Polarizabilities and other properties of the td<i>µ</i> molecular ion
Bibliographic record
Abstract
Wave functions of the Hylleraas type were used earlier to calculate energy levels of muonic systems. Recently, we found in the case of the molecular ions H 2 + , D 2 + , and HD + that it was necessary to include high powers of the internuclear distance in the Hylleraas functions to localize the nuclear motion when treating the ions as three-body systems without invoking the BornOppenheimer approximation. We tried the same approach in a muonic system, tdµ (triton, deuteron, and muon). Improved convergence was obtained for J = 0 and 1 states for shorter expansions when we used this type of generalized Hylleraas function, but as the expansion length increased the high powers were no longer useful. We obtained good energy values for the two lowest J = 0 and 1 states and compared them with the best earlier calculations. Expectation values were obtained for various operators, the Fermi contact parameters, and the permanent quadrupole moment. The cusp conditions were also calculated. The polarizability of the ground state was then calculated using second-order perturbation theory with intermediate J = 1 pseudostates. (It should be possible to measure the polarizability by observing Rydberg states of atoms with tdµ acting as the nucleus.) In addition, the initial sticking probability (an essential quantity in the analysis of muon catalyzed fusion) was calculated and compared with earlier results. PACS Nos.: 30.00, 36.10-k, 02.70-c
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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".