Coulomb wave functions in momentum space

V. Eremenko; N. J. Upadhyay; I. J. Thompson; Ch Elster; F. M. Nunes; G. Arbanas; J. E. Escher; L. Hlophe

doi:10.1016/j.cpc.2014.10.002

Coulomb wave functions in momentum space

V. Eremenko, N. J. Upadhyay, I. J. Thompson, Ch Elster, F. M. Nunes, G. Arbanas, J. E. Escher, L. Hlophe

Nuclear Criticality Safety

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

An algorithm to calculate non-relativistic partial-wave Coulomb functions in momentum space is presented. The arguments are the Sommerfeld parameter η, the angular momentum l, the asymptotic momentum q and the 'running' momentum p, where both momenta are real. Since the partial-wave Coulomb functions exhibit singular behavior when p→q, different representations of the Legendre functions of the 2nd kind need to be implemented in computing the functions for the values of p close to the singularity and far away from it. The code for the momentum-space Coulomb wave functions is applicable for values of |η| in the range of 10^-1 to 10, and thus is particularly suited for momentum space calculations of nuclear reactions. Program Summary Program title: libcwfn Catalogue identifier: AEUQ-v1-0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUQ-v1-0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 864503 No. of bytes in distributed program, including test data, etc.: 7178021 Distribution format: tar.gz Programming language: Fortran 90, Fortran 77, Python, make (GNU Make dialect), GNU Bash shell interpreter (available as /bin/bash). Computer: Apple Powermac (Intel Xeon), ASUS K53U (AMD E-350 (Dual Core)), DELL Precision T3500 (Intel Xeon), NERSC Carver (Intel Nehalem Quad Core). Operating system: Linux, Windows (using Cygwin). RAM: less than 512 Mbytes Classification: 17.8, 17.13, 17.16. Nature of problem: The calculation of partial wave Coulomb functions with integer l and all other arguments real. Solution method: Computing the value of the function using explicit formulae and algorithms. Running time: Less than 10^-3 s.

Original language	English
Pages (from-to)	195-203
Number of pages	9
Journal	Computer Physics Communications
Volume	187
DOIs	https://doi.org/10.1016/j.cpc.2014.10.002
State	Published - Feb 1 2015

Funding

The TORUS Collaboration acknowledges the insight of Prof. Akram Mukhamedzhanov in respect to this project. Eremenko and Upadhyay are grateful to Prof. Akram Mukhamedzhanov and Dr. Ahdior Sattarov for providing invaluable guidance in the early stages of this work. The authors are also grateful to Prof. Jeff Tostevin for many useful discussions. This material is based on work in part supported by the US Department of Energy , Office of Science of Nuclear Physics under contracts DE-SC0004084 and DE-SC0004087 (TORUS Collaboration), DE-FG02-93ER40756 with Ohio University , contract DE-FG52-08NA28552 with Michigan State University , and by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 , and the U.T. Battelle LLC Contract DE-AC-0500OR22725 . F.M. Nunes also acknowledges support from the National Science Foundation under grant PHY-080026 . This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the US Department of Energy under Contract No. DE-AC02-05CH11231 .

Keywords

Coulomb functions
Momentum-space partial-wave

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10.1016/j.cpc.2014.10.002

Cite this

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title = "Coulomb wave functions in momentum space",

abstract = "An algorithm to calculate non-relativistic partial-wave Coulomb functions in momentum space is presented. The arguments are the Sommerfeld parameter η, the angular momentum l, the asymptotic momentum q and the 'running' momentum p, where both momenta are real. Since the partial-wave Coulomb functions exhibit singular behavior when p→q, different representations of the Legendre functions of the 2nd kind need to be implemented in computing the functions for the values of p close to the singularity and far away from it. The code for the momentum-space Coulomb wave functions is applicable for values of |η| in the range of 10-1 to 10, and thus is particularly suited for momentum space calculations of nuclear reactions. Program Summary Program title: libcwfn Catalogue identifier: AEUQ-v1-0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUQ-v1-0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 864503 No. of bytes in distributed program, including test data, etc.: 7178021 Distribution format: tar.gz Programming language: Fortran 90, Fortran 77, Python, make (GNU Make dialect), GNU Bash shell interpreter (available as /bin/bash). Computer: Apple Powermac (Intel Xeon), ASUS K53U (AMD E-350 (Dual Core)), DELL Precision T3500 (Intel Xeon), NERSC Carver (Intel Nehalem Quad Core). Operating system: Linux, Windows (using Cygwin). RAM: less than 512 Mbytes Classification: 17.8, 17.13, 17.16. Nature of problem: The calculation of partial wave Coulomb functions with integer l and all other arguments real. Solution method: Computing the value of the function using explicit formulae and algorithms. Running time: Less than 10-3 s.",

