Algebraic relations from finite-nuclear-mass effects to test atomic transition rates
Bibliographic record
Abstract
General algebraic relations are derived which provide a stringent test of the accuracy of $n$-photon electric dipole transition rates when mass-polarization effects are included. They are a generalization of the well-known equivalence of the length, velocity, and acceleration forms of the transition matrix element that follows from gauge invariance. The algebraic relations connect the coefficients in a power series in powers of $\ensuremath{\mu}/M$ for the three gauges, where $M$ is the nuclear mass and $\ensuremath{\mu}$ is the electron reduced mass. These relations also provide a stringent test of the leading infinite-mass term, a quantity that must be calculated with sufficient accuracy for the higher-order terms in powers of $\ensuremath{\mu}/M$ to be correct. As a check, the length-velocity algebraic relations are used to test the accuracy of high-precision calculations for both one-photon ($1s2p\phantom{\rule{0.16em}{0ex}}^{1}P\ensuremath{-}1{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S$ and $1s2p\phantom{\rule{0.16em}{0ex}}^{3}P\ensuremath{-}1s2s\phantom{\rule{0.16em}{0ex}}^{3}S$) and two-photon ($1s2s\phantom{\rule{0.16em}{0ex}}^{1}S\ensuremath{-}1{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S$) decay for the heliumlike ions with $Z=2--10$.
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.
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 | 0.004 | 0.024 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".