High Precision Atomic Theory for Li and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>Be</mml:mi><mml:mo>+</mml:mo></mml:msup></mml:math>: QED Shifts and Isotope Shifts
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
High-precision results are presented for calculations of the nonrelativistic energies, relativistic corrections, and quantum electrodynamic corrections for the $2\text{ }^{2}S$, $2\text{ }^{2}P$, and $3\text{ }^{2}S$ states of Li and ${\mathrm{Be}}^{+}$, using nonrelativistic wave functions expressed in Hylleraas coordinates. Bethe logarithms are obtained for the states of ${\mathrm{Be}}^{+}$. Finite mass corrections are calculated with sufficient accuracy to extract the nuclear charge radius from measurements of the isotope shift for the $2\text{ }^{2}S\ensuremath{-}2\text{ }^{2}P$ and $2\text{ }^{2}S\ensuremath{-}3\text{ }^{2}S$ transitions. The calculated ionization potential for ${\mathrm{Be}}^{+}$ is $146\text{ }882.923\ifmmode\pm\else\textpm\fi{}0.005\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}1}$.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it