Distorted waves with exact nonlocal exchange: A canonical function approach
Bibliographic record
Abstract
The Canonical Function Method (CFM) is developed and applied, for the first time, to the distorted wave problem with exact nonlocal exchange. In electron impact ionization of hydrogenic systems, the latter originates from the Pauli exclusion principle that leads, in the Hartree–Fock approximation, to a radial Schrodinger equation of an integro-differential type. The application of the CFM with static and polarization potentials allows us to obtain the phaseshifts and scattering lengths in the s-wave singlet and triplet states at high (≥5 eV) and low energies (≤0.1 eV). The results are compared with those obtained by other methods based on exact exchange, local equivalent-exchange potentials and recently developed spectral integral equation methods (S-IEM). The accuracy, stability, and speed of convergence of the CFM are analysed and compare favorably with other methods including the highly accurate S-IEM. At very low energies, the CFM is superior to all known methods.PACS Nos.: 34.00.00, 34.50.–s, 03.65.–w, 02.60.Nm, 02.60.–x
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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 | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 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".