{"id":"https://openalex.org/W2043906925","doi":"https://doi.org/10.1103/physreve.75.056402","title":"Variational theory of average-atom and superconfigurations in quantum plasmas","display_name":"Variational theory of average-atom and superconfigurations in quantum plasmas","publication_year":2007,"publication_date":"2007-05-08","ids":{"openalex":"https://openalex.org/W2043906925","doi":"https://doi.org/10.1103/physreve.75.056402","mag":"2043906925","pmid":"https://pubmed.ncbi.nlm.nih.gov/17677177"},"language":"en","primary_location":{"id":"doi:10.1103/physreve.75.056402","doi":"https://doi.org/10.1103/physreve.75.056402","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreve.75.056402","pdf_url":null,"source":{"id":"https://openalex.org/S35412551","display_name":"Physical Review E","issn_l":"1539-3755","issn":["1539-3755","1550-2376"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","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 E","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","pubmed"],"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/A5042765842","display_name":"Thomas Blenski","orcid":"https://orcid.org/0000-0002-6855-7716","observed_orcids":["https://orcid.org/0000-0002-6855-7716"]},"institutions":[{"id":"https://openalex.org/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131"]},{"id":"https://openalex.org/I2801360556","display_name":"CEA Paris-Saclay - Etablissement de Saclay","ror":"https://ror.org/01fv25t22","country_code":"FR","type":"facility","lineage":["https://openalex.org/I2738703131","https://openalex.org/I277688954","https://openalex.org/I2801360556","https://openalex.org/I4210128565"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"T. Blenski","raw_affiliation_strings":["CEA, Centre d'Etudes de Saclay, DSM/DRECAM/SPAM, B\u00e2timent 522, F91191 Gif-sur-Yvette Cedex, France. thomas.blenski@cea.fr","CEA, Centre d\u2019Etudes de Saclay, DSM/DRECAM/SPAM, B\u00e2timent 522, F91191 Gif-sur-Yvette Cedex, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CEA, Centre d'Etudes de Saclay, DSM/DRECAM/SPAM, B\u00e2timent 522, F91191 Gif-sur-Yvette Cedex, France. thomas.blenski@cea.fr","institution_ids":["https://openalex.org/I2738703131","https://openalex.org/I2801360556"]},{"raw_affiliation_string":"CEA, Centre d\u2019Etudes de Saclay, DSM/DRECAM/SPAM, B\u00e2timent 522, F91191 Gif-sur-Yvette Cedex, France","institution_ids":["https://openalex.org/I2738703131","https://openalex.org/I2801360556"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024869229","display_name":"B. Cichocki","orcid":"https://orcid.org/0000-0003-3059-4172","observed_orcids":["https://orcid.org/0000-0003-3059-4172"]},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"B. Cichocki","raw_affiliation_strings":["Institute of Theoretical Physics, Warsaw University, Hoza 69, 00-681 Warsaw, Poland","Institute of Theoretical Physics, Warsaw University, #N#Hoza 69, 00-681 Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Theoretical Physics, Warsaw University, Hoza 69, 00-681 Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]},{"raw_affiliation_string":"Institute of Theoretical Physics, Warsaw University, #N#Hoza 69, 00-681 Warsaw, Poland","institution_ids":["https://openalex.org/I4654613"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6302,"has_fulltext":false,"cited_by_count":62,"citation_normalized_percentile":{"value":0.82685288,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"75","issue":"5","first_page":"056402","last_page":"056402"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10523","display_name":"Atomic and Molecular Physics","score":0.4318999946117401,"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":0.4318999946117401,"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/T11603","display_name":"Dust and Plasma Wave Phenomena","score":0.3093000054359436,"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/T10384","display_name":"Laser-Plasma Interactions and Diagnostics","score":0.07329999655485153,"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/quantum-plasma","display_name":"quantum plasma","score":0.8220000267028809},{"id":"https://openalex.org/keywords/average-atom-model","display_name":"average atom model","score":0.5910000205039978},{"id":"https://openalex.org/keywords/variational-theory","display_name":"variational theory","score":0.671999990940094},{"id":"https://openalex.org/keywords/thermodynamic-potential","display_name":"thermodynamic potential","score":0.7279999852180481},{"id":"https://openalex.org/keywords/cluster-expansion","display_name":"cluster expansion","score":0.7379999756813049},{"id":"https://openalex.org/keywords/wigner-seitz-cell","display_name":"Wigner-Seitz