Nonvariational and nonadiabatic calculations on the hydrogen molecular ion and its µ <sup></sup> isotopes
Bibliographic record
Abstract
A nonadiabatic, nonvariational, and computationally inexpensive scheme to describe bound and continuum states of three-body molecular ions, including µ -mesonic ions, is proposed. The method relies on treating perturbatively the nonadiabatic coupling between the BornOppenheimer (BO) particle states and nuclear motion terms, such that the appropriate expansion parameter is the mass ratio of the lightest particle in the system to that of the heaviest one. In practice, the method requires solving, numerically, a system of coupled inhomogeneous Schrödinger equations with effective potentials that depend on the "internuclear" separation, R, and allow for the mixing of BO states because of nonadiabatic terms in the Hamiltonian. The utility of our approach is clearly evidenced by the results of the numerical calculations carried out for rovibrational states of several lowest J in the H + 2 and (ppµ ) molecules. These demonstrate that nonadiabatic eigenenergies and eigenstates, both of the bound and scattering type, for ordinary as well as µ-mesonic molecules can be directly and quite accurately calculated from the same principles in the entire range of R, without making use of the variational techniques that more sophisticated studies of this kind are usually based on. PACS Nos.: 31.15Ar, 31.15Pf
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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".