A practical solution of the Bethe equation in the energy range applicable to radiotherapy and radionuclide production
Bibliographic record
Abstract
While the dose deposition of charged hadrons has received much attention over the last decades starting in 1930 with the publication of the Bethe equation, there are still practical obstacles in implementing it in fields like radiotherapy and isotope production on cyclotrons. This is especially true if the target material consists of non-homogeneous materials, either consisting of a mixture of different elements or experiencing phase changes during irradiation. While Monte-Carlo methods have had great success in describing these more difficult target materials, they come at a computational cost, especially if the problem is time-dependent. This can greatly hinder optimal advancement in therapy and isotope targetry. Here, a regular perturbation method is used to solve the Bethe equation in the limit of small relativistic effects. Particular focus is given to incident energy level relevant to radionuclide production and radiotherapy applications, i.e. 10-200 MeV. We present a series solution for the range and dose distribution in terms of elementary functions, as opposed to special functions which will aid in uptake by practitioners.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 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".