Bayesian and Monte Carlo approaches to estimating uncertainty for the measurement of the bound-state <i>β</i> <sup>-</sup> decay of <sup>205</sup>Tl<sup>81+</sup> *
Abstract The measurement of the bound-state decay of 205 Tl at the Experimental Storage Ring (ESR) at GSI, Darmstadt, has recently been reported, with substantial impact on the use of 205 Pb as an early Solar System chronometer and on the low-energy measurement of the solar neutrino spectrum via the LOREX project. Owing to the technical challenges in producing a high-purity 205 Tl 81+ secondary beam, a robust statistical method was developed to estimate the variation in the contaminant 205 Pb 81+ produced in the fragmentation reaction, which was subsequently transmitted and stored in the ESR. Here, we show that Bayesian and Monte Carlo methods produce comparable estimates for the contaminant variation, each with unique advantages and challenges given the complex statistical problems for this experiment. We recommend the adoption of such methods in future experiments that exhibit unknown statistical fluctuations.
Authors
- B. S. Gao (ORCID: https://orcid.org/0000-0002-7911-3950)
- R. S. Sidhu (ORCID: https://orcid.org/0000-0002-1637-7502)
- N. Petridis (ORCID: https://orcid.org/0000-0002-2629-4727)
- R. Heß (ORCID: https://orcid.org/0000-0003-1239-2585)
- Rui Jiu Chen (ORCID: https://orcid.org/0000-0001-6283-8958)
- O. Forstner (ORCID: https://orcid.org/0000-0003-3636-4669)
- C. Brandau (ORCID: https://orcid.org/0000-0001-8825-8820)
- Yu. A. Litvinov (ORCID: https://orcid.org/0000-0002-7043-4993)
- E. Haettner (ORCID: https://orcid.org/0000-0002-5057-9853)
- R. Reifarth (ORCID: https://orcid.org/0000-0002-3855-5816)
- D. Dmytriiev (ORCID: https://orcid.org/0000-0003-3612-2686)
- U. Spillmann (ORCID: https://orcid.org/0000-0001-7281-5063)
- W. Korten (ORCID: https://orcid.org/0000-0002-3940-0816)
- T. Faestermann (ORCID: https://orcid.org/0000-0002-6603-8787)
- C. Scheidenberger (ORCID: https://orcid.org/0000-0003-3409-0350)
- M. Trassinelli (ORCID: https://orcid.org/0000-0003-4414-1801)
- E. Menz (ORCID: https://orcid.org/0000-0003-1451-7089)
- H. Weick (ORCID: https://orcid.org/0000-0003-3672-1961)
- M. Wang (ORCID: https://orcid.org/0000-0003-2408-8089)
- I. Dillmann (ORCID: https://orcid.org/0000-0001-8521-3635)
- L. Varga
- Th. Stöhlker (ORCID: https://orcid.org/0000-0003-0461-3560)
- G. Leckenby (ORCID: https://orcid.org/0000-0001-5002-763X)
- P.‐M. Hillenbrand (ORCID: https://orcid.org/0000-0003-0166-2666)
- C. Kozhuharov (ORCID: https://orcid.org/0000-0001-9487-5681)
- Y. Tanaka (ORCID: https://orcid.org/0000-0002-6622-5179)
- B. Franczak (ORCID: https://orcid.org/0009-0002-0580-5871)
- J. Glorius (ORCID: https://orcid.org/0000-0003-1785-3221)
- H. Geißel (ORCID: https://orcid.org/0000-0002-9656-1819)
- S. Purushothaman (ORCID: https://orcid.org/0000-0003-0526-4913)
- Yu-Hu 张玉虎 Zhang
- Alex Gumberidze
- F. Nolden
- T. Morgenroth
- T. Dickel (ORCID: https://orcid.org/0000-0002-5965-8689)
- Chris Griffin (ORCID: https://orcid.org/0009-0009-3937-6834)
- R. Gernhäuser (ORCID: https://orcid.org/0000-0003-1778-4262)
- Jianwei Zhao (ORCID: https://orcid.org/0000-0001-9566-2178)
- Mei Bai (ORCID: https://orcid.org/0000-0002-2012-1235)
- M. Steck (ORCID: https://orcid.org/0000-0001-5754-738X)
- Ulrich Popp
- Chiara Nociforo
- Phil Woods
- Sergey Litvinov
- Sergiy Trotsenko
- Takayuki Yamaguchi (ORCID: https://orcid.org/0000-0001-5176-6792)
- Paul Kienle
- M.S Sanjari
- Fritz Bosch
- N. Kuzminchuk
Institutions
- Goethe University Frankfurt (DE)
- Helmholtz Institute Jena (DE)
- Centre National de la Recherche Scientifique (FR)
- TRIUMF (CA)
- Los Alamos National Laboratory (US)
- University of British Columbia (CA)
- Université de Bordeaux (FR)
- GSI Helmholtz Centre for Heavy Ion Research (DE)
- University of Cologne (DE)
- Justus-Liebig-Universität Gießen (DE)
- University of Victoria (CA)
- Commissariat à l'Énergie Atomique et aux Énergies Alternatives (FR)
- Université Paris-Saclay (FR)
- Deutsches Elektronen-Synchrotron DESY (DE)
- University of Surrey (GB)
- Sorbonne Université (FR)
- RIKEN (JP)
- Laboratoire de Physique des deux infinis Bordeaux (FR)
- CEA Paris-Saclay (FR)
- Institut des NanoSciences de Paris (FR)
- Institut de Recherche sur les Lois Fondamentales de l'Univers (FR)
- Technical University of Munich (DE)
- Saitama University (JP)
- Friedrich Schiller University Jena (DE)
- University of Edinburgh (GB)
Publication Details
- Journal
- Chinese Physics C
- Published
- 2025-06-29
- DOI
- https://doi.org/10.1088/1674-1137/ade956
- Primary Topic
- Atomic and Subatomic Physics Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Deutsche Forschungsgemeinschaft
- Natural Sciences and Engineering Research Council of Canada
- HORIZON EUROPE European Research Council