Eur. Phys. J. A (2025) 61: 130
https://doi.org/10.1140/epja/s10050-025-01597-3

Regular Article - Experimental Physics

Half-life determination of heavy ions in a storage ring considering feeding and depleting background processes

¹ GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, 64291, Darmstadt, Germany
² CAS Key Laboratory of High Precision Nuclear Spectroscopy, 730000, Lanzhou, China
³ Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117, Heidelberg, Germany
⁴ TRIUMF, 4004 Wesbrook Mall, BC V6T 2A3, Vancouver, Canada
⁵ Department of Physics and Astronomy, University of British Columbia, BC V6T 1Z1, Vancouver, Canada
⁶ School of Physics and Astronomy, The University of Edinburgh, EH9 3FD, Guildford, UK
⁷ School of Mathematics and Physics, University of Surrey, GU2 7XH, Guildford, UK
⁸ Helmholtz Forschungsakademie Hessen für FAIR (HFHF), GSI Helmholtzzentrum für Schwerionenforschung GmbH, Campus Darmstadt, 64291, Darmstadt, Germany
⁹ Institut für Kernphysik, Universität zu Köln, Zülpicher Str. 77, D-50937, Köln, Germany
¹⁰ Department of Physics, Istanbul University, 34134, Istanbul, Turkey
¹¹ Justus-Liebig Universität Giessen, Leihgesterner Weg 217, 35392, Gießen, Germany
¹² Physik Department E12, Technische Universität München, D-85748, Garching, Germany
¹³ IRFU, CEA, Université Paris-Saclay, 91191, Gif-sur-Yvette, France
¹⁴ J.W. Goethe Universität, 60438, Frankfurt, Germany
¹⁵ Helmholtz Forschungsakademie Hessen für FAIR (HFHF), GSI Helmholtzzentrum für Schwerionenforschung GmbH, Campus Gießen, 35392, Gießen, Germany
¹⁶ Helmholtz Institute Jena, 07743, Jena, Germany
¹⁷ Institute of Optics and Quantum Electronics, Friedrich Schiller University, 07743, Jena, Germany
¹⁸ High Energy Nuclear Physics Laboratory, RIKEN, Wako, 351-0198, Saitama, Japan
¹⁹ Institut des NanoSciences de Paris, CNRS, Sorbonne Université, Paris, France
²⁰ Saitama University, 338-8570, Saitama, Japan

^a r.chen@gsi.de

Received: 27 October 2024
Accepted: 12 May 2025
Published online: 3 June 2025

Abstract

Heavy-ion storage rings have relatively large momentum acceptance which allows for multiple ion species to circulate at the same time. This needs to be considered in radioactive decay measurements of highly charged ions, where atomic charge exchange reactions can significantly alter the intensities of parent and daughter ions. In this study, we investigate this effect using the decay curves of ion numbers in the recent $_{}^{205}$Tl$_{}^{81+}$ bound-state beta decay experiment conducted using the Experimental Storage Ring at GSI Darmstadt. To understand the intricate dynamics of ion numbers, we present a set of differential equations that account for various atomic and nuclear reaction processes—bound-state beta decay, atomic electron recombination and capture, and electron ionization. By incorporating appropriate boundary conditions, we develop a set of differential equations that accurately simulate the decay curves of various simultaneously stored ions in the storage ring: $_{}^{205}$Tl$_{}^{81+}$, $_{}^{205}$Pb$_{}^{81+}$, $_{}^{205}$Pb$_{}^{82+}$, $_{}^{200}$Hg$_{}^{79+}$, and $_{}^{200}$Hg$_{}^{80+}$. Through a quantitative comparison between simulations and experimental data, we provide insights into the detailed reaction mechanisms governing stored heavy ions within the storage ring. Our approach effectively models charge-changing processes, reduces the complexity of the experimental setup, and provides a simpler method for measuring the decay half-lives of highly charged ions in storage rings.