Topic

# Born approximation

About: Born approximation is a research topic. Over the lifetime, 8146 publications have been published within this topic receiving 149728 citations.

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TL;DR: It is shown how various well-known asymptotic power laws in S(q) are obtained from the above theory, and the theory is compared with experimental results on x-ray scattering from a polished Pyrex glass surface.

Abstract: The scattering of x rays and neutrons from rough surfaces is calculated. It is split into specular reflection and diffuse scattering terms. These are calculated in the first Born approximation, and explicit expressions are given for surfaces whose roughness can be described as self-affine over finite length scales. Expressions are also given for scattering from liquid surfaces, where it is shown that ``specular'' reflections only exist by virtue of a finite length cutoff to the mean-square height fluctuations. Expressions are also given for the scattering from randomly oriented surfaces, as studied in a typical small-angle scattering experiment. It is shown how various well-known asymptotic power laws in S(q) are obtained from the above theory. The distorted-wave Born approximation is next used to treat the case where the scattering is large (e.g., near the critical angle for total external reflection), and its limits of validity are discussed. Finally, the theory is compared with experimental results on x-ray scattering from a polished Pyrex glass surface.

2,031 citations

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TL;DR: In this paper, a natural time-dependent generalization for the well-known pair distribution function $g(mathrm{r})$ of systems of interacting particles is given, which gives rise to a very simple and entirely general expression for the angular and energy distribution of Born approximation scattering by the system.

Abstract: A natural time-dependent generalization is given for the well-known pair distribution function $g(\mathrm{r})$ of systems of interacting particles. The pair distribution in space and time thus defined, denoted by $G(\mathrm{r}, t)$, 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 Zernike-Prins 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 briefly derived and discussed.

2,015 citations

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IBM

^{1}TL;DR: In this article, the authors generalized the energy-level calculation to include arbitrary orientations of the constant energy ellipsoids in the bulk, the surface or interface, and an external magnetic field.

Abstract: The strong surface electric field associated with a semiconductor inversion layer quantizes the motion normal to the surface. The bulk energy bands split into electric sub-bands near the surface, each of which is a two-dimensional continuum associated with one of the quantized levels. We treat the electric quantum limit, in which only the lowest electric sub-band is occupied. Within the effective-mass approximation, we have generalized the energy-level calculation to include arbitrary orientations of (1) the constant-energy ellipsoids in the bulk, (2) the surface or interface, and (3) an external magnetic field. The potential associated with a charged center located an arbitrary distance from the surface is calculated, taking into account screening by carriers in the inversion layer. The bound states in the inversion layer due to attractive Coulomb centers are calculated for a model potential which assumes the inversion layer to have zero thickness. The Born approximation is compared with a phase-shift calculation of the scattering cross section, and is found to be reasonably good for the range of carrier concentrations encountered in InAs surfaces. The low-temperature mobility associated with screened Coulomb scattering by known charges at the surface and in the semiconductor depletion layer is calculated for InAs and for Si (100) surfaces in the Born approximation, using a potential that takes the inversion-layer charge distribution into account. The InAs results are in good agreement with experiment. In Si, but not in InAs, freeze-out of carriers into inversion-layer bound states is expected at low temperatures and low inversion-layer charge densities, and the predicted behavior is in qualitative agreement with experiment. An Appendix gives the phase-shift method for two-dimensional scattering and the exact cross section for scattering by an unscreened Coulomb potential.

1,468 citations

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TL;DR: The distorted Born iterative method (DBIM) is used to solve two-dimensional inverse scattering problems, thereby providing another general method to solve the two- dimensional imaging problem when the Born and the Rytov approximations break down.

Abstract: The distorted Born iterative method (DBIM) is used to solve two-dimensional inverse scattering problems, thereby providing another general method to solve the two-dimensional imaging problem when the Born and the Rytov approximations break down. Numerical simulations are performed using the DBIM and the method proposed previously by the authors (Int. J. Imaging Syst. Technol., vol.1, no.1, p.100-8, 1989) called the Born iterative method (BIM) for several cases in which the conditions for the first-order Born approximation are not satisfied. The results show that each method has its advantages; the DBIM shows faster convergence rate compared to the BIM, while the BIM is more robust to noise contamination compared to the DBIM. >

1,026 citations