Abstract
The asymptotic form of the radial wave function for positive-energy states is calculated for the case of a repulsive Coulomb field. The cases of a pure Coulomb potential and a modified Coulomb potential are considered. Second-order analytic solutions for the amplitudes and phases are obtained when the modifications to the pure Coulombic potential take the form \ensuremath{\alpha}${\mathit{r}}^{\mathrm{\ensuremath{-}}2}$+\ensuremath{\beta}${\mathit{r}}^{\mathrm{\ensuremath{-}}3}$+\ensuremath{\gamma}${\mathit{r}}^{\mathrm{\ensuremath{-}}4}$, using the Jeffreys or WKB method. For the case of a pure Coulomb field, numerical results obtained from this method were compared with ``exact'' numerical results that were obtained using the analytic properties of the Coulomb wave functions. Tables are presented to show the conditions under which the method is accurate.
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