Analytical method for calculating atomic structures based on the variational method for many-electron atomic structure in plasmas
Bibliographic record
Abstract
Within the framework of the Hartree–Fock method and the irreducible tensor theory, we have proposed an analytic formula for calculating the nonrelativistic energies of many-electron atoms. The relativistic mass, the one- and two-body Darwin, the spin–spin contact interaction, and the orbit–orbit interaction corrections to the energies are considered to make the results more precise. The angular interactions and spin sums involved in the formula are worked out explicitly using the irreducible theory. A program based on the variational method is developed to calculate the wave functions and atomic structure properties. The energies of the 1sns 1,3S (n = 1–4) and 1snp 1,3P (n = 2–4) states of the exemplary ions Ar16+, Fe24+, and Kr34+ in both Debye plasma and quantum plasma environments are given. Moreover, we analyzed the evolution of plasma screening parameters and provided some rules for practical and rapid evaluation in plasma applications.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".