Bibliographic record
Abstract
The time evolution of the muon spin in fully anisotropic muonium $(\mathrm{Mu}={\ensuremath{\mu}}^{+}{+e}^{\ensuremath{-}})$ in the presence of Heisenberg spin exchange has been investigated theoretically. First, the energy levels of anisotropic Mu as a function of field are investigated analytically with a particular emphasis on the crossing and avoidance of energy levels at certain magnetic fields, which have important consequences in muon spin dynamics. Second, the knowledge of the energy levels is applied to investigate the muon spin depolarization due to electron spin exchange with spin-$\frac{1}{2}$ paramagnetic species, where the muon spin depolarization rate and the precession amplitude observed by the muon-spin-rotation (\ensuremath{\mu}SR) technique are explicitly expressed solely in terms of the matrix that diagonalizes the anisotropic Mu hyperfine Hamiltonian. The treatment presented here represents a special systematic and practical method that allows one to investigate the time evolution of the muon spin in anisotropic Mu in the presence of electron spin exchange. Several concrete examples are discussed in detail, including those in which all the \ensuremath{\mu}SR observables can be obtained analytically. The method developed in this work is used to explain the relaxation rate maximum in anisotropic Mu in semiconductors observed at the longitudinal fields at which two of the Mu energy levels avoid each other due to a strong level mixing or avoidance, where the present formalism takes the tensor nature of the anisotropic hyperfine interaction fully into account without invoking the convenient but not necessarily correct notion of an effective magnetic field in an anisotropic Mu. Also discussed is the possibility of observing additional relaxation maximum at a low-avoidance field, where the effective magnetic-field approximation completely breaks down. Observation of such a maximum will provide valuable information on the parameters characterizing the anisotropic Mu in question. The formalism presented here can also be applied to anisotropic positronium on surfaces, anisotropic Mu undergoing both charge exchange and spin exchange, and fast spin exchange.
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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) | 0.001 | 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".