Approximate Three-Dimensional Wave Function and the T-Matrix for the Sharply Cut Off Coulomb Potential
M. Smoluchowski Institute of Physics, Jagiellonian
2 Institut für theoretische Physik II, Ruhr-Universität Bochum, D-44780 Bochum, Germany
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For a sharply cut-oﬀ Coulomb potential we derive analytically the asymptotic form of the threedimensional wave function and the related scattering amplitude. We show a failure of the standard renormalization factor which is believed to be generally valid for any type of screening. We obtain also the asymptotic form of the corresponding three-dimensional half-shell t-matrix. Our results are fully supported by the numerical solutions of the three-dimensional Lippmann-Schwinger equation.
© Owned by the authors, published by EDP Sciences, 2010