The accuracy of iterated JWBK approximations for Coulomb radial wave functions

Iterated JWBK approximations (IJWBK) can be used for the calculation of Coulomb radial wave functions, for non-negative energies and for values of the radial coordinate, r, such that the functions are oscillatory. Burgess (1963) has given analytical expressions for the first-order IJWBK amplitudes and phases. The second-order theory is discussed. Accurate Coulomb functions are computed using power-series expansions and are used to determine the errors in the zero-, first- and second-order IJWBK approximations. Values of rsub(l) [delta] are given, such that for r > rsub(l)[delta] the errors in the first-order approximation are less than delta, where delta = 10-3 or 10-4. (orig.)