Measurement of the bound-state beta decay of 205Tl(81+): analysis scripts and figures

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 Analysis
The 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 Figures
The 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.nb' (again, a static PDF copy is provided). This notebook requires 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.