Calculations of Magnetic Moments for Three-Electron Atomic Systems
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Bibliographic record
Abstract
The first fully correlated calculations of the magnetic moment in lithium are presented. Relative to the free-electron value, the Zeeman ${g}_{J}$ factor for the ground state lithium ${g}_{J}{/g}_{e}\ensuremath{-}1$ is calculated to a computational accuracy of 200 parts in ${10}^{9}$, including relativistic and radiative corrections of orders ${\ensuremath{\alpha}}^{2}$, ${\ensuremath{\alpha}}^{2}m/M$, and ${\ensuremath{\alpha}}^{3}$. The isotope shifts in ${g}_{J}$ are predicted precisely for various isotopes. The extensions to the first excited $S$ state of lithium and the ground state of ${\mathrm{Be}}^{+}$ are made.
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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 | 0.000 | 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it