{"id":"https://openalex.org/W2005463955","doi":"https://doi.org/10.1103/physreva.15.1","title":"Compact and accurate integral-transform wave functions. I. The 1S1 state of the helium-like ions from H\u2212 through Mg10+","display_name":"Compact and accurate integral-transform wave functions. I. The 1S1 state of the helium-like ions from H\u2212 through Mg10+","publication_year":1977,"publication_date":"1977-01-01","ids":{"openalex":"https://openalex.org/W2005463955","doi":"https://doi.org/10.1103/physreva.15.1","mag":"2005463955"},"language":"lv","primary_location":{"id":"doi:10.1103/physreva.15.1","doi":"https://doi.org/10.1103/physreva.15.1","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreva.15.1","pdf_url":null,"source":{"id":"https://openalex.org/S164566984","display_name":"Physical Review A","issn_l":"0556-2791","issn":["0556-2791","1050-2947","1094-1622","1538-4446","2469-9926","2469-9934","2469-9942"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-1","norway-2","poland-100","poland-70","russia-white-list-1","vabb-shw"],"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 A","raw_type":"journal-article"},"volume":null,"type":"article","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/A5051630394","display_name":"Ajit J. Thakkar","orcid":"https://orcid.org/0000-0002-6611-1577","observed_orcids":["https://orcid.org/0000-0002-6611-1577"]},"institutions":[{"id":"https://openalex.org/I204722609","display_name":"Queen's University","ror":"https://ror.org/02y72wh86","country_code":"CA","type":"education","lineage":["https://openalex.org/I204722609"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["CA","DE"],"is_corresponding":false,"raw_author_name":"Ajit J. Thakkar","raw_affiliation_strings":["Department of Chemistry, Queen's University, Kingston, Ontario K7L 3N6, Canada and Lehrstuhl f\u00fcr Theoretische Chemie, Technische Universit\u00e4t, M\u00fcnchen, Federal Republic of Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemistry, Queen's University, Kingston, Ontario K7L 3N6, Canada and Lehrstuhl f\u00fcr Theoretische Chemie, Technische Universit\u00e4t, M\u00fcnchen, Federal Republic of Germany","institution_ids":["https://openalex.org/I204722609","https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110023077","display_name":"Vedene H. Smith","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I204722609","display_name":"Queen's University","ror":"https://ror.org/02y72wh86","country_code":"CA","type":"education","lineage":["https://openalex.org/I204722609"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["CA","DE"],"is_corresponding":false,"raw_author_name":"Vedene H. Smith","raw_affiliation_strings":["Department of Chemistry, Queen's University, Kingston, Ontario K7L 3N6, Canada and Lehrstuhl f\u00fcr Theoretische Chemie, Technische Universit\u00e4t, M\u00fcnchen, Federal Republic of Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemistry, Queen's University, Kingston, Ontario K7L 3N6, Canada and Lehrstuhl f\u00fcr Theoretische Chemie, Technische Universit\u00e4t, M\u00fcnchen, Federal Republic of Germany","institution_ids":["https://openalex.org/I204722609","https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2675,"currency":"USD","value_usd":2675},"apc_paid":null,"fwci":6.2219,"has_fulltext":false,"cited_by_count":280,"citation_normalized_percentile":{"value":0.97542735,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"15","issue":"1","first_page":"1","last_page":"15"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10523","display_name":"Atomic and Molecular Physics","score":0.9804999828338623,"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":0.9804999828338623,"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":0.013100000098347664,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.0006000000284984708,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/helium-like-ions","display_name":"helium-like