Bibliographic record
Abstract
Abstract Atomic hydrogen energy levels calculated to high precision are required to assist experimental researchers working on spectroscopy in the pursuit of testing quantum electrodynamics (QEDs) and probing for physics beyond the Standard Model. There are two important parts to the problem of computing these levels: an accurate evaluation of contributions from QED and using an accurate value for the proton charge radius as an input. Recent progress on QED corrections to the fine structure, as well as increasing evidence that a proton charge radius in the range of 0.84 fm is favored over the previously adopted larger value in the 0.88 fm range, has advanced the field, yet several state-of-the-art measurements remain in contradiction with this smaller value. Motivated by on-going and future work in this area, we present here a simple parameterization for the energy levels of hydrogen at the level of hyperfine structure using the so-called relativistic Ritz approach. The fitting of a finite sample of QED-generated levels at low to intermediate principal quantum number, n , gives a generally applicable formula for all values of n for each distinct angular momentum channel, given in this work up to orbital angular momentum number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>ℓ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>30</mml:mn> </mml:math> . We also provide a simple linear parameterization for the shift in hydrogen energy levels as a function of the proton radius, providing a useful cross check for extant and future measured energy intervals.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".