Electron emission characteristics in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi><mml:mo>−</mml:mo><mml:mi mathvariant="normal">H</mml:mi><mml:mn/><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mi>s</mml:mi><mml:mo>)</mml:mo><mml:mn/></mml:math>collisions from numerical solutions of the time-dependent Schrödinger equation
Bibliographic record
Abstract
The numerical integration of the three-dimensional time-dependent Schr\"odinger equation that appears in the impact-parameter approximation is carried out using a Fourier collocation method that is based on a splitting technique for the time evolution operator. The final wave function is analyzed in momentum space using a histogram approach. Singly and doubly differential cross sections for ionization as a function of polar emission angle and energy are calculated near the maximum in the total cross section, i.e., at 50--60-keV impact energy. They compare well with recent experimental results for intermediate and high electron emission energies, while some discrepancies remain at low energies due to the neglect of residual Coulomb interactions in the ionized wave packet. In order to achieve convergence and to reproduce experimental results at electron energies below 20 eV one needs to extend the calculations to final internuclear separations beyond 30 a.u.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.002 | 0.003 |
| Meta-epidemiology (broad) | 0.001 | 0.004 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.003 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.012 | 0.004 |
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; both teacher heads agree on what is shown here.
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".