ions","score":0.9160000085830688},{"id":"https://openalex.org/keywords/1s-ground-state","display_name":"1s ground state","score":0.7260000109672546},{"id":"https://openalex.org/keywords/variational-wavefunctions","display_name":"variational wave functions","score":0.8420000076293945},{"id":"https://openalex.org/keywords/parallelotopes","display_name":"parallelotopes","score":0.3449999988079071},{"id":"https://openalex.org/keywords/variational-optimization","display_name":"variational optimization","score":0.5009999871253967},{"id":"https://openalex.org/keywords/helium-atom","display_name":"helium atom","score":0.367000013589859},{"id":"https://openalex.org/keywords/expectation-values","display_name":"expectation values","score":0.453000009059906},{"id":"https://openalex.org/keywords/electron-correlation","display_name":"electron correlation","score":0.33899998664855957},{"id":"https://openalex.org/keywords/many-electron-atoms","display_name":"many-electron atoms","score":0.4390000104904175},{"id":"https://openalex.org/keywords/ionization-potential","display_name":"ionization potential","score":0.32499998807907104},{"id":"https://openalex.org/keywords/rydberg-states","display_name":"Rydberg states","score":0.4099999964237213}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6857143640518188},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.5791440010070801},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5238770842552185},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4589788019657135},{"id":"https://openalex.org/C113603373","wikidata":"https://www.wikidata.org/wiki/Q2362761","display_name":"Wave function","level":2,"score":0.452812135219574},{"id":"https://openalex.org/C130979935","wikidata":"https://www.wikidata.org/wiki/Q568954","display_name":"Ansatz","level":2,"score":0.42737406492233276},{"id":"https://openalex.org/C139287275","wikidata":"https://www.wikidata.org/wiki/Q869891","display_name":"Polarizability","level":3,"score":0.4114505648612976},{"id":"https://openalex.org/C184779094","wikidata":"https://www.wikidata.org/wiki/Q26383","display_name":"Atomic physics","level":1,"score":0.3476725220680237},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.33103907108306885},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.23431268334388733},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.13627660274505615},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C32909587","wikidata":"https://www.wikidata.org/wiki/Q11369","display_name":"Molecule","level":2,"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":1,"locations":[{"id":"doi:10.1103/physreva.15.1","doi":"https://doi.org/10.1103/physreva.15.1","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreva.15.1","pdf_url":null,"source":{"id":"https://openalex.org/S164566984","display_name":"Physical Review A","issn_l":"0556-2791","issn":["0556-2791","1050-2947","1094-1622","1538-4446","2469-9926","2469-9934","2469-9942"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-2","ki-jl-1","norway-2","poland-100","poland-70","russia-white-list-1","vabb-shw"],"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 