Isotope shifts in francium isotopes<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">Fr</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>206</mml:mn><mml:mo>−</mml:mo><mml:mn>213</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">Fr</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>221</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>
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Bibliographic record
Abstract
We present the isotope shifts of the $7{s}_{1/2}$ to $7{p}_{1/2}$ transition for francium isotopes ${}^{206\ensuremath{-}213}\mathrm{Fr}$ with reference to $^{221}\mathrm{Fr}$ collected from two experimental periods. The shifts are measured on a sample of atoms prepared within a magneto-optical trap by a fast sweep of radio-frequency sidebands applied to a carrier laser. King plot analysis, which includes literature values for $7{s}_{1/2}$ to $7{p}_{3/2}$ isotope shifts, provides a field shift constant ratio of 1.0520(10) and a difference between the specific mass shift constants of 170(100) GHz amu between the ${D}_{1}$ and ${D}_{2}$ transitions, of sufficient precision to differentiate between ab initio calculations.
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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 | 0.007 | 0.005 |
| Meta-epidemiology (narrow) | 0.004 | 0.007 |
| Meta-epidemiology (broad) | 0.002 | 0.007 |
| Bibliometrics | 0.002 | 0.004 |
| Science and technology studies | 0.006 | 0.006 |
| Scholarly communication | 0.005 | 0.007 |
| Open science | 0.008 | 0.007 |
| Research integrity | 0.006 | 0.008 |
| Insufficient payload (model declined to judge) | 0.179 | 0.010 |
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 it