Analytical formulas for the Stark effect on intensity of hydrogen radiation lines
Bibliographic record
Abstract
A regular method for deriving the consecutive terms of a series in powers of field strength F for the intensities of hydrogen radiation lines is presented both analytically and numerically. Specific modification of the perturbation theory for degenerate states and the Sturm-series expansion for the completely reduced CoulombGreen function in parabolic coordinates are used to derive simple analytical formulas for matrix elements and the intensities of the radiation transitions between circular states. Particular cases of transitions between the closest Rydberg levels are presented and discussed in detail. Analytical expressions are also derived for the quadrupole matrix elements, which may contribute to the probability of σ-transitions with the selection rule for the magnetic quantum number Δm = ±1 and determine the probability of the dipole-forbidden radiation transitions between Stark levels with Δm = ±2. PACS Nos.: 32.60.+i, 32.70.n, 32.70.Fw
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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 | 0.000 |
| 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 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".