King and second-King plots with optimized sensitivity for lithium ions
Bibliographic record
Abstract
King plots constructed from combinations of mass-weighted atomic isotope shifts provide a sensitive technique to search for electron-neutron interactions beyond the standard model mediated by a light boson. Using high-precision variational wave functions in Hylleraas coordinates, we present a comprehensive survey of all possible King plots arising from states of ${\mathrm{Li}}^{+}$ up to principal quantum number $n=10$ and angular momentum $L=7$ in order to identify the ones most sensitive to new physics. A major limitation in previous work due to second-order mass polarization is eliminated by the introduction of a second-King plot defined in terms of second differences. The residual theoretical uncertainty is then of the order of ${\ensuremath{\alpha}}^{2}{(\ensuremath{\mu}/M)}^{3}\ensuremath{\sim}0.4$ Hz, where $\ensuremath{\alpha}$ is the fine-structure constant and $\ensuremath{\mu}$ is the reduced electron mass for a nucleus of mass $M$. Test results are presented for the ${}^{A}{\mathrm{Li}}^{+}$ isotope sequence with $A=6,7,8,9,11$ and are compared with other methods, including the ${\mathrm{Yb}}^{+}$ case recently studied both experimentally and theoretically. It is shown that the second-King plots for ${\mathrm{Li}}^{+}$ have about the same sensitivity to new physics as the ${\mathrm{Yb}}^{+}$ case for boson masses up to about 10 keV, and nuclear size uncertainties (including nuclear polarization) are suppressed. This greatly extends the sensitivity to new physics for light two-electron systems.
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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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".