Transfer-matrix theory of surface spin-echo experiments with molecules
Bibliographic record
Abstract
$^{3}\mathrm{He}$ beam spin-echo experiments have been used to study surface morphology, molecular and atomic surface diffusion, phonon dispersions, phason dispersions, and phase transitions of ionic liquids. However, the interactions between $^{3}\mathrm{He}$ atoms and surfaces or their adsorbates are typically isotropic and weak. To overcome these limitations, one can use molecules instead of $^{3}\mathrm{He}$ in surface spin-echo experiments. The molecular degrees of freedom, such as rotation, may be exploited to provide additional insight into surfaces and the behavior of their adsorbates. Indeed, a recent experiment has shown that orthohydrogen can be used as a probe that is sensitive to the orientation of a Cu(115) surface [O. Godsi, G. Corem, Y. Alkoby, J. T. Cantin, R. V. Krems, M. F. Somers, J. Meyer, G.-J. Kroes, T. Maniv, and G. Alexandrowicz, Nat. Commun. 8, 15357 (2017)]. However, the additional degrees of freedom offered by molecules also pose a theoretical challenge: a large manifold of molecular states and magnetic-field-induced couplings between internal states. Here, we present a fully quantum-mechanical approach to model molecular surface spin-echo experiments and connect the experimental signal to the elements of the time-independent molecule-surface scattering matrix. We present a one-dimensional transfer-matrix method that includes the molecular hyperfine degrees of freedom and accounts for the spatial separation of the molecular wave packets due to the magnetic control fields. We apply the method to the case of orthohydrogen, show that the calculated experimental signal is sensitive to the scattering matrix elements, and perform a preliminary comparison to experiment. This paper sets the stage for Bayesian optimization to determine the scattering matrix elements from experimental measurements and for a framework that describes molecular surface spin-echo experiments to study dynamic surfaces.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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".