{"id":"https://openalex.org/W2005995769","doi":"https://doi.org/10.1007/jhep06(2014)087","title":"Scattering theory without large-distance asymptotics","display_name":"Scattering theory without large-distance asymptotics","publication_year":2014,"publication_date":"2014-06-01","ids":{"openalex":"https://openalex.org/W2005995769","doi":"https://doi.org/10.1007/jhep06(2014)087","mag":"2005995769"},"language":"en","primary_location":{"id":"doi:10.1007/jhep06(2014)087","doi":"https://doi.org/10.1007/jhep06(2014)087","is_oa":true,"landing_page_url":"https://doi.org/10.1007/jhep06(2014)087","pdf_url":"https://link.springer.com/content/pdf/10.1007/JHEP06(2014)087.pdf","source":{"id":"https://openalex.org/S187585107","display_name":"Journal of High Energy Physics","issn_l":"1029-8479","issn":["1029-8479","1126-6708","1127-2236"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","dongbi-a","jufo-3","ki-jl-2","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of High Energy Physics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://link.springer.com/content/pdf/10.1007/JHEP06(2014)087.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100392670","display_name":"Tong Liu","orcid":"https://orcid.org/0000-0002-8251-3250","observed_orcids":["https://orcid.org/0000-0002-8251-3250"]},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tong Liu","raw_affiliation_strings":["Department of Physics, Tianjin University, Tianjin, 300072, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Tianjin University, Tianjin, 300072, P.R. China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032161976","display_name":"Wen-Du Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wen-Du Li","raw_affiliation_strings":["Department of Physics, Tianjin University, Tianjin, 300072, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Tianjin University, Tianjin, 300072, P.R. China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001909929","display_name":"Wu-Sheng Dai","orcid":"https://orcid.org/0000-0002-2085-8907","observed_orcids":["https://orcid.org/0000-0002-2085-8907"]},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]},{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wu-Sheng Dai","raw_affiliation_strings":["Department of Physics, Tianjin University, Tianjin, 300072, P.R. China","LiuHui Center for Applied Mathematics, Nankai University & Tianjin University, Tianjin, 300072, P.R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Tianjin University, Tianjin, 300072, P.R. China","institution_ids":["https://openalex.org/I162868743"]},{"raw_affiliation_string":"LiuHui Center for Applied Mathematics, Nankai University & Tianjin University, Tianjin, 300072, P.R. China","institution_ids":["https://openalex.org/I162868743","https://openalex.org/I205237279"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5001909929"],"corresponding_institution_ids":["https://openalex.org/I162868743","https://openalex.org/I205237279"],"apc_list":{"value":0,"currency":"USD","value_usd":0},"apc_paid":null,"fwci":1.9242,"has_fulltext":true,"cited_by_count":26,"citation_normalized_percentile":{"value":0.81818182,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"2014","issue":"6","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.32179999351501465,"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"}},"topics":[{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.32179999351501465,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.1761000007390976,"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/T10048","display_name":"Particle physics theoretical and experimental studies","score":0.11349999904632568,"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/scattering-theory","display_name":"scattering theory","score":0.8349999785423279},{"id":"https://openalex.org/keywords/scattering-amplitudes","display_name":"scattering amplitudes","score":0.9430000185966492},{"id":"https://openalex.org/keywords/scattering-cross-section","display_name":"scattering cross section","score":0.7910000085830688},{"id":"https://openalex.org/keywords/hankel-functions","display_name":"Hankel functions","score":0.703000009059906},{"id":"https://openalex.org/keywords/bessel-functions","display_name":"Bessel functions","score":0.9599999785423279},{"id":"https://openalex.org/keywords/phase-shift","display_name":"phase shift","score":0.902999997138977}],"concepts":[{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.8809224367141724},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.7487583160400391},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.6960703134536743},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6382471323013306},{"id":"https://openalex.org/C192465680","wikidata":"https://www.wikidata.org/wiki/Q1413450","display_name":"Precondition","level":2,"score":0.6358663439750671},{"id":"https://openalex.org/C67105901","wikidata":"https://www.wikidata.org/wiki/Q903737","display_name":"Scattering theory","level":3,"score":0.6189153790473938},{"id":"https://openalex.org/C153013531","wikidata":"https://www.wikidata.org/wiki/Q1322810","display_name":"Scattering