{"id":"https://openalex.org/W2016596574","doi":"https://doi.org/10.1103/physrev.137.a27","title":"Self-Consistent-Field Dirac-Slater Wave Functions for Atoms and Ions. I. Comparison with Previous Calculations","display_name":"Self-Consistent-Field Dirac-Slater Wave Functions for Atoms and Ions. I. Comparison with Previous Calculations","publication_year":1965,"publication_date":"1965-01-04","ids":{"openalex":"https://openalex.org/W2016596574","doi":"https://doi.org/10.1103/physrev.137.a27","mag":"2016596574"},"language":"en","primary_location":{"id":"doi:10.1103/physrev.137.a27","doi":"https://doi.org/10.1103/physrev.137.a27","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrev.137.a27","pdf_url":null,"source":{"id":"https://openalex.org/S54862371","display_name":"Physical Review","issn_l":"0031-899X","issn":["0031-899X","1536-6065"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111623074","display_name":"David A. Liberman","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. Liberman","raw_affiliation_strings":["University of California, Los Alamos Scientific Laboratory, Los Alamos, New Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Los Alamos Scientific Laboratory, Los Alamos, New Mexico","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054558021","display_name":"James T. Waber","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. T. Waber","raw_affiliation_strings":["University of California, Los Alamos Scientific Laboratory, Los Alamos, New Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Los Alamos Scientific Laboratory, Los Alamos, New Mexico","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087054393","display_name":"DON T. CROMER","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Don T. Cromer","raw_affiliation_strings":["University of California, Los Alamos Scientific Laboratory, Los Alamos, New Mexico"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Los Alamos Scientific Laboratory, Los Alamos, New Mexico","institution_ids":["https://openalex.org/I1343871089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1343871089"],"apc_list":null,"apc_paid":null,"fwci":20.5828,"has_fulltext":false,"cited_by_count":500,"citation_normalized_percentile":{"value":0.99786943,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":99},"biblio":{"volume":"137","issue":"1A","first_page":"A27","last_page":"A34"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10523","display_name":"Atomic and Molecular Physics","score":0.6240000128746033,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10523","display_name":"Atomic and Molecular Physics","score":0.6240000128746033,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10002","display_name":"Advanced Chemical Physics Studies","score":0.3334999978542328,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11733","display_name":"X-ray Spectroscopy and Fluorescence Analysis","score":0.030300000682473183,"subfield":{"id":"https://openalex.org/subfields/3108","display_name":"Radiation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/self-consistent-field","display_name":"self-consistent field","score":0.906000018119812},{"id":"https://openalex.org/keywords/dirac-equation","display_name":"Dirac equation","score":0.8960000276565552},{"id":"https://openalex.org/keywords/relativistic-atomic-structure","display_name":"relativistic atomic structure","score":0.8090000152587891},{"id":"https://openalex.org/keywords/x-ray-spectroscopy","display_name":"X-ray spectroscopy","score":0.47099998593330383},{"id":"https://openalex.org/keywords/energy-eigenvalues","display_name":"energy eigenvalues","score":0.7450000047683716},{"id":"https://openalex.org/keywords/electronic-energy-levels","display_name":"electronic energy levels","score":0.7570000290870667},{"id":"https://openalex.org/keywords/heavy-atoms","display_name":"heavy atoms","score":0.546999990940094},{"id":"https://openalex.org/keywords/mercury","display_name":"mercury","score":0.628000020980835},{"id":"https://openalex.org/keywords/uranium","display_name":"uranium","score":0.9279999732971191},{"id":"https://openalex.org/keywords/copper","display_name":"copper","score":0.6140000224113464},{"id":"https://openalex.org/keywords/iron","display_name":"iron","score":0.972000002861023},{"id":"https://openalex.org/keywords/tungsten","display_name":"tungsten","score":0.996999979019165},{"id":"https://openalex.org/keywords/platinum","display_name":"platinum","score":0.9990000128746033}],"concepts":[{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.7457825541496277},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6946848630905151},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6932079195976257},{"id":"https://openalex.org/C113603373","wikidata":"https://www.wikidata.org/wiki/Q2362761","display_name":"Wave