A","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":116,"referenced_works":["https://openalex.org/W571946218","https://openalex.org/W775073375","https://openalex.org/W1557786636","https://openalex.org/W1965352424","https://openalex.org/W1965892317","https://openalex.org/W1966364339","https://openalex.org/W1966733726","https://openalex.org/W1966740451","https://openalex.org/W1967319789","https://openalex.org/W1970474714","https://openalex.org/W1971054911","https://openalex.org/W1971422892","https://openalex.org/W1973693973","https://openalex.org/W1973732379","https://openalex.org/W1973799503","https://openalex.org/W1977482997","https://openalex.org/W1978588083","https://openalex.org/W1980585959","https://openalex.org/W1980840110","https://openalex.org/W1985583119","https://openalex.org/W1985841451","https://openalex.org/W1986751761","https://openalex.org/W1991952201","https://openalex.org/W1993018050","https://openalex.org/W1993438627","https://openalex.org/W1996085707","https://openalex.org/W1996108736","https://openalex.org/W1996290894","https://openalex.org/W1996305478","https://openalex.org/W1997823125","https://openalex.org/W1998039258","https://openalex.org/W1998399936","https://openalex.org/W1998406195","https://openalex.org/W1998434228","https://openalex.org/W2000586748","https://openalex.org/W2002351104","https://openalex.org/W2003380405","https://openalex.org/W2007333472","https://openalex.org/W2013811797","https://openalex.org/W2014208555","https://openalex.org/W2014209007","https://openalex.org/W2016184293","https://openalex.org/W2019938967","https://openalex.org/W2022308493","https://openalex.org/W2022443098","https://openalex.org/W2023141555","https://openalex.org/W2025628760","https://openalex.org/W2028250558","https://openalex.org/W2028892216","https://openalex.org/W2031004104","https://openalex.org/W2031130806","https://openalex.org/W2031261774","https://openalex.org/W2032134332","https://openalex.org/W2033278298","https://openalex.org/W2033580876","https://openalex.org/W2033824900","https://openalex.org/W2034046177","https://openalex.org/W2035096574","https://openalex.org/W2037274898","https://openalex.org/W2038088933","https://openalex.org/W2039559980","https://openalex.org/W2039927037","https://openalex.org/W2041394212","https://openalex.org/W2046038395","https://openalex.org/W2049269680","https://openalex.org/W2049482190","https://openalex.org/W2049744297","https://openalex.org/W2051203581","https://openalex.org/W2058562581","https://openalex.org/W2059232683","https://openalex.org/W2059437767","https://openalex.org/W2059457073","https://openalex.org/W2060380510","https://openalex.org/W2060641684","https://openalex.org/W2062593471","https://openalex.org/W2064121968","https://openalex.org/W2065880636","https://openalex.org/W2067600085","https://openalex.org/W2068452281","https://openalex.org/W2068674312","https://openalex.org/W2072225793","https://openalex.org/W2078438762","https://openalex.org/W2080476863","https://openalex.org/W2080555715","https://openalex.org/W2080567135","https://openalex.org/W2081701222","https://openalex.org/W2083060096","https://openalex.org/W2086789697","https://openalex.org/W2087296407","https://openalex.org/W2093173804","https://openalex.org/W2093647390","https://openalex.org/W2095647612","https://openalex.org/W2105645632","https://openalex.org/W2113404447","https://openalex.org/W2114013702","https://openalex.org/W2117083307","https://openalex.org/W2119633983","https://openalex.org/W2124741347","https://openalex.org/W2136466805","https://openalex.org/W2167887176","https://openalex.org/W2244501201","https://openalex.org/W2313621700","https://openalex.org/W2316530292","https://openalex.org/W2318653345","https://openalex.org/W2326115069","https://openalex.org/W2327005107","https://openalex.org/W2581611364","https://openalex.org/W3047627558","https://openalex.org/W3092650793","https://openalex.org/W3112012517","https://openalex.org/W4241663002","https://openalex.org/W4249091683","https://openalex.org/W4249709349","https://openalex.org/W4252219792","https://openalex.org/W4256068702","https://openalex.org/W4400449507"],"related_works":["https://openalex.org/W2244501201","https://openalex.org/W4220788560","https://openalex.org/W4205