Born Approximation Research Articles

Phase-preserving theory and its linearization approximation for forward scattering field of scalar acoustic wave equation

The conventional wave-equation linearization methods, such as the first-order Born or Rytov approximation, always implicitly imply a weak-scattering assumption, making it valid only for weak perturbation models. To extend the wave-equation linearization theory to strong perturbation models, we consider a scenario that the reference model is smooth within the scale of the incident wave length, and propose a phase-preserving method which can predict the phase perturbation of forward scattering wave field. First, we introduce the WKBJ approximation to the scattered- and incident wave fields so that the integral of the unknown solution (i.e. the scattered field) in the nonlinear Ricatti integral equation can be replaced by the integral of scattering-angle and model perturbation, yielding an explicit expression of the scattered field. Theoretical derivation shows that the proposed phase-preserving method can accurately predict the phase-perturbation of forward scattered wave field regardless of the strength of velocity perturbations for one-dimensional wave propagation problem. To apply the phase-preserving approximation to the inverse problem, we further consider a scenario of small-angle forward propagation. In this case, the phase-preserving approximation can be linearized by neglecting the influence of scattering angles, leading to a linear relation between the scattered field and the model perturbation, which we refer to as the generalized Rytov approximation. Numerical experiments demonstrate that the generalized Rytov approximation can predict the phase perturbation of the scattered field with higher accuracy for small-angle forward propagation, and is suitable for strong model perturbations. The generalized Rytov approximation extends the validity and the scope of application of the traditional Rytov approximation. In specific application fields such as the seismic traveltime tomography or medical ultrasonic transmission imaging, a new traveltime/phase sensitivity kernel can be derived by replacing the conventional Rytov approximation with the proposed method, which can increase the inversion accuracy and speed up the convergence.

Elastic Reflection Waveform Inversion With a Nonlinear Born Scattering Operator for Multiparameter Reconstruction

Elastic full waveform inversion (FWI) is one of the most popular tools in recovering the subsurface P- and S-velocity models with high resolution. However, it requires either a good starting model or low-frequency data to avoid the cycle-skipping issue. Elastic reflection waveform inversion (ERWI) uses the migration/demigration process to compute the low-wavenumber gradient. One drawback of conventional ERWI is that it mainly relies on the first-order Born scattering and only utilizes primary reflection wave paths, providing limited wavenumber illumination in the update. In this letter, a nonlinear Born scattering operator is incorporated with ERWI for multiparameter reconstruction to mitigate the drawback of the conventional linear Born approximation. Finally, we use numerical examples to show that the nonlinear Born scattering operator allows us to take advantage of the multiples and enlarge the wavenumber illumination in ERWI results.

Unexpected nontriviality of inter-band contribution and huge anisotropy of conductivity in tilted Weyl semimetals

For tilted type-I Weyl semimetals, our theoretical study indicates that the Kubo conductivity parallel to cone tilt direction increases rapidly with the Fermi energy. Hence it deviates from its Boltzmann counterpart sizably even though the electronic wavelength is so short that the quantum interference is seemingly trivial. As a result, such a system shows huge anisotropy of the conductivity. By means of the diagrammatic expansion technique, we find that the absence of backscattering and the breakdown of the time reversal symmetry in tilted Weyl semimetals are two crucial factors which bring about the nontrivial inter-band contribution to the Kubo conductivity. Our findings indicate that Boltzmann theory fails to describe reasonably the electronic transport of a tilted Weyl cone, even in the case of weak scattering and short Fermi wavelength. Though in this regime such a semiclassical transport theory is believed to be valid according to conventional arguments. This situation should be paid attention. • Via SCBA, the high order quantum corrections to conductivity are considered and it makes huge enhancement to diagonal conductivity σ z z , which is missed by the Boltzmann transport equation with the lowest order Born approximation. • The huge anisotropy of diagonal conductivity in tilted WSMs origin from the nature of the absence of backscattering and breakdown of TRS. • The interaction range of impurity potential affects the extent of anisotropy.

