Precise theory of the Stark effect on hydrogen- and helium-like atoms
Bibliographic record
Abstract
The relativistic effects on the dipole polarizabilities and hyperpolarizabilities are considered for different kinds of energy levels in hydrogen- and helium-like atoms. The relativistic Coulomb Green's function is used for calculating the susceptibilities of the ground-state hydrogen up to terms of order (α Z) 10 . Both relativistic and interelectronic corrections are determined for the ground state of helium. The formulas are given for polarizability and hyperpolarizability in the relativistic "screened-charge" approximation. The anticrossing of the triplet 3 P J states with zero magnetic quantum number is studied on the basis of perturbation theory for degenerate states. General expressions are given for the dipole matrix elements, up to the fourth order in field strength, within the basis of close fine-structure substates with equal angular momenta L and different total momenta J. The calculation of the higher order matrix elements is carried out with the use of the Green's function in the model potential approximation. PACS Nos.: 31.10Dk, 31.15Ar, 31.30Jv, 32.10-f, 31.25Eb
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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".