cell","score":0.7269999980926514},{"id":"https://openalex.org/keywords/self-consistent-field-equations","display_name":"self-consistent field equations","score":0.7149999737739563},{"id":"https://openalex.org/keywords/virial-theorem","display_name":"virial theorem","score":0.7319999933242798},{"id":"https://openalex.org/keywords/ionization-model","display_name":"ionization model","score":0.578000009059906},{"id":"https://openalex.org/keywords/opacity","display_name":"opacity","score":0.3630000054836273},{"id":"https://openalex.org/keywords/equation-of-state","display_name":"equation of state","score":0.9890000224113464}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.613425612449646},{"id":"https://openalex.org/C189549420","wikidata":"https://www.wikidata.org/wiki/Q620602","display_name":"Virial theorem","level":3,"score":0.5790296792984009},{"id":"https://openalex.org/C145148216","wikidata":"https://www.wikidata.org/wiki/Q36496","display_name":"Ion","level":2,"score":0.5693029761314392},{"id":"https://openalex.org/C184779094","wikidata":"https://www.wikidata.org/wiki/Q26383","display_name":"Atomic physics","level":1,"score":0.5526778697967529},{"id":"https://openalex.org/C64618476","wikidata":"https://www.wikidata.org/wiki/Q164296","display_name":"Variational method","level":2,"score":0.5395779609680176},{"id":"https://openalex.org/C82706917","wikidata":"https://www.wikidata.org/wiki/Q10251","display_name":"Plasma","level":2,"score":0.5149512887001038},{"id":"https://openalex.org/C58312451","wikidata":"https://www.wikidata.org/wiki/Q4817200","display_name":"Atom (system on chip)","level":2,"score":0.5088961124420166},{"id":"https://openalex.org/C24572877","wikidata":"https://www.wikidata.org/wiki/Q900431","display_name":"Thomas\u2013Fermi model","level":3,"score":0.4979536533355713},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.4888972342014313},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.476239949464798},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.46495378017425537},{"id":"https://openalex.org/C53810900","wikidata":"https://www.wikidata.org/wiki/Q214967","display_name":"Equation of state","level":2,"score":0.43788665533065796},{"id":"https://openalex.org/C198291218","wikidata":"https://www.wikidata.org/wiki/Q190382","display_name":"Ionization","level":3,"score":0.4275176227092743},{"id":"https://openalex.org/C2780846936","wikidata":"https://www.wikidata.org/wiki/Q3877353","display_name":"Helium atom","level":3,"score":0.42405232787132263},{"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/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.0},{"id":"https://openalex.org/C98444146","wikidata":"https://www.wikidata.org/wiki/Q318","display_name":"Galaxy","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1103/physreve.75.056402","doi":"https://doi.org/10.1103/physreve.75.056402","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physreve.75.056402","pdf_url":null,"source":{"id":"https://openalex.org/S35412551","display_name":"Physical Review E","issn_l":"1539-3755","issn":["1539-3755","1550-2376"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","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 E","raw_type":"journal-article"},{"id":"pmid:17677177","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/17677177","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical review. E, Statistical, nonlinear, and soft matter physics","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":23,"referenced_works":["https://openalex.org/W1970088499","https://openalex.org/W1980778096","https://openalex.org/W1988783340","https://openalex.org/W1990433560","https://openalex.org/W1991835166","https://openalex.org/W1992904159","https://openalex.org/W2008957178","https://openalex.org/W2027594093","https://openalex.org/W2034027341","https://openalex.org/W2044583466","https://openalex.org/W2050130677","https://openalex.org/W2050729144","https://openalex.org/W2051094029","https://openalex.org/W2051348100","https://openalex.org/W2059872777","https://openalex.org/W2068929730","https://openalex.org/W2076483242","https://openalex.org/W2077896657","https://openalex.org/W2082649174","https://openalex.org/W2127761960","https://openalex.org/W2131628398","https://openalex.org/W2139387316","https://openalex.org/W2947596026"],"related_works":["https://openalex.org/W2042963183","https://openalex.org/W4361283555","https://openalex.org/W2080640884","https://openalex.org/W2328003372","https://openalex.org/W3102107423","https://openalex.org/W2027594093","https://openalex.org/W1962761539","https://openalex.org/W2047857028","https://openalex.org/W2002208685","https://openalex.org/W1973980760"],"abstract_inverted_index":{"Models":[0],"of":[1,17,116,128