amplitude","level":3,"score":0.60163813829422},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5343543291091919},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45443031191825867},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.4308586120605469},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4184546172618866},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26246118545532227},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.15821778774261475},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.101477712392807},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/jhep06(2014)087","doi":"https://doi.org/10.1007/jhep06(2014)087","is_oa":true,"landing_page_url":"https://doi.org/10.1007/jhep06(2014)087","pdf_url":"https://link.springer.com/content/pdf/10.1007/JHEP06(2014)087.pdf","source":{"id":"https://openalex.org/S187585107","display_name":"Journal of High Energy Physics","issn_l":"1029-8479","issn":["1029-8479","1126-6708","1127-2236"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","dongbi-a","jufo-3","ki-jl-2","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of High Energy Physics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1403.5646","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1403.5646","pdf_url":"https://arxiv.org/pdf/1403.5646","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.1403.5646","doi":"https://doi.org/10.48550/arxiv.1403.5646","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1403.5646","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":"article-journal"}],"best_oa_location":{"id":"doi:10.1007/jhep06(2014)087","doi":"https://doi.org/10.1007/jhep06(2014)087","is_oa":true,"landing_page_url":"https://doi.org/10.1007/jhep06(2014)087","pdf_url":"https://link.springer.com/content/pdf/10.1007/JHEP06(2014)087.pdf","source":{"id":"https://openalex.org/S187585107","display_name":"Journal of High Energy Physics","issn_l":"1029-8479","issn":["1029-8479","1126-6708","1127-2236"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","ddh","doaj","dongbi-a","jufo-3","ki-jl-2","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of High Energy Physics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2047555845","display_name":null,"funder_award_id":"11075115","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2005995769.pdf","grobid_xml":"https://content.openalex.org/works/W2005995769.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W10877979","https://openalex.org/W1479923323","https://openalex.org/W1556559448","https://openalex.org/W1968947080","https://openalex.org/W1973243384","https://openalex.org/W1980330198","https://openalex.org/W1987241088","https://openalex.org/W2028017249","https://openalex.org/W2046659644","https://openalex.org/W2047791030","https://openalex.org/W2066581247","https://openalex.org/W2075144340","https://openalex.org/W2075775885","https://openalex.org/W2081509843","https://openalex.org/W2141439954","https://openalex.org/W2143951885","https://openalex.org/W2154483950","https://openalex.org/W2157174221","https://openalex.org/W2169151906","https://openalex.org/W2313299119","https://openalex.org/W2684562462","https://openalex.org/W3099980895","https://openalex.org/W4300223101"],"related_works":["https://openalex.org/W7097385547","https://openalex.org/W1525777291","https://openalex.org/W3147844515","https://openalex.org/W2734872977","https://openalex.org/W2761171199","https://openalex.org/W3150927534","https://openalex.org/W7040069591","https://openalex.org/W7075583979","https://openalex.org/W1972957247","https://openalex.org/W2072859186"],"abstract_inverted_index":{"In":[0,68,97],"conventional":[1],"scattering":[2,95,105,135,174],"theory,":[3],"to":[4],"obtain":[5,89],"an":[6,48,90,102,162],"explicit":[7,49,91,104],"result,":[8],"one":[9,28,45,86],"imposes":[10],"a":[11,54,75,94,121,124,153],"precondition":[12,76],"that":[13,44,73,119],"the":[14,23,32,36,40,56,59,109,128,134,139,144,146,157,168,173],"distance":[15,60,112],"between":[16,61,113],"target":[17,62,114],"and":[18,35,63,115],"observer":[19,64],"is":[20,65,77,150,161],"infinite.":[21],"With":[22],"help":[24],"of":[25,58,84,93,111,167],"this":[26,69],"precondition,":[27],"can":[29,46,87],"asymptotically":[30],"replace":[31],"Hankel":[33],"function":[34,38],"Bessel":[37,129,169],"with":[39],"sine":[41],"functions":[42],"so":[43],"achieve":[47],"result.":[50],"Nevertheless,":[51],"after":[52],"such":[53,74],"treatment,":[55],"information":[57,83,110],"inevitably":[66],"lost.":[67],"paper,":[70],"we":[71,100],"show":[72,118],"not":[78],"necessary:":[79],"without":[80],"losing":[81],"any":[82],"distance,":[85,123,145],"still":[88],"result":[92,106],"rigorously.":[96],"other":[98],"words,":[99],"give":[101],"rigorous":[103],"which":[107],"contains":[108],"observer.":[116],"We":[117],"at":[120],"finite":[122],"modification":[125],"factor":[126],"\u2014":[127,131],"polynomial":[130],"appears":[132,171],"in":[133,172],"amplitude,":[136],"and,":[137,155],"consequently,":[138],"cross":[140],"section":[141],"depends":[142],"on":[143],"outgoing":[147],"wave-front":[148],"surface":[149],"no":[151],"longer":[152],"sphere,":[154],"besides":[156],"phase":[158,164],"shift,":[159],"there":[160],"additional":[163],"(the":[165],"argument":[166],"polynomial)":[170],"wave":[175],"function.":[176]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2}],"updated_date":"2026-11-13T13:42:25.865203","created_date":"2016-06-24T00:00:00"}