Experimental setup for interaction between highly charged ions and laser-produced plasma near Bohr velocity energy region

Ion energy loss in the interaction between highly charged ions and dense plasma near Bohr velocity energy region is one of the important physical problems in the field of high-energy density physics driven by intense heavy ion beams. Based on the 320 kV experimental platform at the Institute of Modern Physics, Chinese Academy of Sciences, a new experimental setup was built for the research of interaction between ions and laser-produced plasma near the Bohr velocity, where the ion energy loss and charge state distribution can be experimentally investigated. In this paper we introduce the new setup in detail, including the generation and controlling of pulsed ion beam ( ≥ 200 ns); the preparation of high-density laser plasma target (10<sup>17</sup>—10<sup>21</sup> cm<sup>–3</sup>); the diagnostics of plasma and the developed high energy resolution ion measurement system (< 1%). In the experiment, the charge distribution of Xe<sup>15+</sup> ions with 4 MeV penetrating through the laser-produced Al plasma target is measured. The charge-state analysis device observes different results without and with the plasma, in which the outgoing Xe ion charge-state changes correspondingly from the 15+ to 10+, thus the electron capture process is believed to be dominant. In addition, the proton energy loss is also measured by using the magnetic spectrometer, showing that the experimental energy loss is about 2.0 keV, 30% higher than those theoretical predictions , which can be attributed to the fact that in the near Bohr velocity energy regime, the first-order Born approximation condition is not valid, thus the Bethe model and SSM model are inapplicable to the experimental results. In future, a systematic study will be performed based on our ions-plasma ineteraction setup, and the energy loss and charge state data will be introduced.

Longitudinal Form Factors and Quadrupole Moments of 22,26Na Isotopes with Different Interactions

The longitudinal electron scattering form factors and the electric quadrupole moments are calculated for the states with Jπ T= 3+0 (ground state) and 1+ 0 (583keV excited state) of 22Na and Jπ T= 3+2 (ground state) of 26Na. Shell model calculations are based on USDA, USDB and Wildenthal interactions. The exact center of mass correction is included in Born approximation picture to generate the longitudinal form factors. The core polarization (CP) effect with the values of effective nucleon charges ep=1.35, en= 0.35, with Bohr Mottelson formula gave a good agreement with the measured electric quadrupole moments. The structure of the nuclei under consideration shows that the 1d5/2 orbit is dominant configuration for 22Na, and 2s1/2 orbit for 26Na.

Collision-induced atomic alignment of silver after [formula omitted] ionization by 10–50 keV electron impact: Influence of Coster–Kronig transition effect

This work reports atomic alignment of silver after L3-subshell ionization in collisions with electrons in energy range 10–50 keV, i.e., (3∼15)EL3, where EL3(=3.351 keV) is the binding energy of electrons in the L3-subshell. The characteristic spectra are measured at different emission angles from -40∘ to 40∘ intervals of 10∘. The angular dependence of X-ray emission is studied for Lα(L3→M4,5) and Lβ2(L3→N5) lines respectively, using a thin target. The anisotropy parameter β is determined from two angular distribution measurements of differential X-ray intensity ratios dI(Lα,θ)/dI(Lβ1,θ) and dI(Lβ2,θ)/dI(Lβ1,θ). This served to reduce the experimental uncertainties. For the derivation of the alignment factor A20 we took into account the Coster–Kronig (CK) correction factor κ, which allows for, CK transition probabilities fij among L-subshells. We found that the sign of A20 is mostly negative, and the influence of CK transition is significant for large alignment parameters. In addition, the experimental results are compared to theoretical predictions within the framework of Plane Wave Born Approximation (PWBA) and reasonable agreement is found in the energy range studied in the present work. Simultaneously, good scaling property of atomic alignment is demonstrated when we consider also previous experimental results. Our measurement extends the scaled velocity V (=vp/vt) to a range of 1∼4 for medium-Zt targets, and the results of atomic alignment can provide a fundamental testing ground for ionization models.