282230","https://openalex.org/W7096847966","https://openalex.org/W4210284296","https://openalex.org/W3044272944","https://openalex.org/W2151769273","https://openalex.org/W4226429129","https://openalex.org/W1975510534","https://openalex.org/W3108097462"],"abstract_inverted_index":{"Accurate":[0],"and":[1,40,45,56,117,128,132,153,166,183,204],"compact":[2,206],"integral-transform":[3],"wave":[4,109],"functions":[5,110,192,197,210],"are":[6,33,47,130,163,171,179,198,230],"constructed":[7],"for":[8,60,74,173,181],"the":[9,13,25,31,37,41,51,75,88,105,108,135,157,174,186,213,216,226],"$1^{1}S$":[10],"state":[11],"of":[12,24,53,71,81,91,97,107,113,160,188,191,218],"helium-like":[14],"ions":[15],"from":[16,145],"${\\mathrm{H}}^{\\ensuremath{-}}$":[17,182],"through":[18],"${\\mathrm{Mg}}^{10+}$.":[19],"The":[20,139,196],"variational":[21],"ansatz":[22],"is":[23,143],"form":[26,187],"$\\ensuremath{\\Psi}({r}_{1},":[27],"{r}_{2},":[28],"{r}_{12})={(4\\ensuremath{\\pi})}^{\\ensuremath{-}1}{\\ensuremath{\\Sigma}}_{k=1}^{N}{c}_{k}(1+{P}_{12})\\mathrm{exp}(\\ensuremath{-}{\\ensuremath{\\alpha}}_{k}{r}_{1}\\ensuremath{-}{\\ensuremath{\\beta}}_{k}{r}_{2}\\ensuremath{-}{\\ensuremath{\\gamma}}_{k}{r}_{12})$":[29],"where":[30],"${c}_{k}$":[32],"found":[34,199],"by":[35],"solving":[36],"secular":[38],"equation":[39],"exponents":[42],"${\\ensuremath{\\alpha}}_{k}$,":[43],"${\\ensuremath{\\beta}}_{k}$,":[44],"${\\ensuremath{\\gamma}}_{k}$":[46],"chosen":[48],"to":[49,103,150,200,225],"be":[50,201],"abscissas":[52],"Monte":[54],"Carlo":[55],"number-theoretic":[57],"quadrature":[58],"formulas":[59],"a":[61,111,146,189],"variationally":[62],"optimized":[63],"parallelotope":[64],"in":[65,185,212],"$\\ensuremath{\\alpha}\\ensuremath{-}\\ensuremath{\\beta}\\ensuremath{-}\\ensuremath{\\gamma}$":[66],"space.":[67],"A":[68],"66-term":[69],"function":[70,90],"this":[72,161],"type":[73],"helium":[76],"atom":[77],"yields":[78,94],"an":[79,95],"energy":[80,96],"-2.903":[82,98],"724363":[83],"a.u.":[84,100],"as":[85],"compared":[86,133],"with":[87,119,134,193,215],"1078-term":[89],"Pekeris":[92],"which":[93],"724376":[99],"In":[101],"order":[102],"test":[104],"accuracy":[106,159],"number":[112],"properties":[114],"including":[115],"$\u3008{r}^{n}\u3009$":[116],"$\u3008{r}_{12}^{n}\u3009$":[118],"$n=\\ensuremath{-}2,":[120],"\\ensuremath{-}1,":[121],"1,":[122],"\\dots{},":[123],"4$,":[124],"$\u3008{\\stackrel{\\ensuremath{\\rightarrow}}{\\mathrm{r}}}_{1}\\ifmmode\\cdot\\else\\textperiodcentered\\fi{}{\\stackrel{\\ensuremath{\\rightarrow}}{\\mathrm{r}}}_{2}\u3009$,":[125],"$\u3008{cos\\ensuremath{\\theta}}_{12}\u3009$,":[126],"$\u3008\\ensuremath{\\delta}({\\stackrel{\\ensuremath{\\rightarrow}}{\\mathrm{r}}}_{1})\u3009$,":[127],"$\u3008\\ensuremath{\\delta}({\\stackrel{\\ensuremath{\\rightarrow}}{\\mathrm{r}}}_{12})\u3009$":[129],"computed":[131,144],"best":[136],"available":[137,211],"results.":[138],"electric":[140],"dipole":[141],"polarizability":[142],"simple":[147],"formula":[148,162],"due":[149],"Thorhallsson,":[151],"Fisk,":[152],"Fraga.":[154],"Comments":[155],"on":[156],"limiting":[158],"made.":[164],"Electron-nuclear":[165],"electron-electron":[167],"cusp":[168],"condition":[169],"tests":[170],"made":[172],"functions.":[175],"Detailed":[176],"convergence":[177],"studies":[178],"presented":[180],"He":[184],"sequence":[190],"increasing":[194],"$N$.":[195],"rather":[202],"accurate":[203],"more":[205],"than":[207],"any":[208],"other":[209],"literature":[214],"exception":[217],"those":[219],"containing":[220],"logarithmic":[221],"terms.":[222],"Possible":[223],"refinements":[224],"basis":[227],"set":[228],"used":[229],"discussed.":[231]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-10-20T09:52:01.089006","created_date":"2016-06-24T00:00:00"}
