{"id":"https://openalex.org/W7225400950","doi":"https://doi.org/10.5281/zenodo.24013723","title":"Bookkeeping, Not a Derivation: The Pronic Identity Charged Against One Spin-Orbit Strength","display_name":"Bookkeeping, Not a Derivation: The Pronic Identity Charged Against One Spin-Orbit Strength","publication_year":2026,"publication_date":"2026-11-06","ids":{"openalex":"https://openalex.org/W7225400950","doi":"https://doi.org/10.5281/zenodo.24013723"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24013723","doi":"https://doi.org/10.5281/zenodo.24013723","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24013723","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24013723","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159396451","display_name":"William Alexander Aldred","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Aldred, William Alexander","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0000-1215-577X","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5159396451"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T10093","display_name":"Nuclear physics research studies","score":0.9735999703407288,"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"}},"topics":[{"id":"https://openalex.org/T10093","display_name":"Nuclear physics research studies","score":0.9735999703407288,"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"}},{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.009600000455975533,"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/T13458","display_name":"Astronomical and nuclear sciences","score":0.005100000184029341,"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/shell-closure","display_name":"shell closure","score":0.6850000023841858},{"id":"https://openalex.org/keywords/harmonic-oscillator","display_name":"harmonic oscillator","score":0.6380000114440918},{"id":"https://openalex.org/keywords/shell-model","display_name":"shell model","score":0.8230000138282776},{"id":"https://openalex.org/keywords/nuclear-magic-numbers","display_name":"nuclear magic numbers","score":0.4050000011920929}],"concepts":[{"id":"https://openalex.org/C2781052500","wikidata":"https://www.wikidata.org/wiki/Q2230313","display_name":"Shell (structure)","level":2,"score":0.6632000207901001},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.5976999998092651},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5230000019073486},{"id":"https://openalex.org/C24872484","wikidata":"https://www.wikidata.org/wiki/Q126818","display_name":"Dimensionless quantity","level":2,"score":0.5149999856948853},{"id":"https://openalex.org/C188082385","wikidata":"https://www.wikidata.org/wiki/Q73792","display_name":"Charge (physics)","level":2,"score":0.49720001220703125},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.46369999647140503},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4318000078201294},{"id":"https://openalex.org/C99191460","wikidata":"https://www.wikidata.org/wiki/Q906725","display_name":"Oscillator strength","level":3,"score":0.41769999265670776},{"id":"https://openalex.org/C40934718","wikidata":"https://www.wikidata.org/wiki/Q190070","display_name":"Harmonic oscillator","level":2,"score":0.37790000438690186},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3765999972820282},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.3181999921798706},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3127000033855438},{"id":"https://openalex.org/C2778751112","wikidata":"https://www.wikidata.org/wiki/Q835016","display_name":"Window (computing)","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2903999984264374},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.28299999237060547},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.2653999924659729},{"id":"https://openalex.org/C2776479727","wikidata":"https://www.wikidata.org/wiki/Q7685907","display_name":"Target strength","level":3,"score":0.2558000087738037},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25529998540878296}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5281/zenodo.24013723","doi":"https://doi.org/10.5281/zenodo.24013723","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24013723","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24013724","doi":"https://doi.org/10.5281/zenodo.24013724","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24013724","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24041934","doi":"https://doi.org/10.5281/zenodo.24041934","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24041934","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24013723","doi":"https://doi.org/10.5281/zenodo.24013723","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24013723","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7225422815","https://openalex.org/W7225266364","https://openalex.org/W2034842306","https://openalex.org/W2004380490","https://openalex.org/W4280644936","https://openalex.org/W3124197453","https://openalex.org/W4241227675","https://openalex.org/W811045938","https://openalex.org/W7154239235","https://openalex.org/W7225064901"],"abstract_inverted_index":{"AF-7":[0],"found":[1],"that":[2,84],"the":[3,8,19,24,35,38,45,51,89,105,112,119,171,181,191,220],"shell":[4,31,66,88,133,144],"closures'":[5],"departures":[6,186],"from":[7],"oscillator":[9,28,117],"closures":[10],"\u2014":[11,16,115,131,219,226],"12,":[12],"20,":[13],"30,":[14],"42":[15],"are":[17],"exactly":[18,83,203],"pronic":[20],"numbers":[21],"k(k+1),":[22],"each":[23],"capacity":[25],"of":[26],"one":[27,30,87,208],"shell,":[29],"down,":[32],"and":[33,57,81,100,184,188,195,233],"charged":[34],"successor:":[36],"treat":[37],"identity":[39,198],"as":[40],"a":[41],"derivation":[42,202],"charge":[43,52],"on":[44],"spin\u2013orbit":[46,121,221],"strength.":[47],"This":[48],"paper":[49],"separates":[50],"into":[53],"its":[54,71,231,234],"two":[55],"halves":[56],"grades":[58],"both.":[59],"The":[60,107,152,197],"count":[61],"half":[62,109],"is":[63,91,154,161],"bookkeeping,":[64],"exactly:":[65],"k":[67],"holds":[68,79],"(k+1)(k+2)":[69,92],"states,":[70],"top":[72,135],"j":[73],"=":[74,95],"l":[75],"+":[76],"\u00bd":[77],"orbit":[78,85,136,147],"2k+2,":[80],"if":[82],"drops":[86,167,179],"departure":[90],"\u2212":[93],"(2k+2)":[94],"k(k+1)":[96],"with":[97,123,230],"no":[98,101],"remainder":[99],"strength":[102,108,126,209],"anywhere":[103],"in":[104,111,163,210],"arithmetic.":[106],"fails:":[110],"declared":[113],"bench":[114],"harmonic":[116],"plus":[118],"Nilsson-form":[120],"term":[122,222],"ONE":[124],"dimensionless":[125],"\u03ba":[127,138,149,159],"for":[128,176],"all":[129,177],"shells":[130,183],"dropping":[132],"3's":[134],"requires":[137,148],">":[139],"1/3,":[140],"while":[141],"not":[142,214,224],"over-dropping":[143],"6's":[145],"second":[146],"\u2264":[150],"1/4.":[151],"window":[153],"empty":[155],"by":[156],"1/12.":[157],"Every":[158],"regime":[160],"enumerated":[162],"\u00a72:":[164],"too":[165],"weak":[166],"nothing":[168],"or":[169],"only":[170],"heavy":[172,182],"closures;":[173],"strong":[174],"enough":[175],"four":[178],"over-drops":[180],"returns":[185],"22":[187],"32":[189],"where":[190],"record":[192],"says":[193],"30":[194],"42.":[196],"tells":[199],"any":[200],"future":[201],"what":[204],"it":[205],"must":[206],"return;":[207],"this":[211],"form":[212],"does":[213],"return":[215],"it.":[216],"AF-2's":[217],"deficit":[218],"fitted,":[223],"derived":[225],"stands":[227],"untouched,":[228],"now":[229],"target":[232],"simplest":[235],"would-be":[236],"supplier":[237],"both":[238],"evaluated.":[239]},"counts_by_year":[],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2026-11-07T00:00:00"}
