#+TITLE: CoulombIntegrals.jl #+AUTHOR: Stefanos Carlström #+EMAIL: stefanos.carlstrom@gmail.com

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  • Introduction Small library to calculate the different integrals that arise from Coulomb repulsion. Among these are e.g. the Slater integrals. There are different methods of varying speed and accuracy, and the intention is to implement at least a few to be able to compare.

    The library is intended to be independent of basis chosen, and is based off [[https://github.com/JuliaApproximation/ContinuumArrays.jl][ContinuumArrays.jl]]. However, at the moment only [[https://github.com/JuliaApproximation/CompactBases.jl][CompactBases.jl]] are supported. Moreover, it is only possible to work with 1d bases, i.e. tensorial bases are not yet supported.

  • References

    • Froese Fischer, C., Brage, T., & Jönsson, P. (1997). Computational Atomic Structure : An MCHF Approach. Bristol, UK Philadelphia, Penn: Institute of Physics Publ.

    • Brage, T., & Fischer, C. F. (1994). Spline-Galerkin Methods for Rydberg Series, Including Breit-Pauli Effects. Journal of Physics B: Atomic, Molecular and Optical Physics, 27(22), 5467–5484. http://dx.doi.org/10.1088/0953-4075/27/22/007

    • Qiu, Y., & Fischer, C. F. (1999). Integration by cell algorithm for slater integrals in a spline basis. Journal of Computational Physics, 156(2), 257–271. http://dx.doi.org/10.1006/jcph.1999.6361

    • McCurdy, C. W., & Martín, F. (2004). Implementation of exterior complex scaling in b-splines to solve atomic and molecular collision problems. Journal of Physics B: Atomic, Molecular and Optical Physics, 37(4), 917–936. http://dx.doi.org/10.1088/0953-4075/37/4/017

    • McCurdy, C. W., Baertschy, M., & Rescigno, T. N. (2004). Solving the three-body coulomb breakup problem using exterior complex scaling. Journal of Physics B: Atomic, Molecular and Optical Physics, 37(17), 137–187. http://dx.doi.org/10.1088/0953-4075/37/17/r01

    • Zatsarinny, O. (2006). Bsr: b-spline atomic R-matrix codes. Computer Physics Communications, 174(4), 273–356. http://dx.doi.org/10.1016/j.cpc.2005.10.006