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

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 |η||η| or |ℑ(ℓ)||ℑ(ℓ)|. Moreover, a simple analytic continuation for R(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 |η||η| and |ℑ(ℓ)||ℑ(ℓ)| are large and |R(ℓ)| comparable or smaller than |ℑ(ℓ)||ℑ(ℓ)|.Program summaryTitle of program: cwfcomplexCatalogue number:ADYO_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYO_v1_0Program obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandLicensing provisions: noneComputers on which the program has been tested: DELL GX400Operating systems: Linux, WindowsProgramming language used: C++No. of bits in a word: 64No. of processors used: 1Has the code been vectorized?: noNo. of bytes in distributed program, including test data, etc.: 33 092No. of lines in distributed program, including test data, etc.: 3210Distribution format:tar.gzNature of physical problem: The calculation of Coulomb wave functions with all of their arguments complex is revisited. The new methods introduced allow to greatly augment the range of accessible ℓ, η, and z.Method of solution:   Power/asymptotic series and continued fractions are supplemented with direct integrations of the Coulomb Schrödinger equation. Analytic continuation for R(z)<0 is also precisely computed using linear combinations of the functions provided by standard methods, which do not follow the branch cut requirements demanded for Coulomb wave functions.Typical running time: N/AUnusual features of the program: none