Solving the Coulomb scattering problem using the complex scaling method

Details Solving the Coulomb scattering problem using the complex scaling method Solving the Coulomb scattering problem using the complex scaling method

2011-02-02

arxiv.org/abs/1102.0567v1

Europhys.Lett.85:30001,2009

Physics

Atomic Physics

3 pages, 3 figures

Scientific paper

Based on the work of Nuttall and Cohen [Phys. Rev. {\bf 188} (1969) 1542] and Resigno et al{} [Phys. Rev. A {\bf 55} (1997) 4253] we present a rigorous formalism for solving the scattering problem for long-range interactions without using exact asymptotic boundary conditions. The long-range interaction may contain both Coulomb and short-range potentials. The exterior complex scaling method, applied to a specially constructed inhomogeneous Schr\"odinger equation, transforms the scattering problem into a boundary problem with zero boundary conditions. The local and integral representations for the scattering amplitudes have been derived. The formalism is illustrated with numerical examples.

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