Exponential variational expansion in relative coordinates and scalar coupling coefficients for three-body systems
Bibliographic record
Abstract
The exponential variational expansion is applied to highly accurate computations of the ground states in the Ps − and ∞ H − ions. The determined variational energies for these systems are −0.262 005 070 232 980 107 7335 and −0.527 751 016 544 377 196 5668 au respectively. These energies and corresponding wavefunctions are significantly more accurate than values known from earlier studies. A number of bound state properties are determined for the Ps − ion. The method of scalar coupling for three-body systems is developed. A general analytical expression is derived for the overlap integral between two scalar functions ϕ( r 32 , r 31 , r 21 ) and ψ( r 32 , r 31 ), written in relative coordinates and one-particle coordinates respectively. The case of bound S( L = 0) states in Coulomb three-body systems is discussed in detail. In this case, explicit analytical formulae for the three-body scalar coupling coefficients have been produced and tested in actual highly accurate calculations for the Ps − and ∞ H − ions. The approach developed in this work can be applied to a large number of real three-body problems.
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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 | 0.003 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".