{"id":"https://openalex.org/W4309124231","doi":"https://doi.org/10.48550/arxiv.1108.3893","title":"Parabolic Sturmians approach to the three-body continuum Coulomb problem","display_name":"Parabolic Sturmians approach to the three-body continuum Coulomb problem","publication_year":2011,"publication_date":"2011-08-19","ids":{"openalex":"https://openalex.org/W4309124231","doi":"https://doi.org/10.48550/arxiv.1108.3893"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1108.3893","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1108.3893","pdf_url":"https://arxiv.org/pdf/1108.3893","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1108.3893","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108110187","display_name":"Sergey A. Zaytsev","orcid":"https://orcid.org/0000-0003-3771-3541","observed_orcids":["https://orcid.org/0000-0003-3771-3541"]},"institutions":[{"id":"https://openalex.org/I27238560","display_name":"Pacific National University","ror":"https://ror.org/03cjece29","country_code":"RU","type":"education","lineage":["https://openalex.org/I27238560"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Zaytsev, S. A.","raw_affiliation_strings":["Pacific National University , Khabarovsk , 680035 , Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Pacific National University , Khabarovsk , 680035 , Russia","institution_ids":["https://openalex.org/I27238560"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017477054","display_name":"Yu. V. Popov","orcid":"https://orcid.org/0000-0002-0216-5998","observed_orcids":["https://orcid.org/0000-0002-0216-5998"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Popov, Yu. V.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5112581799","display_name":"B. Piraux","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]},{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Piraux, B.","raw_affiliation_strings":["Institute of Condensed Matter and Nanosciences , Universit\u00e9 catholique de Louvain ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Condensed Matter and Nanosciences , Universit\u00e9 catholique de Louvain ,","institution_ids":["https://openalex.org/I95674353","https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10523","display_name":"Atomic and Molecular Physics","score":0.9771000146865845,"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":0.9771000146865845,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.010200000368058681,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10093","display_name":"Nuclear physics research studies","score":0.0024999999441206455,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"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/lippmann-schwinger-equation","display_name":"Lippmann-Schwinger equation","score":0.9800000190734863},{"id":"https://openalex.org/keywords/green-s-function","display_name":"Green's function","score":0.847000002861023},{"id":"https://openalex.org/keywords/integral-equations","display_name":"integral equations","score":0.44699999690055847},{"id":"https://openalex.org/keywords/basis-set-convergence","display_name":"basis set convergence","score":0.6330000162124634}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6388227343559265},{"id":"https://openalex.org/C9342510","wikidata":"https://www.wikidata.org/wiki/Q25406","display_name":"Coulomb","level":3,"score":0.6111825704574585},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.597873866558075},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.5474269986152649},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.5408244132995605},{"id":"https://openalex.org/C58570533","wikidata":"https://www.wikidata.org/wiki/Q55451","display_name":"Electric potential","level":3,"score":0.5076891183853149},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5060815215110779},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.47889891266822815},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4610776901245117},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4511685371398926},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.38926810026168823},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3727002739906311},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.2828194499015808},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1659693717956543},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15675348043441772},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","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},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:1108.3893","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1108.3893","pdf_url":"https://arxiv.org/pdf/1108.3893","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.1108.3893","doi":"https://doi.org/10.48550/arxiv.1108.3893","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1108.3893","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1108.3893","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1108.3893","pdf_url":"https://arxiv.org/pdf/1108.3893","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4309124231.pdf","grobid_xml":"https://content.openalex.org/works/W4309124231.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4308833284"],"related_works":["https://openalex.org/W2141294911","https://openalex.org/W2162159901","https://openalex.org/W6891872997","https://openalex.org/W2030237447","https://openalex.org/W2009852433","https://openalex.org/W2053584334","https://openalex.org/W43703188","https://openalex.org/W7095236949","https://openalex.org/W2013089344","https://openalex.org/W7099626681"],"abstract_inverted_index":{"The":[0],"three-body":[1],"continuum":[2],"Coulomb":[3],"problem":[4],"is":[5,70,92,103],"treated":[6],"in":[7,18],"terms":[8],"of":[9,21,34,50,58,80,85,89],"the":[10,19,27,31,35,39,44,47,51,61,65,75,81,86,90,95,101],"generalized":[11],"parabolic":[12,76],"coordinates.":[13],"Approximate":[14],"solutions":[15],"are":[16],"expressed":[17],"form":[20],"a":[22,56],"Lippmann-Schwinger":[23],"type":[24],"equation,":[25],"where":[26],"Green's":[28],"function":[29],"includes":[30],"leading":[32],"term":[33],"kinetic":[36,52],"energy":[37,53],"and":[38],"total":[40],"potential":[41,45,102],"energy,":[42],"whereas":[43],"contains":[46],"non-orthogonal":[48],"part":[49],"operator.":[54],"As":[55],"test":[57],"this":[59],"approach,":[60],"integral":[62],"equation":[63],"for":[64],"$(e^-,\\,":[66],"e^-,\\,":[67],"{{He}^{++}})$":[68],"system":[69],"solved":[71],"numerically":[72],"by":[73],"using":[74],"Sturmian":[77],"basis":[78,96],"representation":[79],"(approximate)":[82],"potential.":[83],"Convergence":[84],"expansion":[87],"coefficients":[88],"solution":[91],"obtained":[93],"as":[94],"set":[97],"used":[98],"to":[99],"describe":[100],"enlarged.":[104]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2022-11-23T00:00:00"}