RADIAL: A Fortran subroutine package for the solution of the radial Schrödinger and Dirac wave equations

The Fortran subroutine package RADIAL for the numerical solution of the Schrödinger and Dirac wave equations of electrons in central potentials V(r) is described. The considered potentials are such that the function V(r) ≡ rV (r) is finite for all r and tends to constant values when r → 0 and r → ∞....

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Detalles Bibliográficos
Autores: Salvat Gavaldà, Francesc, Fernández Varea, José María
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2019
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/226459
Acceso en línea:https://hdl.handle.net/2445/226459
Access Level:acceso abierto
Palabra clave:Equació de Schrödinger
Equació de Dirac
Electrons
Equació d'ona
Schrödinger equation
Dirac equation
Electrones
Wave equation
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spelling RADIAL: A Fortran subroutine package for the solution of the radial Schrödinger and Dirac wave equationsSalvat Gavaldà, FrancescFernández Varea, José MaríaEquació de SchrödingerEquació de DiracElectronsEquació d'onaSchrödinger equationDirac equationElectronesWave equationThe Fortran subroutine package RADIAL for the numerical solution of the Schrödinger and Dirac wave equations of electrons in central potentials V(r) is described. The considered potentials are such that the function V(r) ≡ rV (r) is finite for all r and tends to constant values when r → 0 and r → ∞. This includes finite-range potentials as well as combinations of Coulomb and finite-range potentials. The function V(r) used in the numerical calculation is the natural cubic spline that interpolates a table of values provided by the user. The radial wave equations are solved by using piecewise exact power series expansions of the radial functions, which are summed up to the prescribed accuracy so that truncation errors can be completely avoided. The RADIAL subroutines compute radial wave functions, eigenvalues for bound states and phase shifts for free states. Specific subroutines are also provided for computing the radial functions and phase shifts for free states of complex optical potentials having a finite-range absorptive imaginary part. The solution subroutines are accompanied by example main programs, as well as with specific programs that perform calculations relevant in atomic, nuclear, and radiation physics (the self-consistent solution of the Dirac-Hartee-Fock-Slater equations for neutral atoms and positive ions, and the calculation of cross sections for elastic scattering of high-energy electrons and positrons by atoms and of nucleons by nuclei). The distribution package includes a detailed manual with a description of the basic physics and the mathematical formulas implemented in the subroutines.Elsevier B.V.2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/226459Articles publicats en revistes (Física Quàntica i Astrofísica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: https://doi.org/10.1016/j.cpc.2019.02.011Computer Physics Communications, 2019, vol. 240, num.07, p. 165-177https://doi.org/10.1016/j.cpc.2019.02.011(c) Elsevier B.V., 2019info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/2264592026-05-27T06:46:51Z
dc.title.none.fl_str_mv RADIAL: A Fortran subroutine package for the solution of the radial Schrödinger and Dirac wave equations
title RADIAL: A Fortran subroutine package for the solution of the radial Schrödinger and Dirac wave equations
spellingShingle RADIAL: A Fortran subroutine package for the solution of the radial Schrödinger and Dirac wave equations
Salvat Gavaldà, Francesc
Equació de Schrödinger
Equació de Dirac
Electrons
Equació d'ona
Schrödinger equation
Dirac equation
Electrones
Wave equation
title_short RADIAL: A Fortran subroutine package for the solution of the radial Schrödinger and Dirac wave equations
title_full RADIAL: A Fortran subroutine package for the solution of the radial Schrödinger and Dirac wave equations
title_fullStr RADIAL: A Fortran subroutine package for the solution of the radial Schrödinger and Dirac wave equations
title_full_unstemmed RADIAL: A Fortran subroutine package for the solution of the radial Schrödinger and Dirac wave equations
title_sort RADIAL: A Fortran subroutine package for the solution of the radial Schrödinger and Dirac wave equations
dc.creator.none.fl_str_mv Salvat Gavaldà, Francesc
Fernández Varea, José María
author Salvat Gavaldà, Francesc
author_facet Salvat Gavaldà, Francesc
Fernández Varea, José María
author_role author
author2 Fernández Varea, José María
author2_role author
dc.subject.none.fl_str_mv Equació de Schrödinger
Equació de Dirac
Electrons
Equació d'ona
Schrödinger equation
Dirac equation
Electrones
Wave equation
topic Equació de Schrödinger
Equació de Dirac
Electrons
Equació d'ona
Schrödinger equation
Dirac equation
Electrones
Wave equation
description The Fortran subroutine package RADIAL for the numerical solution of the Schrödinger and Dirac wave equations of electrons in central potentials V(r) is described. The considered potentials are such that the function V(r) ≡ rV (r) is finite for all r and tends to constant values when r → 0 and r → ∞. This includes finite-range potentials as well as combinations of Coulomb and finite-range potentials. The function V(r) used in the numerical calculation is the natural cubic spline that interpolates a table of values provided by the user. The radial wave equations are solved by using piecewise exact power series expansions of the radial functions, which are summed up to the prescribed accuracy so that truncation errors can be completely avoided. The RADIAL subroutines compute radial wave functions, eigenvalues for bound states and phase shifts for free states. Specific subroutines are also provided for computing the radial functions and phase shifts for free states of complex optical potentials having a finite-range absorptive imaginary part. The solution subroutines are accompanied by example main programs, as well as with specific programs that perform calculations relevant in atomic, nuclear, and radiation physics (the self-consistent solution of the Dirac-Hartee-Fock-Slater equations for neutral atoms and positive ions, and the calculation of cross sections for elastic scattering of high-energy electrons and positrons by atoms and of nucleons by nuclei). The distribution package includes a detailed manual with a description of the basic physics and the mathematical formulas implemented in the subroutines.
publishDate 2019
dc.date.none.fl_str_mv 2019
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/226459
url https://hdl.handle.net/2445/226459
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.1016/j.cpc.2019.02.011
Computer Physics Communications, 2019, vol. 240, num.07, p. 165-177
https://doi.org/10.1016/j.cpc.2019.02.011
dc.rights.none.fl_str_mv (c) Elsevier B.V., 2019
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Elsevier B.V., 2019
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier B.V.
publisher.none.fl_str_mv Elsevier B.V.
dc.source.none.fl_str_mv Articles publicats en revistes (Física Quàntica i Astrofísica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.811543

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