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.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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".