Excitation energies, E1, M1, and E2 transition rates, and lifetimes in Ca<sup>+</sup>, Sr<sup>+</sup>, Cd<sup>+</sup>, Ba<sup>+</sup>, and Hg<sup>+</sup> <sup>1</sup>This article is part of a Special Issue on the 10th International Colloquium on Atomic Spectra and Oscillator Strengths for Astrophysical and Laboratory Plasmas.
Bibliographic record
Abstract
Excitation energies of ns1/2, npj, and ndj states in Cd+ (n = 5), Hg+ (n = 5) and ns1/2, npj, and (n – 1)dj states in Ca+ (n = 4), Sr+ (n = 5), and Ba+ (n = 6) are evaluated using the linearized coupled-cluster (all-order) method. Reduced matrix elements, oscillator strengths, and transition rates are determined for the ns–npj–ndj (or ns–npj–(n – 1)dj) possible electric dipole transitions in Ca+, Sr+, Ba+, Cd+, and Hg+. Electric quadrupole matrix elements are evaluated to obtain ns1/2–(n – 1)dj transition rates in Ca+ (n = 5), Sr+ (n = 5), and Ba+ (n = 6). The matrix elements are calculated using both relativistic many-body perturbation theory, complete through third order, and the relativistic all-order method restricted to single and double (SD) excitations. The SD lifetime results for the np and nd states in Ca+, Sr+, Ba+, Cd+, and Hg+, are compared with the latest available experimental measurements. The contribution of the magnetic dipole nd3/2–nd5/2 transition to the lifetimes of the lowest nd5/2 level ln Ca+, Sr+, and Ba+ ions is discussed. These calculations provide a theoretical benchmark for comparison with experiment and theory as well as data needed for various applications.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.006 | 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 source (direct Gemma or distilled Codex), 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".