Reconstruction of the potential from scattering data

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Abstract
We propose an efficient method for reconstruction of the potential from scattering data. Starting from experimentally determined phase shifts and taking into consideration the incompleteness and inexactness of the input information, we construct iteratively a local potential that approximates the input phase shifts. The method is first tested on model examples and is then used for construction of a local effective potential describing the scattering of low-energy electrons by noble-gas atoms. Convergence of the method is usually very fast, and the reconstructed potential is close to the true one. A relation between the inverse-scattering problem and the Fourier analysis of experimental data is discussed.