Born Approximation Research Articles

Scattering of spin waves by a Bloch domain wall: Effect of the dipolar interaction

It is known that if the dipolar interaction is ignored or replaced by an effective magnetic anisotropy, the theoretical computations predict that a domain wall is transparent to spin waves. Taking into account the full complexity of this interaction, the authors show that the domain wall does indeed reflect spin waves. The scattering parameters are computed by treating the dipolar interaction perturbatively in the Born approximation, which is not straightforward due to the nonlocality of this interaction. A lateral shift of the scattered waves is also predicted.

Parabolic quasi-Sturmian approach to proton-impact ionization of helium

A method for calculating ion-atom ionizing collisions is formulated and applied to single ionization of helium induced by energetic proton impact. Within the frozen-core model for the residual helium ion, the four-body problem in the exit channel is recast as an inhomogeneous Schr\"odinger equation for the Coulomb three-body system $({e}^{\ensuremath{-}},{\text{He}}^{+},{p}^{+})$. The asymptotic behavior of its solution contains the transition amplitude. We suggest to solve the driven equation in the representation of so-called parabolic convoluted quasi-Sturmian (CQS) basis functions which are constructed using quasi-Sturmians (QSs) for the $({e}^{\ensuremath{-}},{\text{He}}^{+})$ and $({p}^{+},{\text{He}}^{+})$ subsystems. By applying the corresponding Coulomb Green's function operators, these QSs are generated from orthogonal complements to square-integrable (${L}^{2}$) Sturmian functions in parabolic coordinates. In the proposed parabolic CQS approach explicit asymptotic expressions for the basis functions provide an expansion of the transition amplitude in terms of ``basis amplitudes,'' which we express analytically. The proton-electron interaction is treated as a perturbation and is approximated by a truncated Sturmian basis-set expansion. It is found that, at least in the high-energy limit, the ionization amplitude converges pretty fast as the number of terms in the separable expansion for the proton-electron potential is increased. The calculated fully differential cross sections for singly ionizing 1-MeV $p$-He collisions in several kinematical regimes in the scattering plane are found to be in reasonable agreement with experimental data and with the theoretical results obtained using the first Born approximation, the 3C model, and the wave-packet convergent close-coupling method. The theory-experiment discrepancy over the binary peak position observed by other authors remains unexplained.

Experimental study of the isomeric state in N16 using the Ng,m16(d,He3) reaction

The isomeric state of $^{16}\mathrm{N}$ was studied using the $^{16}\mathrm{N}{}^{g,m}(d,^{3}\mathrm{He})$ proton-removal reactions at 11.8 MeV/u in inverse kinematics. The $^{16}\mathrm{N}$ beam, of which 24% was in the isomeric state, was produced using the Argonne Tandem-Linac Accelerator System (ATLAS) in-flight system and delivered to the Helical Orbit Spectrometer (HELIOS), which was used to analyze the $^{3}\mathrm{He}$ ions from the $(d,^{3}\mathrm{He})$ reactions. The simultaneous measurement of reactions on both the ground state and the isomeric states, reduced the systematic uncertainties from the experiment and in the analysis. A direct and reliable extraction of the relative spectroscopic factors was made based on a distorted-wave Born approximation approach. The experimental results suggest that the isomeric state of $^{16}\mathrm{N}$ is an excited neutron-halo state. The results can be understood through calculations using a Woods-Saxon potential model, which captures the effects of weak binding.

Time evolution of quantum correlations in presence of state dependent bath

The emerging quantum technologies heavily rely on the understanding of dynamics in open quantum systems. In the Born approximation, the initial system-bath correlations are often neglected which can be violated in the strong coupling regimes and quantum state preparation. In order to understand the influence of initial system-bath correlations, we study the extent to which these initial correlations and the distance of separation between the qubits influence the dynamics of quantum entanglement and coherence. It is shown that at low temperatures, the initial correlations have no role to play while at high temperatures, these correlations strongly influence the dynamics. Furthermore, we have shown that the distance of separation between the qubits in presence of a collective bath helps to maintain entanglement and coherence at long times.

