Revisiting dipolar relaxation of a homonuclear spin pair in the presence of a radio frequency field: A tutorial
Bibliographic record
Abstract
NMR studies exploit spin relaxation in a multitude of different ways, providing information on molecular structure and dynamics. Calculating the relaxation rates of NMR active nuclei in multi-spin systems is often a prerequisite for the proper analysis of experimental data. For many researchers the calculations appear complex, often involving different basis sets or expressions describing relaxation in different frames. In this tutorial paper we derive expressions for dipolar relaxation of an I-S two spin spin-system in the presence of a B1 radio frequency field, where spins I and S can be either like or unlike. We consider two different approaches for the derivation of relaxation elements that have been used in the literature, including one where a series of transformations are carried out to the interaction representation of the effective field, comprising B1 and Zeeman components. A second procedure is based on the well-known Solomon equations. We show that both approaches lead to identical results, in the process presenting a pedagogical description of relaxation theory.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.005 | 0.005 |
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".