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Precise Coulomb wave functions for a wide range of complex l, eta and z

N. Michel
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Abstract

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 Schrodinger equation in order to provide very stable calculations, even for large values of |eta| or |Im(l)|. Moreover, a simple analytic continuation for Re(z) < 0 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 |eta| and |Im(l)| are large and |Re(l)| comparable or smaller than |Im(l)|.

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N. Michel. 2007-02-06. Precise Coulomb wave functions for a wide range of complex l, eta and z. https://doi.org/10.1016/j.cpc.2006.10.004

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