keywords = "Coulomb functions, Momentum-space partial-wave",

author = "V. Eremenko and Upadhyay, {N. J.} and Thompson, {I. J.} and Ch Elster and Nunes, {F. M.} and G. Arbanas and Escher, {J. E.} and L. Hlophe",

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doi = "10.1016/j.cpc.2014.10.002",

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T1 - Coulomb wave functions in momentum space

AU - Eremenko, V.

AU - Upadhyay, N. J.

AU - Thompson, I. J.

AU - Elster, Ch

AU - Nunes, F. M.

AU - Arbanas, G.

AU - Escher, J. E.

AU - Hlophe, L.

PY - 2015/2/1

Y1 - 2015/2/1

N2 - An algorithm to calculate non-relativistic partial-wave Coulomb functions in momentum space is presented. The arguments are the Sommerfeld parameter η, the angular momentum l, the asymptotic momentum q and the 'running' momentum p, where both momenta are real. Since the partial-wave Coulomb functions exhibit singular behavior when p→q, different representations of the Legendre functions of the 2nd kind need to be implemented in computing the functions for the values of p close to the singularity and far away from it. The code for the momentum-space Coulomb wave functions is applicable for values of |η| in the range of 10-1 to 10, and thus is particularly suited for momentum space calculations of nuclear reactions. Program Summary Program title: libcwfn Catalogue identifier: AEUQ-v1-0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUQ-v1-0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 864503 No. of bytes in distributed program, including test data, etc.: 7178021 Distribution format: tar.gz Programming language: Fortran 90, Fortran 77, Python, make (GNU Make dialect), GNU Bash shell interpreter (available as /bin/bash). Computer: Apple Powermac (Intel Xeon), ASUS K53U (AMD E-350 (Dual Core)), DELL Precision T3500 (Intel Xeon), NERSC Carver (Intel Nehalem Quad Core). Operating system: Linux, Windows (using Cygwin). RAM: less than 512 Mbytes Classification: 17.8, 17.13, 17.16. Nature of problem: The calculation of partial wave Coulomb functions with integer l and all other arguments real. Solution method: Computing the value of the function using explicit formulae and algorithms. Running time: Less than 10-3 s.

AB - An algorithm to calculate non-relativistic partial-wave Coulomb functions in momentum space is presented. The arguments are the Sommerfeld parameter η, the angular momentum l, the asymptotic momentum q and the 'running' momentum p, where both momenta are real. Since the partial-wave Coulomb functions exhibit singular behavior when p→q, different representations of the Legendre functions of the 2nd kind need to be implemented in computing the functions for the values of p close to the singularity and far away from it. The code for the momentum-space Coulomb wave functions is applicable for values of |η| in the range of 10-1 to 10, and thus is particularly suited for momentum space calculations of nuclear reactions. Program Summary Program title: libcwfn Catalogue identifier: AEUQ-v1-0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUQ-v1-0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 864503 No. of bytes in distributed program, including test data, etc.: 7178021 Distribution format: tar.gz Programming language: Fortran 90, Fortran 77, Python, make (GNU Make dialect), GNU Bash shell interpreter (available as /bin/bash). Computer: Apple Powermac (Intel Xeon), ASUS K53U (AMD E-350 (Dual Core)), DELL Precision T3500 (Intel Xeon), NERSC Carver (Intel Nehalem Quad Core). Operating system: Linux, Windows (using Cygwin). RAM: less than 512 Mbytes Classification: 17.8, 17.13, 17.16. Nature of problem: The calculation of partial wave Coulomb functions with integer l and all other arguments real. Solution method: Computing the value of the function using explicit formulae and algorithms. Running time: Less than 10-3 s.

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KW - Momentum-space partial-wave

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ER -

Coulomb wave functions in momentum space

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Keywords

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