Splitting Isotope Shift in the $1s2p\,^3\!P_{0,1,2}$ Fine-Structure Triplet in $^{12,13,14}$C$^{4+}$: Experiment and Theory
Bibliographic record
Abstract
We report measurements and theoretical calculations of the fine-structure splittings in all three $1s2s\,^3\!S_1\rightarrow\,1s2p\,^3\!P_{0,1,2}$ transitions in the heliumlike systems of the isotopes $^{12,13,14}$C. The metastable triplet state was efficiently populated in an electron beam ion source and the C$^{4+}$ ions were electrostatically accelerated to 50\,keV to perform collinear laser spectroscopy. From the determined transition frequencies, the splitting isotope shift (SIS), i.e., the difference in fine-structure splittings between different isotopes of the same element, was extracted. In the SIS, theoretical uncertainties due to higher-order quantum electrodynamic corrections are strongly suppressed since they are independent of both nuclear mass and the fine-structure quantum number $J$ in lowest order. Comparison with theory provides an important test of experimental accuracy, particularly in the $^{13}$C$^{4+}$ case, for which the nuclear spin leads to hyperfine-induced fine-structure mixing. At the same time, the even-even isotopes $^{12,14}$C$^{4+}$ without nuclear spin can be used to confirm theory. Theoretical values of the SIS are given for all the heliumlike ions with $2\le Z\le 10$.
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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 | 0.000 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".