Query: Born Approximation

title: Justification of the Cauchy Born Approximation of Elastodynamics
abstract: We present sharp convergence results for the Cauchy Born approximation of general classical atomistic interactions, for static problems with small data and for dynamic problems on a macroscopic time interval.

title: Electromagnetic subsurface prospecting by a multifocusing inexact Newton method within the second order Born approximation.
abstract: In this paper the reconstruction of a shallow buried object is addressed by an electromagnetic inverse scattering method based on combining different imaging modalities. In particular, the proposed approach integrates the inexact Newton (IN) method with an iterative multiscaling approach. Moreover, the use of the second order Born approximation is exploited. A numerical validation is provided concerning the potentialities arising by combining the regularization capabilities of the IN method and the effectiveness of the multifocusing strategy to mitigate the nonlinearity and ill posedness of the inversion problem. Comparisons with the standard "bare" approach in terms of accuracy, robustness, noise levels, and computational efficiency are also included.

title: Improved master equation approach to quantum transport: from Born to self consistent Born approximation.
abstract: Beyond the second order Born approximation, we propose an improved master equation approach to quantum transport under self consistent Born approximation. The basic idea is to replace the free Green's function in the tunneling self energy diagram by an effective reduced propagator under the Born approximation. This simple modification has remarkable consequences. It not only recovers the exact results for quantum transport through noninteracting systems under arbitrary voltages, but also predicts the challenging nonequilibrium Kondo effect. Compared to the nonequilibrium Green's function technique that formulates the calculation of specific correlation functions, the master equation approach contains richer dynamical information to allow more efficient studies for such as the shot noise and full counting statistics.

title: Grazing incidence transmission X ray scattering: surface scattering in the Born approximation
abstract: Determination of the three dimensional order in thin nanostructured films remains challenging. Real space imaging methods, including electron microscopies and scanning probe methods, have difficulty reconstructing the depth of a film and suffer from limited statistical sampling. X ray and neutron scattering have emerged as powerful complementary techniques but have substantial data collection and analysis challenges. This article describes a new method, grazing incidence transmission small angle X ray scattering, which allows for fast scattering measurements that are not burdened by the refraction and reflection effects that have to date plagued grazing incidence X ray scattering. In particular, by arranging a sample/beam geometry wherein the scattering exits through the edge of the substrate, it is possible to record scattering images that are well described by straightforward (Born approximation) scattering models.

title: Search for effects beyond the born approximation in polarization transfer observables in e(over )p elastic scattering.
abstract: Intensive theoretical and experimental efforts over the past decade have aimed at explaining the discrepancy between data for the proton electric to magnetic form factor ratio, G(E)/G(M) obtained separately from cross section and polarization transfer measurements. One possible explanation for this difference is a two photon exchange contribution. In an effort to search for effects beyond the one photon exchange or Born approximation, we report measurements of polarization transfer observables in the elastic H(e[over ,e()p[over reaction for three different beam energies at a Q(2)=2.5 GeV(2) spanning a wide range of the kinematic parameter e. The ratio R, which equals m(p)G(E)/G(M) in the Born approximation, is found to be independent of e at the 1.5% level. The e dependence of the longitudinal polarization transfer component P(l) shows an enhancement of (2.3+ 0.6) relative to the Born approximation at large e.

title: Correlations in Space and Time and Born Approximation Scattering in Systems of Interacting Particles
abstract: A natural time dependent generalization is given for the well known pair distribution function g(r) of systems of interacting particles. The pair distribution in space and time thus defined, denoted by G(r, t) gives rise to a very simple and entirely general expression for the angular and energy distribution of Born approximation scattering by the system. This expression is the natural extension of the familiar ZernikePrins formula to scattering in which the energy transfers are not negligible compared to the energy of the scattered particle. It is therefore of particular interest for scattering of slow neutrons by general systems of interacting particles: G is then the proper function in terms of which to analyze the scattering data. After defining the G function and expressing the Born approximation scattering formula in terms of it, the paper studies its general properties and indicates its role for neutron scattering. The qualitative behavior of G for liquids and dense gases is then described and the long range part exhibited by the function near the critical point is calculated. The explicit expression of G for crystals and for ideal quantum gases is brieRy derived and discussed.