Photoproduction of pion pairs at high energy and small angles

We explore the photoproduction mechanisms for charged and neutral pion pairs off a heavy nucleus at threshold. We calculate the production of charged pairs in the Coulomb field of the nucleus in the Born approximation using explicit expressions for the differential cross sections and their connection with the total cross section $\ensuremath{\sigma}(\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})$. The production of $\ensuremath{\sigma}$ mesons at threshold and their subsequent decay into pions is an important mechanism and is investigated quantitatively in a framework that can be used for both charged and neutral pions. $\ensuremath{\sigma}$ mesons can be produced via electromagnetic (photon exchange) or strong ($\ensuremath{\omega}$ exchange) interactions. For neutral pions, another production mechanism consists of the two-step process where charged pions are produced first and then charge exchange into two neutral pions. Differential and total cross sections are computed for each production mechanism.

Triple-differential cross section for the twisted-electron-impact ionization of the water molecule

In this communication, we present the results of the triple differential cross-section (TDCS) for the (e,2e) process on H2O molecule for the plane wave and the twisted electron beam impact. The formalism is developed in the first Born approximation. We describe the plane/twisted wave, plane wave, the linear combination of atomic orbitals (LCAO) (self-consistent field LCAO method) and Coulomb wave for the incident electron, scattered electron, the molecular state of H2O, and the ejected electron, respectively. We investigate the angular profiles of the TDCS for the outer orbitals 1B1, 3A1, 1B2, and 2A1 of the water molecule. We compare the angular profiles of the TDCS for the different values of orbital angular momentum (OAM) number m of the twisted electron beam with that of the plane wave beam. We also study the TDCS for macroscopic H2O target to explore the effect of opening angle {\theta}p of the twisted electron beam on the TDCS. Our results clearly show the effect of the twisted electron's OAM number (m) and the opening angle {\theta}p on the TDCS of the water molecule.

Born approximation imaging technique for electrical source multi-component TEM

Abstract In this study, to obtain higher-resolution geoinformation in the electrical source transient electromagnetic method (TEM) interpretation, the pseudo-seismic Born approximation imaging method is applied to the vertical magnetic induction intensity ${B_z}$ and the horizontal electric field ${E_y}$, which is paralleled to the source. First, the differences between the two components are compared, and the results reveal that different components can reflect varied geological information. ${E_y}$ has a stronger signal and is more sensitive to the high-resistivity layer at a long offset, whereas ${B_z}$ has a greater relative difference in the low-resistivity layer at a short offset. The TEM field is then transformed into the pseudo-wavefield using the wavefield transformation method and the Born approximation pseudo-seismic imaging method is adopted to locate the electrical interface. After calculating the 3D model, the results indicate that the multi-component Born approximate imaging can intuitively and effectively locate the depth of the geological interface. Furthermore, the imaging results of a coal mine located in Gansu Province, China, proves that the proposed method can pinpoint the buried location of the coal goaf as well as the stratum trend. In general, the multi-component pseudo-seismic imaging technique plays a significant role in interpreting the electrical source TEM data.

Electron impact studies on the imidogen (NH+) molecular ion

Low energy electron collision calculations have been performed on the imidogen molecular ion NH+ at its equilibrium geometry using the R-matrix method. A suitable model is first built to represent the NH+ target ion. With this target model we have performed scattering calculations to obtain cross sections for electronic excitation from the X2Π ground state of NH+ to few of its excited states. The excitation cross sections are then used to approximately obtain the cross section for dissociation for the production of N+ ions. We also report the cross sections for rotational excitation of NH+ in its ground state within the Coulomb–Born approximation.

Mapping coal water-filled zones using multi-radiation source transient electromagnetic pseudo-seismic Born approximation imaging and apparent resistivity imaging in Gansu, China

The coal water-filled zones have become a growing safety hazard, so effective detection techniques and accurate interpretation methods are of great concern. In this paper, we adopt multi-radiation source transient electromagnetic method (TEM) in the data collection, and employ joint imaging method in the data interpretation. A single-radiation source can only be coupled with the geological body from one side, making holographic photography problematic, but multi-radiation source can suppress random noise, improve the signal-to-noise ratio, and reduce the volume effect. Typically, the apparent resistivity method can reflect the electrical distribution characteristics, while the pseudo-seismic imaging method (PSI) can quickly locate the position and shape of the geological structure, so the two imaging methods can be combined. Therefore, firstly using multi-window time-sweep wavefield inverse transformation technology converts the TEM data into the multi-resolution pseudo-wave, then utilizing the joint interpretation method obtains the underground electrical distribution characteristics, the location of the water-filled zones and stratum's continuous undulations. In this paper, through the calculation of the theoretical model, the results verify the effectiveness of the proposed method. Through processing the field data in Gansu, China, the results demonstrate that the joint interpretation method can map the coal water-filled zones and reflect the geological structures.

