Theoretical calculations for isotope shifts of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Be</mml:mi><mml:none/><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>7</mml:mn><mml:mo>,</mml:mo><mml:mn>9</mml:mn><mml:mo>,</mml:mo><mml:mn>10</mml:mn><mml:mo>,</mml:mo><mml:mn>11</mml:mn><mml:mo>,</mml:mo><mml:mn>12</mml:mn><mml:mo>,</mml:mo><mml:mn>14</mml:mn></mml:mrow></mml:mmultiscripts></mml:math> ions
Bibliographic record
Abstract
Standard perturbation theory in quantum mechanics is employed to calculate the mass shifts of $2^{1}S_{0}\ensuremath{-}2^{3}S_{1}$ and $2^{3}S_{1}\ensuremath{-}2^{3}P_{J}$ transitions in $^{7,9,10,11,12,14}\mathrm{Be}^{2+}$ ions. These mass shifts are determined with high precision, typically having uncertainties of 1--2 ppm. The sensitivity of the isotope shifts between $^{7,10,11,12,14}\mathrm{Be}^{2+}$ and $^{9}\mathrm{Be}^{2+}$ to differences in nuclear charge radii is examined. Moreover, we present the fine-structure splitting isotope shifts, which serve as valuable tools for testing the consistency of experimental results. The study presented here will provide valuable insights for future measurements aimed at extracting atomic physics values of Be nuclear charge radii differences with an accuracy of 5% or higher.
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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 | 0.009 | 0.009 |
| Meta-epidemiology (narrow) | 0.007 | 0.012 |
| Meta-epidemiology (broad) | 0.004 | 0.017 |
| Bibliometrics | 0.003 | 0.008 |
| Science and technology studies | 0.008 | 0.011 |
| Scholarly communication | 0.007 | 0.007 |
| Open science | 0.013 | 0.011 |
| Research integrity | 0.009 | 0.011 |
| Insufficient payload (model declined to judge) | 0.203 | 0.011 |
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".