An exact one-electron model of the helium atom ground state
Bibliographic record
Abstract
Expression of the Helium atom ground state wavefunction as a product of marginal and conditional factors together with averaging over the configuration space except for the distance of one electron from the nucleus, leads to a radial Schrödinger equation for the motion of one electron in an effective field produced by the nucleus and the other electron. The potential in this radial Schrödinger equation is in principle exact (i.e. it includes all of the correlation energy). Values of the potential are reported computed from correlated wavefunctions and from a Hartree-Fock wavefunction; the correlated and Hartree-Fock potentials are similar, the former being below the latter by and amount that averages to the correlation energy (0.04 a.u.). Thus Hartree's concept of a self-consistent field for the motion of one electron is seen to be in principle exact. The exact theory has not, however, thus far yielded a set of simultaneous equations analogous with the Hartree-Fock equations; the exact theory if a one-electron model rather than an ab initio method for computing wave functions.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 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) | 0.005 | 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".