{"id":"W4415964450","doi":"10.48550/arxiv.2510.17495","title":"Theory for the Rydberg states of helium: Results for $2 \\le n \\le 35$ and comparison with experiment for the singlet and triplet $P$-states","year":2025,"lang":"","type":"preprint","venue":"ArXiv.org","topic":"Atomic and Molecular Physics","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Alliance de recherche numérique du Canada","keywords":"Rydberg formula; Extrapolation; Ionization; Principal quantum number; Quantum defect; Singlet state; Ionization energy; Helium; Excited state; Rydberg state","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001033977,0.0006754874,0.000948142,0.0009477668,0.001376326,0.0009372427,0.002824342,0.0008644064,0.007046386],"category_scores_gemma":[0.0008619628,0.0003019296,0.0009036117,0.0009977815,0.001368201,0.00106177,0.001027367,0.001114746,0.001099951],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00169426,"about_ca_system_score_gemma":0.001492465,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.005986876,"about_ca_topic_score_gemma":0.01127985,"domain_scores_codex":[0.9995415,0.0001140622,0.00001162012,0.00003231056,0.0002178413,0.00008261428],"domain_scores_gemma":[0.9995424,0.0001564328,0.00003945019,0.0001075187,0.0001037269,0.00005048356],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001634884,0.000125867,0.003988775,0.000478453,0.0001242895,0.0002880989,0.0002635479,0.4708811,0.01329152,0.4781261,0.002278526,0.02999011],"study_design_scores_gemma":[0.00003823889,0.00007755187,0.002739451,0.00004581416,0.00002316697,0.0001030012,0.0001286401,0.9256889,0.006707081,0.06149777,0.002916318,0.00003409656],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5202444,0.001640392,0.3375918,0.001498994,0.0001258869,0.0003425148,0.00116004,0.001009219,0.1363868],"genre_scores_gemma":[0.9344056,0.000794062,0.05215232,0.0001809715,0.00006966257,0.0003746779,0.0007672342,0.0003302985,0.01092536],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007046386,"threshold_uncertainty_score":0.02357244,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02819611461868367,"score_gpt":0.2871948480917978,"score_spread":0.2589987334731142,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}