Brain Stroke Classification via Machine Learning Algorithms Trained with a Linearized Scattering Operator

This paper proposes an efficient and fast method to create large datasets for machine learning algorithms applied to brain stroke classification via microwave imaging systems. The proposed method is based on the distorted Born approximation and linearization of the scattering operator, in order to minimize the time to generate the large datasets needed to train the machine learning algorithms. The method is then applied to a microwave imaging system, which consists of twenty-four antennas conformal to the upper part of the head, realized with a 3D anthropomorphic multi-tissue model. Each antenna acts as a transmitter and receiver, and the working frequency is 1 GHz. The data are elaborated with three machine learning algorithms: support vector machine, multilayer perceptron, and k-nearest neighbours, comparing their performance. All classifiers can identify the presence or absence of the stroke, the kind of stroke (haemorrhagic or ischemic), and its position within the brain. The trained algorithms were tested with datasets generated via full-wave simulations of the overall system, considering also slightly modified antennas and limiting the data acquisition to amplitude only. The obtained results are promising for a possible real-time brain stroke classification.

Holes and magnetic polarons in a triangular lattice antiferromagnet

The intricate interplay between charge motion and magnetic order in geometrically frustrated lattices is central for the properties of many two-dimensional quantum materials. The triangular lattice antiferromagnet is a canonical example of a frustrated system, and here we analyze the dynamics of a hole in such a lattice focusing on observables that have become accessible in a new generation of experiments. Using the $t\ensuremath{-}J$ model, we solve the problem exactly within linear spin wave theory in the limit of strong magnetic interactions, showing that the ground state is described by a coherent state of spin waves. The derivation highlights the crucial role played by the interaction between a static hole and the neighboring spins, which originates in the geometric frustration and has often been omitted in earlier works. Furthermore, we show that the nonequilibrium dynamics after a hole has abruptly been inserted at a lattice site is given by a coherent state with time-dependent oscillatory coefficients. Physically, this describes a burst of magnetic frustration propagating through only two-thirds of the lattice sites, since a destructive interference of spin waves leaves spins parallel to that removed by the hole unperturbed. After the wave has propagated through the lattice, the magnetization relaxes to that of the ground state. We then use our analytical solution to benchmark the widely used self-consistent Born approximation (SCBA) in the limit of strong magnetic interactions, showing that it is very accurate also for a triangular lattice. The magnetic polaron spectrum is analyzed for general magnetic interactions using the SCBA, and we compare our results with those for a square lattice.

On magnetic monopole and Dirac quantization condition in the minimal length formalism

In this article, we study the effects of minimal length corrections on the cyclotron acceleration and radiation of a charged particle moving in a magnetic monopole field. Using the modified Hamiltonian describing the dynamics of a charged particle moving in a magnetic monopole field, we derive the modified cyclotron frequency and modified acceleration. Also, we derive the modified power for the cyclotron radiation using the modified acceleration. We find that all modified quantities are dependent on the deformation parameter α. In addition, we find that the modified electromagnetic angular momentum and magnetic charges are not quantized as an integer multiple; thus, we establish that the modified Dirac quantization condition and the usual Dirac quantization condition is just the term of zero order in α. The modified Dirac quantization condition allows fractional charges that arise from vacuum fluctuations. In the Born approximation, we derive the modified scattering cross-section and then we estimate the upper bound on the minimal length.

Electron impact elastic scattering by a calcium atom using the first order distorted wave method with a complex potential

Electron-atom scattering data is required in diverse fields of physics. In particular, inelastic collision cross sections data are needed in photonics and radiation physics. Elastic collision data, on the other hand, are useful in material science for surface analysis. There is a lack of accuracy and completeness of atomic data obtained using theoretical methods relative to experimental techniques. Furthermore, the distorted wave Born approximation method with a complex potential is yet to be applied in calculating cross sections. Differential and total cross sections have been calculated for electron-calcium scattering in the impact energy range 10 – 100 eV. There is good shape resonance between the present results with a complex potential and experimental values as well as other theoretical results

Quantum transport of a spin-1 chiral fermion

We theoretically study the quantum transport in a three-dimensional spin-1 chiral fermion system in the presence of impurity scattering. Within the self-consistent Born approximation, we find peak structure of the density of states and significant suppression of electrical conductivity around the zero energy. The zero-energy conductivity depends less on impurity concentration, unlike a Weyl fermion. These properties originate from the flat-band structure of the spin-1 chiral fermion.

