Bound-state properties of four-body muonic quasiatoms
Bibliographic record
Abstract
Total energies and various bound-state properties are determined for the ground states in all six four-body muonic ${a}^{+}{b}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ quasiatoms. These quasiatoms contain two nuclei of the hydrogen isotopes ${p}^{+},{d}^{+},{t}^{+}$, one negatively charged muon ${\ensuremath{\mu}}^{\ensuremath{-}}$, and one electron ${e}^{\ensuremath{-}}$. In general, each of the four-body muonic ${a}^{+}{b}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ quasiatoms, where $(a,b)=(p,d,t)$, can be considered as the regular one-electron (hydrogen) atom with the complex nucleus ${a}^{+}{b}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ that has a finite number of bound states. Furthermore, all properties of such quasinuclei ${a}^{+}{b}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ are determined from highly accurate computations performed for the three-body muonic ions ${a}^{+}{b}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ with the use of pure Coulomb interaction potentials between particles. It is shown that the bound-state spectra of such quasiatoms are similar to the spectrum of the regular hydrogen atom, but there are a few important differences. Such differences can be used in future experiments to improve the overall accuracy of current evaluations of various properties of hydrogenlike systems, including the lowest-order relativistic and quantum electrodynamics corrections to the total energies.
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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) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 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) | 0.010 | 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".