Abstract
Publisher Summary This chapter presents recent advances in the numerical calculation of ionization amplitudes. The chapter focuses on directly solving the stationary Schrodinger equation thus overcoming the limitations of wave packets. In particular, it is possible to probe the threshold region in great detail without analytic approximations. The chapter presents the simplest case where the target is a hydrogen atom. At impact energies below about 50 eV, the dynamics of two electrons moving freely in a correlated fashion is described. The formal apparatus needed to calculate scattering amplitudes, which is no more than a generalization of the theory of Frauenhofer diffraction in elementary optics, is also described. The chapter also provides an overview of the boundary function method and path integral and semiclassical methods. Several calculations on a two-dimensional model and calculations in three dimensions are also explained.
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