Isomeric excitation of U235 by inelastic scattering of low-energy electrons

The nucleus of $^{235}\mathrm{U}$ has a low-lying isomeric state of energy about 76.7 eV. Excitation cross sections of the nucleus from the ground state to the isomeric state by inelastic electron scattering are calculated on the level of the Dirac distorted-wave Born approximation. The cross sections are about six orders of magnitude higher than known values based on the Dirac plane-wave Born approximation, emphasizing the vital importance of wave function distortion in the nuclear excitation. In addition, we find that even with low-energy electrons on the order of 100 eV, relativistic effects are significant without which the excitation cross sections drop by an order of magnitude.

Relativistic elastic scattering of a muon neutrino by an electron in an elliptically polarized laser field

Within the framework of electroweak theory, we investigate the elastic scattering process e−+νμ→e−+νμ in the presence of an intense elliptically polarized laser field. We derive an analytical expression for the spin-unpolarized differential cross section using the first Born approximation and the Dirac-Volkov states to describe the incident and scattered electrons. Our results generalize those found for the linearly polarized field by Bai et al. (2012) [24] and for the circularly polarized field by El Asri et al. (2021) [23]. We find that the differential cross section is significantly enhanced for linear polarization and reduced for circular and elliptical polarizations.

Two-dimensional exciton-polariton interactions beyond the Born approximation

We present a many-body theory for the interactions of two-dimensional exciton-polaritons beyond the Born approximation. Taking into account Gaussian quantum fluctuations via the Bogoliubov theory, we find that the exciton-exciton scattering is strongly renormalized by the light-matter coupling and acquires an inverse logarithmic dependence on the lower polariton energy. As a result, the polariton interaction strength may be enhanced at red photon-exciton detuning when the exciton-exciton scattering length is large. We also derive the exact Tan relations for exciton-polaritons, calculate Tan's contact coefficient and find an even more significant enhancement. Our predictions may provide a qualitatively correct guide for studies of exciton and polariton nonlinearities and suggest a route to achieving strongly nonlinear polariton gases.

Nonequilibrium Hole Dynamics in Antiferromagnets: Damped Strings and Polarons

We develop a nonperturbative theory for hole dynamics in antiferromagnetic spin lattices, as described by the t-J model. This is achieved by generalizing the self-consistent Born approximation to nonequilibrium systems, making it possible to calculate the full time-dependent many-body wave function. Our approach reveals three distinct dynamical regimes, ultimately leading to the formation of magnetic polarons. Following the initial ballistic stage of the hole dynamics, coherent formation of string excitations gives rise to characteristic oscillations in the hole density. Their damping eventually leaves behind magnetic polarons that undergo ballistic motion with a greatly reduced velocity. The developed theory provides a rigorous framework for understanding nonequilibrium physics of defects in quantum magnets and quantitatively explains recent observations from cold-atom quantum simulations in the strong coupling regime.

Investigation the fully differential cross section of helium atom single ionization by fast protons impact with three and four-body formalism

In the present work, the fully differential cross section of atomic helium ionization by protons impact at high energy ranges is calculated. The calculations of the fully differential cross section have been performed by using the three-body formalism in the first order Born-Faddeev approximation with an active electron model and four body formalism with the first Born approximation. In order to investigate the collision dynamics accurately, the first order Born-Faddeev approximation has been performed by using the single parameter and Hartree Fock as single-electron wave functions and in the first order Born approximation, the two-electron wave functions of Hylleraas and Silverman are used with considering the electron correlation. The fully differential cross sections at different ejected electron energies and momentum transfers are compared with the available experiment and theoretical results. The results show that the effects of electronic correlation are considerable at high impact energy range and ionization process.‎

Optical diffraction tomography of second-order nonlinear structures in weak scattering media: theoretical analysis and experimental consideration.

