Precise Coulomb wave functions for a wide range of complex ℓ, η and z Original Research Article

A new algorithm to calculate Coulomb wave functions with all of its arguments complex is proposed. For that purpose, standard methods such as continued fractions and power/asymptotic series are combined with direct integrations of the Schrödinger equation in order to provide very stable calculations, even for large values of image or image. Moreover, a simple analytic continuation for image is introduced, so that this zone of the complex z-plane does not pose any problem. This code is particularly well suited for low-energy calculations and the calculation of resonances with extremely small widths. Numerical instabilities appear, however, when both image and image are large and image comparable or smaller than image.