The Born approximation is based on the assumption of small slowness perturbation. We investigate the limits of the Born approximation when applied to wave-equation migration velocity analysis and propose two new schemes which allow for larger slowness anomalies, while improving accuracy and increasing stability. The new schemes are based on linearizations of exponential functions using bilinear...

With the aim of studying magnetic effects in time-distance helioseismology, we use the first-order Born approximation to compute the scattering of acoustic plane waves by a magnetic cylinder embedded in a uniform medium. We show, by comparison with the exact solution, that the travel-time shifts computed in the Born approximation are everywhere valid to first order in the ratio of the magnetic ...

The first and second Born approximation are studied with the path integral representation for T matrix. The T matrix is calculated for Woods-Saxon potential scattering. To make corresponding integrals solvable analytically, an approximate function for the Woods-Saxon potential is used. Finally it shown that the Born series is converge at high energies and orders higher than two in Born approxim...

In the present work, fully differential cross section of atomic helium ionization by protons impact at high energy ranges is calculated. The calculations have been performed using three-body formalism in first order Born-Faddeev approximation with an active electron model and four body Born approximation. to investigate collision dynamics accurately, has single parameter Hartree Fock as single-...