function","level":2,"score":0.6335493326187134},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.6313219666481018},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.543286144733429},{"id":"https://openalex.org/C145148216","wikidata":"https://www.wikidata.org/wiki/Q36496","display_name":"Ion","level":2,"score":0.5329649448394775},{"id":"https://openalex.org/C184779094","wikidata":"https://www.wikidata.org/wiki/Q26383","display_name":"Atomic physics","level":1,"score":0.5209664106369019},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.5117873549461365},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.39710018038749695},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3544577360153198},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.08306652307510376},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C186453547","wikidata":"https://www.wikidata.org/wiki/Q2126","display_name":"Neutrino","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1103/physrev.137.a27","doi":"https://doi.org/10.1103/physrev.137.a27","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrev.137.a27","pdf_url":null,"source":{"id":"https://openalex.org/S54862371","display_name":"Physical Review","issn_l":"0031-899X","issn":["0031-899X","1536-6065"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1610184775","https://openalex.org/W1961355503","https://openalex.org/W1965223497","https://openalex.org/W1967472649","https://openalex.org/W1991983989","https://openalex.org/W2001611328","https://openalex.org/W2008158244","https://openalex.org/W2011351588","https://openalex.org/W2020461665","https://openalex.org/W2028380131","https://openalex.org/W2030288387","https://openalex.org/W2031897236","https://openalex.org/W2038167210","https://openalex.org/W2038487951","https://openalex.org/W2038814839","https://openalex.org/W2047009615","https://openalex.org/W2059849350","https://openalex.org/W2072197588","https://openalex.org/W2077394341","https://openalex.org/W2083422855","https://openalex.org/W2086628812","https://openalex.org/W2094732937","https://openalex.org/W2123778996","https://openalex.org/W2326115069","https://openalex.org/W2619609791","https://openalex.org/W4230866049"],"related_works":["https://openalex.org/W1992526264","https://openalex.org/W2998613716","https://openalex.org/W2169400534","https://openalex.org/W7113415615","https://openalex.org/W2052921398","https://openalex.org/W2020461665","https://openalex.org/W2047009615","https://openalex.org/W2088029850","https://openalex.org/W2346782175","https://openalex.org/W2318074429"],"abstract_inverted_index":{"Self-consistent-field":[0],"solutions":[1,19],"have":[2,71],"been":[3,72],"obtained":[4,31,93],"of":[5,26,36],"the":[6,15,21,27,33,37,59,101],"two":[7],"first-order":[8],"linear":[9],"differential":[10],"equations":[11],"that":[12,92],"result":[13],"from":[14,67],"Dirac":[16],"equation.":[17],"These":[18],"for":[20,43,74,82],"major":[22],"and":[23,40,62,78,80,84],"minor":[24],"components":[25],"($\\mathrm{nlj}$)":[28],"eigenfunctions":[29],"were":[30],"by":[32,52],"relativistic":[34],"equivalent":[35],"method":[38],"Herman":[39],"Skillman":[41],"used":[42],"atomic":[44],"structure":[45],"calculations":[46,98],"in":[47,94],"which":[48],"exchange":[49],"was":[50,88],"handled":[51],"Slater's":[53],"${\\ensuremath{\\rho}}^{\\frac{1}{3}}$":[54],"method.":[55],"Detailed":[56],"comparisons":[57],"between":[58],"energy":[60,64],"eigenvalues":[61],"electronic":[63],"levels":[65],"determined":[66],"x-ray":[68],"spectroscopic":[69],"data":[70],"made":[73],"${\\mathrm{Cu}}^{+1}$,":[75],"Fe,":[76],"W,":[77],"Pt,":[79],"particularly":[81],"Hg":[83],"U.":[85],"The":[86],"agreement":[87],"very":[89],"good---better":[90],"than":[91],"any":[95],"previous":[96],"self-consistent-field":[97],"available":[99],"to":[100],"authors.":[102]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":14}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