title: Cavity Born Oppenheimer Approximation for Correlated Electron Nuclear Photon Systems
abstract: In this work, we illustrate the recently introduced concept of the cavity Born Oppenheimer approximation [Flick et al. PNAS2017, 10.1073/pnas.1615509114] for correlated electron nuclear photon problems in detail. We demonstrate how an expansion in terms of conditional electronic and photon nuclear wave functions accurately describes eigenstates of strongly correlated light matter systems. For a GaAs quantum ring model in resonance with a photon mode we highlight how the ground state electronic potential energy surface changes the usual harmonic potential of the free photon mode to a dressed mode with a double well structure. This change is accompanied by a splitting of the electronic ground state density. For a model where the photon mode is in resonance with a vibrational transition, we observe in the excited state electronic potential energy surface a splitting from a single minimum to a double minimum. Furthermore, for a time dependent setup, we show how the dynamics in correlated light matter systems can be understood in terms of population transfer between potential energy surfaces. This work at the interface of quantum chemistry and quantum optics paves the way for the full ab initio description of matter photon systems.

title: Structural length scale sensitivities of reflectance measurements in continuous random media under the Born approximation.
abstract: Which range of structures contributes to light scattering in a continuous random media, such as biological tissue? In this Letter, we present a model to study the structural length scale sensitivity of scattering in continuous random media under the Born approximation. The scattering coefficient ms, backscattering coefficient mb, anisotropy factor g, and reduced scattering coefficient ms* as well as the shape of the spatial reflectance profile are calculated under this model. For media with a biologically relevant Henyey Greenstein phase function with g~0.93 at wavelength l=633 nm, we report that ms* is sensitive to structural length scales from 46.9 nm to 2.07 mm (i.e. l/13 to 3l) mb is sensitive from 26.7 to 320 nm (i.e. l/24 to l/2) and the spatial reflectance profile is sensitive from 30.8 nm to 2.71 mm (i.e. l/21 to 4l)

title: Electron impact single ionization of the water molecule in the second Born approximation
abstract: A general formalism is presented to calculate the triple differential cross section for the ionization of neutral atoms and simple molecules with the chemical form XHn in the frame of the second Born approximation using the closure approximation. The first Born term and a part of the second term are calculated analytically and the remainder is calculated semi analytically. A new method is given to eliminate analytically the singularities occurring in the second Born term. The post collision interaction between the scattered and ejected electrons is considered approximately using the Gamow factor. To check the accuracy of the present formalism, the ionization of the atomic hydrogen by electron impact is considered. The present formalism is developed to investigate the single ionization of the water molecule by electron impact. The comparison of our results with the experiments and previous theoretical findings shows good agreement and contrary to the previous theoretical calculations, our results predict two peaks in the recoil region.

title: The second Born approximation for the single and double ionization of atoms by electrons and positrons
abstract: Recently, Lahmam Bennani et al (2010  105201) have shown that the second Born approximation is necessary to describe the experimental results of the double ionization of atoms and molecules. The second Born approximation needs a difficult triple numerical integration and often many authors find some controversial results. We now investigate, in greater detail, the application of the second Born approximation for the easier case: the ionization of atomic hydrogen by electrons. The ionization of atomic hydrogen allows us to check accurately this approximation because the wavefunctions describing the target are known exactly. Moreover, sophisticated models such as convergent close coupling (CCC) and the continuum distorted wave eikonal initial state (CDW EIS) exist and give closer results leading to easier comparisons. We report accurate second Born results for differential cross sections for the ionization of atomic hydrogen using a basis including 100 discrete states, and another basis including 32 discrete states and pseudo states. The results of the present method are compared with other calculations and experiment. The single ionization of helium is also investigated in order to answer an old controversy between two different theoretical results. Finally, an application of the second Born approximation to the double ionization of helium has been performed.