Two-photon decay rates in heliumlike ions: Finite-nuclear-mass effects
Bibliographic record
Abstract
The spontaneous two-photon decay rates from the $1s2s\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$ level to the ground state $1{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$ in helium and its isoelectronic ions through neon ($Z=10$) are calculated, including the effects of finite nuclear mass. In all cases the length and velocity results agree to eight or more figures, demonstrating that the theoretical formulation correctly takes into account the effects of mass scaling, mass polarization, and motion of the nucleus in the center-of-mass frame. Algebraic relationships are derived and tested relating the expansion coefficients in powers of $\ensuremath{\mu}/M$ for mass polarization, where $\ensuremath{\mu}$ is the electron reduced mass and $M$ is the nuclear mass. Muonic, pionic, and antiprotonic helium are included as extreme test cases where mass polarization is large. The results are compared with experiment and previous calculations.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".