Muonic–electronic quasi molecules based on a fully stripped multicharged ion
Bibliographic record
Abstract
In our previous paper (Can. J. Phys. 91, 715 (2013) doi: 10.1139/cjp-2013-0077 ) we studied a system consisting of a proton, a muon, and an electron; the muon and the electron being in circular states. The study was motivated by numerous applications of muonic atoms and molecules, where one of the electrons is substituted by the heavier lepton μ–. We demonstrated that in such a μpe quasi molecule, the muonic motion can represent a rapid subsystem while the electronic motion can represent a slow subsystem — a result that may seem counterintuitive. In other words, the muon rapidly revolves in a circular orbit about the axis connecting the proton and electron while this axis slowly rotates following a relatively slow electronic motion. We showed that the spectral lines, emitted by the muon in the quasi molecule, μpe, experience a red shift compared to the corresponding spectral lines that would have been emitted by the muon in a muonic hydrogen atom. In the present paper we generalize this study by replacing the proton in the μpe quasi molecule by a fully stripped ion of nuclear charge Z > 1. We show that in this case, just as in the previously studied case of Z = 1, the muonic motion can represent a rapid subsystem while the electronic motion can represent a slow subsystem. For this to be valid, the ratio of the muonic and electronic angular momenta should be slightly greater than in the case of Z = 1. We demonstrate that the binding energies of the muon for Z > 1 are much greater than for Z = 1 at any finite value of the nucleus–electron distance. Finally we show that the red shift of the spectral lines emitted by the muon (compared to the spectral lines of the corresponding muonic hydrogen-like ion of nuclear charge Z) decreases as Z increases. However, the relative red shift remains within the spectral resolution of available spectrometers at least up to Z = 5. Observing this red shift should be one of the ways to detect the formation of the quasi molecules, μZe.
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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 | 0.000 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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".