,154,159,200,213,222,259,269,277,438,487],"screened":[2],"ions":[3,176,189,234],"in":[4,13,93,178,192,206,309,316,339,363,382,455,459,463,496],"equilibrium":[5],"plasmas":[6],"with":[7,508],"all":[8,424,497],"quantum":[9,85,156],"electrons":[10],"are":[11,53,112,141,181,190,307,418],"important":[12,275],"opacity":[14],"and":[15,69,89,104,137,183,240,265,295,303,350,367,374,406,442,458,470,505],"equation":[16],"state":[18],"calculations.":[19],"Although":[20],"such":[21],"models":[22,34],"have":[23,35],"to":[24,31,78,232,247,322,347,355,370,379,392,482],"be":[25,323,348,393],"derived":[26],"from":[27,114,133,395],"variational":[28,45,54,376,485],"principles,":[29],"up":[30],"now":[32],"existing":[33],"not":[36,468,476,500],"been":[37],"fully":[38,44,484],"variational.":[39],"In":[40,143,172,413,427],"this":[41,179,359],"paper":[42],"a":[43,117,210,214,226,287],"theory":[46,75],"respecting":[47],"virial":[48,510],"theorem":[49],"is":[50,76,122,152,186,217,224,235,252,280,286,320,330,336,391,408,453,467,475,506],"proposed-all":[51],"variables":[52],"except":[55,420],"the":[56,59,62,65,70,79,84,90,96,101,105,108,125,129,135,138,144,147,155,169,173,193,198,201,207,220,238,253,256,260,266,270,278,290,296,301,304,310,317,331,340,343,371,375,396,409,414,428,431,436,439,445,456,460,465,471,479,483,490,493,509],"parameters":[57],"defining":[58],"equilibrium,":[60],"i.e.,":[61],"temperature":[63],"T,":[64],"ion":[66,151,251],"density":[67,163,230],"ni":[68,167],"atomic":[71],"number":[72],"Z.":[73],"The":[74,228,244,313,451],"applied":[77],"quasiclassical":[80],"Thomas-Fermi":[81],"(TF)":[82],"atom,":[83],"average":[86,449],"atom":[87],"(QAA),":[88],"superconfigurations":[91,425],"(SC)":[92],"plasmas.":[94],"Both":[95,300],"self-consistent-field":[97],"(SCF)":[98],"equations":[99,381],"for":[100,107,433,492],"electronic":[102],"structure":[103,298],"condition":[106,397,432],"mean":[109,291],"ionization":[110,292],"Z*":[111,166,294],"found":[113,321,394],"minimization":[115,311],"thermodynamic":[118,494],"potential.":[119,412],"This":[120],"potential":[121,473],"constructed":[123],"using":[124],"cluster":[126],"expansion":[127],"plasma":[130,158,180,385],"free":[131,148,248,257,267],"energy":[132,149,249,258,268],"which":[134,285,464],"zero":[136,145,236,477],"first-order":[139,245,297,332],"terms":[140],"retained.":[142],"order":[146],"per":[150,250],"that":[153,338,351,421],"homogeneous":[157],"an":[160,281,383],"unknown":[161,225],"free-electron":[162],"n0":[164,387,434],"=":[165],"occupying":[168],"volume":[170],"1/ni.":[171],"first":[174],"order,":[175],"submerged":[177],"considered":[182,191],"local":[184,305],"neutrality":[185,199,306,437],"assumed.":[187],"These":[188],"infinite":[194,384],"space":[195],"without":[196],"imposing":[197],"Wigner-Seitz":[202],"(WS)":[203],"cell.":[204],"As":[205],"Inferno":[208],"model,":[209],"central":[211],"cavity":[212,239,466],"radius":[215,373],"R":[216,223,361],"introduced,":[218],"however,":[219],"value":[221],"priori.":[227],"charge":[229,293],"due":[231],"noncentral":[233],"inside":[237],"equals":[241],"en0":[242],"outside.":[243],"contribution":[246],"difference":[254],"between":[255,289],"system":[261,271],"\"central":[262],"ion+infinite":[263],"plasma\"":[264],"\"infinite":[272],"plasma.\"":[273],"An":[274],"part":[276],"approach":[279,489],"\"ionization":[282],"model\"":[283],"(IM),":[284],"relation":[288],"variables.":[299],"IM":[302,315,345,360],"respected":[308],"procedure.":[312],"correct":[314],"TF":[318,429,447],"case":[319,342,416,430],"Z-Z*=":[324],"integral":[325,398],"d3":[326],"r[n(r)-n0],":[327],"where":[328,401],"n(r)":[329],"electron":[333],"density.":[334],"It":[335],"shown":[337],"QAA":[341,457],"same":[344],"has":[346],"used":[349],"other":[352],"IMs":[353],"lead":[354],"unphysical":[356],"solutions.":[357],"With":[358],"becomes":[362],"both":[364],"cases":[365,462,498],"(TF":[366],"QAA)":[368],"equal":[369],"WS":[372,440],"calculation":[377],"leads":[378],"SCF":[380,410,472],"while":[386],"(or":[388],"equivalently":[389],"Z*)":[390],"d3r":[399],"theta(r-R)Vel(r)=0,":[400],"theta":[402],"denotes":[403],"Heaviside":[404],"function":[405],"Vel(r)":[407,474],"electrostatic":[411],"SC":[415,461],"results":[417],"similar":[419],"averages":[422],"over":[423],"appear.":[426],"gives":[435],"sphere":[441],"one":[443],"gets":[444],"classical":[446],"ion-in-cell":[448],"atom.":[450],"situation":[452],"different":[454],"neutral":[469],"outside":[478],"cavity.":[480],"Due":[481],"character":[486],"our":[488],"expression":[491],"pressure":[495],"does":[499],"require":[501],"any":[502],"numerical":[503],"differentiation":[504],"consistent":[507],"theorem.":[511]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}