Contribution of the nonresonant mechanism to the double and single differential distributions over the invariant variables in the reaction e++e−→N+N¯+π0

The general analysis of the differential cross section and various polarization observables is performed for the process ${e}^{+}+{e}^{\ensuremath{-}}\ensuremath{\rightarrow}N+\overline{N}+{\ensuremath{\pi}}^{0}$ assuming that the annihilation occurs through the exchange of one virtual photon. The dependence of the differential distributions over invariant variables is derived for the reaction ${e}^{+}+{e}^{\ensuremath{-}}\ensuremath{\rightarrow}N+\overline{N}+{\ensuremath{\pi}}^{0}$ in the so-called nonresonant mechanism, applying the conservation of the hadron electromagnetic currents and the P-invariance of the hadron electromagnetic interaction. The detection in an exclusive experimental setup where the nucleon (or antinucleon) and pion are detected in coincidence is considered. A number of single and double differential distributions have been calculated analytically and numerical estimates are given for the $p\overline{p}{\ensuremath{\pi}}^{0}$ and $n\overline{n}{\ensuremath{\pi}}^{0}$ channels, in the Born (nonresonant) approximation, in the energy range from threshold up to $s=16\text{ }\text{ }{\mathrm{GeV}}^{2}$.

Positron impact elastic scattering by calcium atom using first order distorted wave born approximation with a complex potential

Precise positron scattering cross section data are essential for the development of a wide range of technological fields such as astrophysics, plasma sciences, material sciences and bio-medicine. Thus, lack of complete agreement among the available theoretical data, unavailability of experimental data and the first-order distorted wave born approximation with a complex potential at impact energy range 10-200 eV not having been utilized in such a study; are the reasons that informed this investigation. After formulating the complex potential, with positronium formation channel proficiently incorporated, the radial equation was solved numerically. The extracted phase shifts were used to compute the transition matrix. The Roothaan-Hartree-Fock ground state wavefunctions of calcium were utilized in evaluation of the distorting potential and the transition matrix. The transition matrix was then used to determine the differential cross sections while the optical theorem was used to compute total cross sections. With only static potential, the present distorted wave Born approximation and optical potential models yield results that are in close agreement while the effect of positronium formation channel on the cross sections is insignificant at impact energies beyond 150 eV.

Nucleon and Δ resonances in γn→K+Σ− photoproduction

The most recent data on beam asymmetries $\mathrm{\ensuremath{\Sigma}}$ and beam-target asymmetries $E$ from the CLAS Collaboration, together with the previous data on differential cross sections and beam asymmetries from the CLAS and LEPS Collaborations, for the $\ensuremath{\gamma}n\ensuremath{\rightarrow}{K}^{+}{\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}$ reaction are studied based on an effective Lagrangian approach in the tree-level Born approximation. The $t$-channel $K$ and ${K}^{*}(892)$ exchanges, the $u$-channel $\mathrm{\ensuremath{\Sigma}}$ exchange, the interaction current, and the exchanges of $N$, $\mathrm{\ensuremath{\Delta}}$, and their excited states in the $s$ channel are considered in constructing the reaction amplitudes to describe the available experimental data. The reaction mechanisms of $\ensuremath{\gamma}n\ensuremath{\rightarrow}{K}^{+}{\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}$ are analyzed, and the associated resonances' parameters are extracted. The numerical results show that the $\mathrm{\ensuremath{\Delta}}$ exchange and the $N(1710)1/{2}^{+}$, $N(1880)1/{2}^{+}$, $N(1900)3/{2}^{+}$, and $\mathrm{\ensuremath{\Delta}}(1920)3/{2}^{+}$ resonance exchanges in the $s$ channel dominate the $\ensuremath{\gamma}n\ensuremath{\rightarrow}{K}^{+}{\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}$ reaction in the lower energy region, and the $t$-channel ${K}^{*}(892)$ exchange plays a crucial role at forward angles in the higher energy region.

