{
"date" : "2012-05-30",
"identifier_doecontract" : "",
"subject" : "72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; ALGORITHMS; ANALYTICAL SOLUTION; COMPUTER CODES; DIRAC EQUATION; ELECTRON-ION COLLISIONS; FUNCTIONALS; GREEN FUNCTION; IMPURITIES; LIPPMANN-SCHWINGER EQUATION; MATRICES; NUMERICAL SOLUTION; PHASE SHIFT; POLYNOMIALS; POTENTIAL SCATTERING; RECURSION RELATIONS; RELATIVISTIC RANGE; RUBIDIUM; SCHROEDINGER EQUATION; SERIES EXPANSION; SPHERICAL HARMONICS; TUNGSTEN; WAVE FUNCTIONS",
"description" : "I present an elaborated analytical examination of the Green function of an electron scattered at a single-site potential, for both the Schroedinger and the Dirac equation, followed by an efficient numerical solution, in both cases for potentials of arbitrary shape without an atomic sphere approximation. A numerically stable way to calculate the corresponding regular and irregular wave functions and the Green function is via the angular Lippmann-Schwinger integral equations. These are solved based on an expansion in Chebyshev polynomials and their recursion relations, allowing to rewrite the Lippmann-Schwinger equations into a system of algebraic linear equations. Gonzales et al. developed this method for the Schroedinger equation, where it gives a much higher accuracy compared to previous perturbation methods, with only modest increase in computational effort. In order to apply it to the Dirac equation, I developed relativistic Lippmann-Schwinger equations, based on a decomposition of the potential matrix into spin spherical harmonics, exploiting certain properties of this matrix. The resulting method was embedded into a Korringa-Kohn-Rostoker code for density functional calculations. As an example, the method is applied by calculating phase shifts and the Mott scattering of a tungsten impurity. (orig.)",
"language" : "English",
"identifier_report" : "INIS-DE-1280",
"publisher_sponsor" : "",
"publisher_country" : "Germany",
"source" : "DEN",
"purl" : "https://www.osti.gov/etdeweb/servlets/purl/21555650",
"title" : "Single-site Green function of the Dirac equation for full-potential electron scattering",
"type" : "Miscellaneous",
"subject_related" : "",
"relation" : "Related Information: Schriften des Forschungszentrums Juelich. Reihe Schluesseltechnologien/Key Technologies v. 34",
"entry_date" : "2012-12-10",
"subject_list" : [ "72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS", "71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS", "ALGEBRA", "ALGORITHMS", "ANALYTICAL SOLUTION", "COMPUTER CODES", "DIRAC EQUATION", "ELECTRON-ION COLLISIONS", "FUNCTIONALS", "GREEN FUNCTION", "IMPURITIES", "LIPPMANN-SCHWINGER EQUATION", "MATRICES", "NUMERICAL SOLUTION", "PHASE SHIFT", "POLYNOMIALS", "POTENTIAL SCATTERING", "RECURSION RELATIONS", "RELATIVISTIC RANGE", "RUBIDIUM", "SCHROEDINGER EQUATION", "SERIES EXPANSION", "SPHERICAL HARMONICS", "TUNGSTEN", "WAVE FUNCTIONS" ],
"publisher_availability" : "Commercial reproduction prohibited; INIS; OSTI as DE21555650",
"rights" : "",
"announced_date" : "2012-05-31",
"type_qualifier" : "",
"has_fulltext" : true,
"coverage" : "",
"identifier" : "ISBN 978-3-89336-760-3; ISSN 1866-1807",
"creator" : "Kordt, Pascal",
"site_ownership_code" : "DEN",
"osti_id" : "21555650",
"resource_type" : "RPRT",
"format" : "Medium: ED; Size: 157 pages",
"journal_name" : "",
"citation_location" : "https://www.osti.gov/etdeweb/biblio/21555650",
"publication_year" : 2012,
"subject_list_commas" : "72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS, 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS, ALGEBRA, ALGORITHMS, ANALYTICAL SOLUTION, COMPUTER CODES, DIRAC EQUATION, ELECTRON-ION COLLISIONS, FUNCTIONALS, GREEN FUNCTION, IMPURITIES, LIPPMANN-SCHWINGER EQUATION, MATRICES, NUMERICAL SOLUTION, PHASE SHIFT, POLYNOMIALS, POTENTIAL SCATTERING, RECURSION RELATIONS, RELATIVISTIC RANGE, RUBIDIUM, SCHROEDINGER EQUATION, SERIES EXPANSION, SPHERICAL HARMONICS, TUNGSTEN, WAVE FUNCTIONS",
"publisher" : "",
"identifier_other" : "Other: ISBN 978-3-89336-760-3; ISSN 1866-1807; TRN: DE12F5358",
"publisher_research" : "Forschungszentrum Juelich GmbH (Germany). Peter Gruenberg Institut (PGI), Quantum Theory of Materials (PGI-1/IAS-1)",
"creators_list" : [ "Kordt, Pascal" ],
"doi" : ""
}