Characteristics of the scattering states in the most weakly bound electron potential model have been studied, and certain analytical solutions of a distorted Coulomb wave were obtained. The normalized wave functions of scattering states on the k /2π scale and the calculation formula of phase shift are presented. Analytical properties of the scattering amplitude are discussed, and analytical formulas for calculating bound continuous transition matrix elements are also given. The results may be useful in a wide class of scattering problems.
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