New methods for old Coulomb few‐body problems
Bibliographic record
Abstract
Abstract Coulomb problems involving three or four particles can advantageously be described using wavefunctions that explicitly involve all the interparticle distances. In what is known as the Hylleraas method, a set of Slater‐type orbitals for the electrons of an atom is augmented by linear (or in some cases higher powers) of the interelectron separation(s). An alternative approach, of particular value when all the particles have comparable masses, is to use a wavefunction containing exponentials in all the interparticle distances. This “exponential ansatz” is straightforward to implement when there are three particles but has only recently been implemented for four‐body systems. Integral evaluation is reviewed for both the exponential ansatz and the Hylleraas method, the treatment of general angular symmetry is discussed, and kinetic‐energy matrix elements are examined and related to simpler integrals. Some illustrative results for the positronium molecule ( e + e − e + e − ) are included. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004
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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".