Half-life determination of heavy ions in a storage ring considering feeding and depleting background processes
Bibliographic record
Abstract
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 $$^{205}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>205</mml:mn> </mml:mmultiscripts> </mml:math> Tl $$^{81+}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mrow> <mml:mn>81</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:mmultiscripts> </mml:math> 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: $$^{205}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>205</mml:mn> </mml:mmultiscripts> </mml:math> Tl $$^{81+}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mrow> <mml:mn>81</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:mmultiscripts> </mml:math> , $$^{205}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>205</mml:mn> </mml:mmultiscripts> </mml:math> Pb $$^{81+}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mrow> <mml:mn>81</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:mmultiscripts> </mml:math> , $$^{205}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>205</mml:mn> </mml:mmultiscripts> </mml:math> Pb $$^{82+}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mrow> <mml:mn>82</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:mmultiscripts> </mml:math> , $$^{200}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>200</mml:mn> </mml:mmultiscripts> </mml:math> Hg $$^{79+}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mrow> <mml:mn>79</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:mmultiscripts> </mml:math> , and $$^{200}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>200</mml:mn> </mml:mmultiscripts> </mml:math> Hg $$^{80+}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mrow> <mml:mn>80</mml:mn> <mml:mo>+</mml:mo> </mml:mrow> </mml:mmultiscripts> </mml:math> . 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.
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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 | 0.000 | 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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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".