NMR quadrupole liouvillians for arbitrary spin: Exact symbolic expressions and perturbation solutions
Bibliographic record
Abstract
Abstract The NMR of quadrupolar nuclei with half‐integer spins is almost always described by treating the quadrupole interaction with second‐order perturbation theory. The standard practice is to perturb the wave functions, then calculate the transitions. In this article, we elaborate on the so‐called direct method in which the transitions are calculated directly without the requirement of knowing the operators and the wavefunctions. The method is set up using a set of formulae giving fully symbolic expressions. First of all, this provides a convenient way for a full and exact numerical solution that goes beyond perturbation theory. The other possibility is that it allows us to see the effect of the quadrupole perturbation on the unperturbed transitions. The results are the same, as they must be, but this approach reveals a number of important symmetries. Perturbations will mix the unperturbed transitions, but despite the use of high‐order perturbation theory, the mixing is very simple, specific, and controlled by selection rules. This gives a clear physical picture of the physical basis of the effects of perturbation theory. The approach is systematic and general and is easily extended to an arbitrary half‐integral spin. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part 42A: 45–358, 2013.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".