Bibliographic record
Abstract
The critical nuclear charge Z c for a three-body quantum mechanical system consisting of positive and negative charges is the minimum charge for the system to remain in a bound state. This work presents a study of the critical nuclear charge for heliumlike systems with infinite nuclear mass, and also a range of the reduced mass up to 0.5. The results help us to resolve a discrepancy in the literature for the infinite mass case, and they are the first to study the dependence on reduced mass. It is found that Z c has a maximum at [Special characters omitted.] mM = 3525, which is intermediate between the atomic structure of helium, and the molecular structure of [Special characters omitted.] H+2 . Z c for the infinite mass case is found to be 0.911028267. This value is compatible with the result of Baker, et al, who found the upper bound for Z c to be 0.91103. However, it does not agree with other results in the literature. The understanding of the critical charge will bring us a deeper appreciation of the stability of a three-body system as a function of the reduced mass, correlation effects of coulombic potential and more importantly, the physics of a three-body quantum mechanical system.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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 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".