle consisting of the exciton surrounded by a cloud of magnetic frustration in the moiré lattice sites below. For the antiferromagnet, we furthermore demonstrate the presence of the elusive geometric string excitations and discuss how they can be observed via their smoking gun energy dependence on the spin-spin coupling, which can be tuned by varying the twist angle of the moiré bilayer. All these phenomena have clear signatures in the exciton spectrum, and as such our results illustrate that excitons are promising quantum probes providing optical access to the spin correlations of new phases predicted to exist in TMD materials. Published by the American Physical Society 2024