Computed tomography (CT) allows for high lateral and axial resolution imaging of the endogenous structure of matter thanks to its large spatial frequency support and has been realized in X-ray and linear optical domain known as optical diffraction tomography (ODT). Here, we present the theoretical basis and experimental considerations for ODT of second-order nonlinear structures in weak scattering media. We have derived the relation between second harmonic wave and the anisotropic nonlinear tensor in spatial frequency domain under first-order Born approximation. Our results show that, under a plane wave illumination, the two dimensional (2D) spatial spectra of generated second harmonic complex field relates to the inverse lattice of nonlinear structure on Ewald sphere shells. The centers of the Ewald spheres are determined by 2 times wavevector of the incident fundamental wave and the radii are determined by the modulus of the second harmonic wavevector. More importantly, it shows that the 2D spatial spectra is a superposition of the Ewald spheres of different components of the anisotropic nonlinear tensor. We propose to solve the inverse problem by controlling the polarizations of the fundamental and second harmonic signal. We tested the feasibility of the proposed method using a numerical phantom and make some discussions on practical implementations, including angular scanning schemes, polarization detection and illumination profile for optimizing reconstruction region. Possessing high resolution, wide-field imaging and polarization-sensitive property, we believe that the proposed scheme would have important applications in nonlinear microscopy.

Elastic Form Factors and Matter Density Distributions of Some Neutron-Rich Nuclei

The ground-state properties of exotic 18N and 20F nuclei, including the neutron, proton and matter densities and related radii are investigated using the two-body model of within Gaussian (GS) and Woods Saxon (WS) wave functions. The long tail is evident in the computed neutron and matter densities of these nuclei. The plane wave Born approximation (PWBA) is calculate the elastic form factors of these exotic nuclei. The variation in the proton density distributions due to the presence of the extra neutrons in 18N and 20F leads to a major difference between the elastic form factors of these exotic nuclei and their stable isotopes 14N and 19F. The reaction cross sections for these nuclei are investigated using the Kox and Glauber models. Furthermore, the Glauber model is employed to calculate the matter radii of these exotic nuclei. The calculated results for the selected exotic nuclei are in a good agreement with the experimental data.

Exploring the sensitivity of charge-exchange(p,n)reactions to the neutron density distribution

$Background:$ The determination of the nuclear neutron properties suffers from uncontrolled uncertainties, which attracted considerable attention recently, such as in the context of the PREX experiment. $Purpose:$ Our aim is to analyze the sensitivity of charge-exchange ($p, n$) reactions to the neutron density distribution $\rho_{n}$ and constrain the neutron characteristics in the nuclear structure models. $Method:$ By combing the folding and the mean-field models, the nucleon-nucleus ($NA$) potential can be obtained from the nuclear density distribution. Further, the ($p, p$) and ($p, n$) cross sections for $^{48}$Ca and $^{208}$Pb are calculated following the distorted-wave Born approximation (DWBA) method. $Results:$ Compared with the ($p, p$) cross section, the effects of $\rho_{n}$ variation on the ($p, n$) cross section are significant, which is due to the impact of isovector properties. Based on the global folding model analyses of data, it is found that $^{48}$Ca and $^{208}$Pb have relatively large neutron skin thickness $\Delta R_{n p}$. $Conclusions:$ Results illustrate that the charge-exchange ($p, n$) reaction is a sensitive probe of $\rho_{n}$. The results in this paper can offer useful guides for future experiments of neutron characteristics.

Study of Differential Scattering Cross-Section Using Yukawa Term of Medium-Modified Cornell Potential

In the present work, we have studied the differential scattering cross-section for ground states of charmonium and bottomonium in the frame work of the medium-modified form of quark-antiquark potential and Born approximation using the nonrelativistic quantum chromodynamics approach. To reach this end, quasiparticle (QP) Debye mass depending upon baryonic chemical potential ( μ b ) and temperature has been employed, and hence the variation of differential scattering cross-section with baryonic chemical potential and temperature at fixed value of the scattering angle ( θ = 9 0 o ) has been studied. The variation of differential scattering cross-section with scattering angle θ (in degree) at fixed temperature and baryonic chemical potential has also been studied. We have also studied the effect of impact parameter and transverse momentum on differential scattering cross-section at θ = 90 o .