Approximate Three-Dimensional Wave Function and the T-Matrix for the Sharply Cut Off Coulomb Potential

J. Golak^1a, W. Glöckle², R. Skibiński¹ and H. Witała¹

¹ M. Smoluchowski Institute of Physics, Jagiellonian University, PL-30059 Kraków, Poland
² Institut für theoretische Physik II, Ruhr-Universität Bochum, D-44780 Bochum, Germany

^a e-mail: jacek.golak@uj.edu.pl

Published online: 12 April 2010

Abstract

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.