Q-compensated least-squares reverse time migration in TTI media using the visco-acoustic TTI wave equation based on the SLS model

The anelasticity and anisotropy widely exist in real subsurface media. Strong anelasticity will lead to phase dispersion and amplitude attenuation during seismic wave propagation. Anisotropy cause seismic waves to have obviously different kinematic characteristics from that of isotropy. For seismic migration, ignoring the anelasticity and anisotropy of subsurface media will significantly reduce the quality of migration images, even cause imaging failure. We propose a Q-compensated least-squares reverse time migration (Q-LSRTM) in tilted transversely isotropic (TTI) media to correct these effects. According to the Born approximation of seismic wave equation, a linearized visco-acoustic TTI pure qP-wave modeling operator is derived using a new visco-acoustic TTI wave equation for one standard linear solid (SLS) model, which can deal with the anelasticity and can simulate pure qP-wave steadily in attenuating anisotropic media without qSV-wave artifacts. Then, the corresponding adjoint equation is formulated using the adjoint-state method to calculate the gradient sensitivity kernel for the visco-acoustic TTI media. Because of the least-squares inversion, the Q compensation can be achieved during the iterations, so that the over-amplification of noises can be avoided naturally. In addition, compared with conventional LSRTM, the proposed method compensates for the anelasticity and corrects the anisotropy, so as to produce images with better spatial resolution and amplitude fidelity. Numerical examples demonstrate the feasibility and advantages of the proposed method for the data including strong attenuation effects over conventional LSRTM.

Shape Reconstruction of Eccentric Defect in Cylindrical Component by Modified Born Approximation Method

In this paper, a cylindrical aluminum sample with an eccentric circular hole was prepared, and ultrasonic measurements were carried out by experimental means. The measurement area was limited to a plane edge perpendicular to the axis of the cylindrical component. The measured waveform data were input into the formula of approximate correction method, and the section image was obtained by using a modified Born approximation (MBA) method. Then, the three-dimensional (3D) shape of the defects in the aluminum sample was reconstructed by superimposing the cross-sectional images. Results showed that the defect reconstruction effect of the two-dimensional section and the 3D defect reconstruction effect were significantly improved by the MBA method.

BREMS: Partial-wave calculation of spectra and angular distributions of electron-atom bremsstrahlung at electron energies less than 30 MeV (New Version Announcement)

BREMS: Partial-wave calculation of spectra and angular distributions of electron-atom bremsstrahlung at electron energies less than 30 MeV (New Version Announcement)

Spin accumulation without spin current

The spin Hall (SH) effect is a phenomenon in which the spin current flows perpendicular to an applied electric field and causes the spin accumulation at the boundaries. However, in the presence of spin-orbit couplings, the spin current is not well defined. Here, we calculate the spin response to an electric field gradient, which naturally appears at the boundaries. We derive a generic formula using the Bloch wave functions and the phenomenological relaxation time. We also calculate the response for the Rashba model with $\delta$-function nonmagnetic disorder within the first-order Born approximation and corresponding vertex corrections. We find the nonzero spin accumulation, although the SH conductivity exactly vanishes.

Combined Coulombic and magnetic contributions to dispersion in e + C12 collisions

Dispersion corrections to elastic electron scattering from a $^{12}\mathrm{C}$ nucleus are calculated within the second-order Born approximation. Three strong transient nuclear excitations are considered, at 4.439 MeV $({2}^{+})$, 17.7 MeV $({1}^{\ensuremath{-}}),$ and 23.5 MeV $({1}^{\ensuremath{-}})$. The Friar-Rosen-type Coulomb term is supplemented with the transverse part of the photon propagator. It is found that the dispersive cross-section changes in the first diffraction minimum reach nearly 10%, rising more slowly with collision energy beyond 400 MeV. Magnetic scattering can be strong for the individual excited states and lowers the dispersion effect considerably at energies below 400 MeV. However, it contributes at most 10% at the higher energies investigated.

