Lifetimes of fine structure levels of the Li atom for 20 < <i>n</i> < 31 by an extended Ritz formula
Bibliographic record
Abstract
Lithium and lithium-like elements look like hydrogen atoms if their two electrons and the nucleus are considered as having a core around which a single electron is orbiting. The energy and radii expressions for hydrogen atoms can be used for lithium and lithium-like elements; an important modification is introducing an effective principal quantum number. The effective principal quantum number differs from the principal quantum number of hydrogen by the quantum defect. The quantum defect has respective values for various levels of lithium and lithium-like ions. In this study, we used extended Ritz formulas to calculate quantum defects required to calculate the energies of the ns, np, nd, and nf series up to n < 31. Using these energies, we calculated transition probabilities and then the lifetimes of the lithium levels. The lifetimes were compared with the available published data; an excellent agreement was noticed. The work also extended the available list of lifetimes to higher quantum numbers. Forty lifetimes are newly calculated and presented for the first time. A polynomial formula for each of the ns, np, nd, and nf series lifetimes has been developed that fits well the lifetime values.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".