Precision Calculation of Hyperfine Structure and the Zemach Radii of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>Li</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>6</mml:mn><mml:mo>,</mml:mo><mml:mn>7</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:mrow></mml:math> Ions
Bibliographic record
Abstract
The hyperfine structures of the 2^{3}S_{1} states of the ^{6}Li^{+} and ^{7}Li^{+} ions are investigated theoretically to extract the Zemach radii of the ^{6}Li and ^{7}Li nuclei by comparing with precision measurements. The obtained Zemach radii are larger than the previous values of Puchalski and Pachucki [Phys. Rev. Lett. 111, 243001 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.243001] and disagree with them by about 1.5 and 2.2 standard deviations for ^{6}Li and ^{7}Li, respectively. Furthermore, our Zemach radius of ^{6}Li differs significantly from the nuclear physics value, derived from the nuclear charge and magnetic radii [Phys. Rev. A 78, 012513 (2008)PLRAAN1050-294710.1103/PhysRevA.78.012513] by more than 6σ, indicating an anomalous nuclear structure for ^{6}Li. The conclusion that the Zemach radius of ^{7}Li is about 40% larger than that of ^{6}Li is confirmed. The obtained Zemach radii are used to calculate the hyperfine splittings of the 2^{3}P_{J} states of ^{6,7}Li^{+}, where an order of magnitude improvement over the previous theory has been achieved for ^{7}Li^{+}.
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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 | 0.004 | 0.004 |
| Meta-epidemiology (narrow) | 0.003 | 0.005 |
| Meta-epidemiology (broad) | 0.001 | 0.007 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.004 | 0.006 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.006 | 0.006 |
| Research integrity | 0.004 | 0.006 |
| Insufficient payload (model declined to judge) | 0.601 | 0.003 |
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; both teacher heads agree on what is shown here.
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".