Fate of pairing and spin-charge separation in the presence of long-range antiferromagnetism

We present a numerical study of competing orders in the 1D $t$-$J$ model with long-range RKKY-like staggered spin interactions. By circumventing the constraints imposed by Mermin-Wagner's theorem, this Hamiltonian can realize long-range N\'eel order at half-filling. We determine the full phase diagram as a function of the exchange and particle density using the density matrix renormalization group (DMRG) method. We show that pairing is disfavored and the AFM insulator and metallic phases are separated by a broad regime with phase segregation, before spin-charge separation re-emerges at low densities. Upon doping, interactions induce a confining potential that binds holons and spinons into full fledged fermionic quasi-particles in a range of parameters and densities. We numerically calculate the photoemission spectrum of the model, showing the appearance of a coherent quasi-particle band splitting away from the holon-spinon continuum with a width determined by $J$ that survives at finite doping. Comparison with analytical results using the self-consistent Born approximation (SCBA) and by solving the spinon-holon problem offer insight into the internal structure of the quasi-particles and help us explain the different features in the spectrum. We discuss how this simple toy-model can teach us about the phenomenology of its higher dimensional counterpart.

The RayGalGroupSims cosmological simulation suite for the study of relativistic effects: An application to lensing-matter clustering statistics

Context. General relativistic effects on the clustering of matter in the Universe provide a sensitive probe of cosmology and gravity theories that can be tested with the upcoming generation of galaxy surveys. These will require the availability of accurate model predictions, from large linear scales to small non-linear ones. Aims. Here, we present a suite of large-volume high-resolution N-body simulations specifically designed to generate light-cone data for the study of relativistic effects on lensing-matter observables without the use of simplifying approximations. As a case study application of these data, we perform an analysis of the relativistic contributions to the lensing-matter power spectra and cross-power spectra. Methods. The RayGalGroupSims suite (RAYGAL for short) consists of two N-body simulations of (2625 h−1 Mpc)3 volume with 40963 particles of a standard flat ΛCDM model and a non-standard wCDM phantom dark energy model with a constant equation of state. Light-cone data from the simulations have been generated using a parallel ray-tracing algorithm that has integrated more than 1 billion geodesic equations without the use of the flat-sky or Born approximation. Results. Catalogues and maps with relativistic weak lensing that include post-Born effects, magnification bias (MB), and redshift-space distortions (RSDs) due to gravitational redshift, Doppler, transverse Doppler, and integrated Sachs-Wolfe–Rees-Sciama effects are publicly released. Using this dataset, we are able to reproduce the linear and quasi-linear predictions from the CLASS relativistic code for the ten power spectra and cross-spectra (3 × 2 points) of the matter-density fluctuation field and the gravitational convergence at z = 0.7 and z = 1.8. We find a 1–30% level contribution from both MB and RSDs to the matter power spectrum, while the fingers-of-God effect is visible at lower redshift in the non-linear regime. Magnification bias also contributes at the 10−30% level to the convergence power spectrum, leading to a deviation between the shear power spectrum and the convergence power spectrum. Magnification bias also plays a significant role in the galaxy-galaxy lensing by decreasing the density-convergence spectra by 20% and coupling non-trivial configurations (such as the configuration with the convergence at the same redshift as the density, or at even lower redshifts). Conclusions. The cosmological analysis shows that the relativistic 3 × 2 points approach is a powerful cosmological probe. Our unified approach to relativistic effects is an ideal framework for the investigation of gravitational effects in galaxy studies (e.g., clustering and weak lensing) as well as their effects in galaxy cluster, group, and void studies (e.g., gravitational redshifts and weak lensing) and cosmic microwave background studies (e.g., integrated Sachs-Wolfe–Rees-Sciama and weak lensing).

Simultaneous Use of the Born and Rytov Approximations in Real-Time Imaging With Fourier-Space Scattered Power Mapping

The Fourier-space scattered-power mapping (F-SPM) is proposed as a computationally efficient alternative to the original real-space SPM method for real-time quantitative image reconstruction with an emphasis on close-range and near-field applications. Similar to SPM, F-SPM can employ either the Born or the Rytov data approximations in a linear scattering model, resulting in two distinct algorithms. However, to exploit the complementarity of the two approximations, a strategy is proposed for their combined use in a single inversion process. The combined Born–Rytov F-SPM method consistently improves the image quality in comparison with the images generated when using either approximation separately. The improvement is most significant when the limitations of either the Born or the Rytov approximations are violated. In the cases where neither or both of these limitations are violated, the images are of comparable quality to those generated by the standalone algorithms. The proposed Born–Rytov F-SPM algorithm is verified and compared to the standalone Born-based F-SPM and Rytov-based F-SPM in examples utilizing simulated and measured data. The gain in computational speed compared to the original real-space SPM is also demonstrated.