{"id":"https://openalex.org/W2166775848","doi":"https://doi.org/10.1137/080727956","title":"Rate of Convergence of the Configuration Interaction Model for the Helium Ground State","display_name":"Rate of Convergence of the Configuration Interaction Model for the Helium Ground State","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2166775848","doi":"https://doi.org/10.1137/080727956","mag":"2166775848"},"language":"en","primary_location":{"id":"doi:10.1137/080727956","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080727956","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.research.ed.ac.uk/en/publications/ac7885c2-9fa9-468d-80ae-2234df2bd89a","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071177310","display_name":"Benjamin D. Goddard","orcid":"https://orcid.org/0000-0002-8781-014X"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Benjamin D. Goddard","raw_affiliation_strings":["Mathematics Institute, University of Warwick, Coventry CV4, United Kingdom"],"affiliations":[{"raw_affiliation_string":"Mathematics Institute, University of Warwick, Coventry CV4, United Kingdom","institution_ids":["https://openalex.org/I39555362"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071177310"],"corresponding_institution_ids":["https://openalex.org/I39555362"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.21486013,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"41","issue":"1","first_page":"77","last_page":"116"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10425","display_name":"Cold Atom Physics and Bose-Einstein Condensates","score":0.9990000128746033,"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/T10425","display_name":"Cold Atom Physics and Bose-Einstein Condensates","score":0.9990000128746033,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T10523","display_name":"Atomic and Molecular Physics","score":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ground-state","display_name":"Ground state","score":0.7421008348464966},{"id":"https://openalex.org/keywords/wave-function","display_name":"Wave function","score":0.7100223302841187},{"id":"https://openalex.org/keywords/helium-atom","display_name":"Helium atom","score":0.6515570878982544},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6481168866157532},{"id":"https://openalex.org/keywords/angular-momentum","display_name":"Angular momentum","score":0.6076518297195435},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6014330983161926},{"id":"https://openalex.org/keywords/helium","display_name":"Helium","score":0.5723941326141357},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5670857429504395},{"id":"https://openalex.org/keywords/total-angular-momentum-quantum-number","display_name":"Total angular momentum quantum number","score":0.5300334095954895},{"id":"https://openalex.org/keywords/momentum","display_name":"Momentum (technical analysis)","score":0.47357258200645447},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.44900450110435486},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4464784562587738},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43160760402679443},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.39937645196914673},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3344533443450928}],"concepts":[{"id":"https://openalex.org/C69523127","wikidata":"https://www.wikidata.org/wiki/Q4480008","display_name":"Ground state","level":2,"score":0.7421008348464966},{"id":"https://openalex.org/C113603373","wikidata":"https://www.wikidata.org/wiki/Q2362761","display_name":"Wave function","level":2,"score":0.7100223302841187},{"id":"https://openalex.org/C2780846936","wikidata":"https://www.wikidata.org/wiki/Q3877353","display_name":"Helium atom","level":3,"score":0.6515570878982544},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6481168866157532},{"id":"https://openalex.org/C155675718","wikidata":"https://www.wikidata.org/wiki/Q161254","display_name":"Angular momentum","level":2,"score":0.6076518297195435},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6014330983161926},{"id":"https://openalex.org/C546029482","wikidata":"https://www.wikidata.org/wiki/Q560","display_name":"Helium","level":2,"score":0.5723941326141357},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5670857429504395},{"id":"https://openalex.org/C45193367","wikidata":"https://www.wikidata.org/wiki/Q1141095","display_name":"Total angular momentum quantum number","level":3,"score":0.5300334095954895},{"id":"https://openalex.org/C60718061","wikidata":"https://www.wikidata.org/wiki/Q1414747","display_name":"Momentum (technical analysis)","level":2,"score":0.47357258200645447},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.44900450110435486},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4464784562587738},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43160760402679443},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.39937645196914673},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3344533443450928},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/080727956","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080727956","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:pure.ed.ac.uk:openaire/ac7885c2-9fa9-468d-80ae-2234df2bd89a","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/ac7885c2-9fa9-468d-80ae-2234df2bd89a","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Goddard, B D 2009, 'Rate of convergence of the configuration interaction model for the helium ground state', SIAM Journal on Mathematical Analysis, vol. 41, no. 1, pp. 77-116. https://doi.org/10.1137/080727956","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.ed.ac.uk:publications/ac7885c2-9fa9-468d-80ae-2234df2bd89a","is_oa":false,"landing_page_url":"http://www.scopus.com/inward/record.url?partnerID=yv4JPVwI&eid=2-s2.0-70450202124&md5=e725fa86919e621e540ce5994bdd69c2","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/10459","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/10459","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"116","raw_type":"Journal Article"}],"best_oa_location":{"id":"pmh:oai:pure.ed.ac.uk:openaire/ac7885c2-9fa9-468d-80ae-2234df2bd89a","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/ac7885c2-9fa9-468d-80ae-2234df2bd89a","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Goddard, B D 2009, 'Rate of convergence of the configuration interaction model for the helium ground state', SIAM Journal on Mathematical Analysis, vol. 41, no. 1, pp. 77-116. https://doi.org/10.1137/080727956","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1647244435","https://openalex.org/W1964123532","https://openalex.org/W1977507434","https://openalex.org/W1980875578","https://openalex.org/W1983200535","https://openalex.org/W1996160600","https://openalex.org/W1998434228","https://openalex.org/W2006204334","https://openalex.org/W2010399932","https://openalex.org/W2029465995","https://openalex.org/W2050277563","https://openalex.org/W2060212575","https://openalex.org/W2068266385","https://openalex.org/W2069342338","https://openalex.org/W2070295485","https://openalex.org/W2078438762","https://openalex.org/W2092067295","https://openalex.org/W2117083307","https://openalex.org/W2151752974","https://openalex.org/W2154558448","https://openalex.org/W2159136592","https://openalex.org/W2159618521","https://openalex.org/W2801179766","https://openalex.org/W2883197357","https://openalex.org/W2998268161","https://openalex.org/W2999526552","https://openalex.org/W3101716684"],"related_works":["https://openalex.org/W2612155445","https://openalex.org/W2070927465","https://openalex.org/W2045992282","https://openalex.org/W2356869148","https://openalex.org/W2076057534","https://openalex.org/W2731614535","https://openalex.org/W2013205737","https://openalex.org/W2769690660","https://openalex.org/W4248922453","https://openalex.org/W1981196691"],"abstract_inverted_index":{"The":[0],"rate":[1],"of":[2,4,12,25,32,67],"convergence":[3],"a":[5],"CI":[6],"calculation":[7],"on":[8,22],"the":[9,13,23,26,45,54,68],"ground":[10],"state":[11],"helium":[14],"atom":[15],"is":[16,60],"rigorously":[17],"derived":[18],"under":[19],"suitable":[20],"assumptions":[21],"regularity":[24],"exact":[27,69],"wavefunction.":[28,70],"For":[29],"bases":[30],"consisting":[31],"all":[33],"partial":[34],"waves":[35],"with":[36],"angular":[37],"momentum":[38],"less":[39],"than":[40],"or":[41],"equal":[42],"to":[43,52],"L,":[44],"large":[46],"L":[47],"asymptotic":[48],"energies":[49],"are":[50],"found":[51],"obey":[53],"well-known":[55],"formula":[56],"$E_L-E=CL^{-3}+o(L^{-3})$,":[57],"where":[58],"C":[59],"an":[61],"explicit":[62],"constant":[63],"defined":[64],"in":[65],"terms":[66]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-03-04T09:10:02.777135","created_date":"2025-10-10T00:00:00"}
