Measurement of the bound-state beta decay of 205Tl(81+): analysis scripts and figures
Bibliographic record
Abstract
The scripts presented here are Monte Carlo half-life analysis for the measurement of the bound-state beta decay of 205Tl(81+), experiment G-20-0E121, that was performed at the Experimental Storage Ring (ESR) at the GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt (Germany) in the frame of FAIR Phase-0. The experimental measurement was done from the 26th March 2020 to 6th April 2020, whilst the analysis was developed over the course of 2020--2023. In addition, scripts for creating the figures for application to 205Pb in the early Solar System, namely the publication Leckenby et al. (2024) Nature 635:321–326, are also provided. The data used by these scripts is provided in the data release: DOI 10.5281/zenodo.11556665. Monte Carlo Half-life AnalysisThe Monte Carlo half-life analysis is provided in the Mathematica notebook 'final_halflife_MC-s6_clsd.nb' (a static PDF copy is provided for those without access to a Mathematica kernel). This notebook requires the input data file 'BSBD_205Tl-finals_vals.txt' from the data release and a supplementary input file 'SC_MC_vals.txt' provided here, both of which should be in the same directory as the notebook. The supplementary input file 'SC_MC_vals.txt' contains Monte Carlo sampled values for the Saturation Correction parameter, which was not automated due to formatting complexities. The notebook contains 4 sections:1. Monte Carlo Error Analysis - this section runs the main Monte Carlo analysis and produces an N-dimensional array of best fit parameters for both λβb and R0.2. Analyse Results - this section produces helpful plots and does the half-life calculation correctly.3. Missing Exp Uncertainty - this section estiamtes the contamination variation from the observed missing stochastic uncertainty in the chi squared.4. Uncertainty Components - this section records the results of MC runs that isolated specific sources of uncertainties and evaluates the fractional contribution to the final uncertainty. 205Pb in the early Solar System FiguresThe code used to create the figures for the publication Leckenby et al. (2024) Nature 635:321–326 are provided in the Mathematica notebook `isolation_time_figures-Mathematica.nb' and in the Python Jupiter notebook as well `isolation_time_figures-Python.ipynb' (again, a static PDF copy is provided). Both notebooks require the input files `mcHist-box_1e8_1e10-gamma_X-tau_Y.dat' files, which are found in the `SLR_abund_MC_hists.tar.gz' repository. These files encode the Monte Carlo results described in Côté et al. (2019) ApJ 887(2):213 to simulate the stochastic variation of the radioactive abundance in the interstellar medium. Kernel densities are used to describe Monte Carlo distributions to create smooth probability distribution functions. V2.0 Updates from Chinese Physics C PaperV2.0 of this analysis release includes refined edits to 'final_halflife_MC-s6_clsd.nb' from an additional paper we published in Chinese Physics C: Leckenby et al. (2025) Chinese Physics C 49:114001. This paper further refined the Monte Carlo analysis by explicitly handling the Poisson counting statistics rather than implicitly including them in the unquantified uncertainty. The final half-life result changes miniminally, but it is clearer what components come from counting statistics and which from contamination variation. Additionally P. Kanizsai has kindly translated the isolation time figures notebook into a Python Jupiter notebook for further accessibility.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 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".