Wave Functions for Large Arguments by the Amplitude-Phase Method

Abstract

The two independent solutions of the radial wave equation required in the treatment of collision problems may be expressed in terms of a common amplitude and phases differing by $\frac{\ensuremath{\pi}}{2}$, following a method due to Milne. The determination of phase shifts is simplified by this procedure. Analytical expressions for the amplitude and phase and their derivatives are given in the case of zero field for $L=0,1,2,3,4$. In other cases these quantities may rapidly be determined for large arguments by numerical integration of Eqs. (7) and (5b). Values of the amplitude and phase of the coulomb functions needed in the treatment of the scattering of alpha-particles in helium for $L=0$ and $L=2$ were obtained in this way and are tabulated.