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REVIEW 4 major objections 7 minor 51 references

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

T0 review · 4 major / 7 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read A five-species coupled-equation model validated against co-circulating mercury and lead decay curves supports a bound-state beta decay half-life $T_{1/2} = 291^{+33}_{-27}$ days for fully ionized $^{205}\mathrm{Tl}$ and a 97% stripping…

desk verdict Solid modelling framework for storage-ring decay curves, but the new no-overlap claim and the scaling-based rates are softer than the text suggests; the half-life is the authors' own published value. read the letter →

arxiv 2506.04784 v1 pith:P7WYTTZ2 submitted 2025-06-05 nucl-ex physics.atom-ph

R. J. Chen , G. Leckenby , R. S. Sidhu , J. Glorius , M. S. Sanjari , Yu. A. Litvinov , F. C. Akinci , M. Bai
show 44 more authors
K. Blaum F. Bosch C. Brandau T. Dickel I. Dillmann D. Dmytriiev T. Faestermann O. Forstner B. Franczak B. S. Gao H. Geissel R. Gernhäuser C. Griffin A. Gumberidze E. Haettner R. He{ss} P.-M. Hillenbrand P. Kienle W. Korten Ch. Kozhuharov N. Kuzminchuk S. Litvinov E. Menz T. Morgenroth C. Nociforo F. Nolden N. Petridis U. Popp S. Purushothaman R. Reifarth C. Scheidenberger U. Spillmann M. Steck Th. Stöhlker Y. K. Tanaka M. Trassinelli S. Trotsenko L. Varga M. Wang H. Weick P. J. Woods T. Yamaguchi Y. Zhang J. Zhao
This is my paper
classification nucl-exphysics.atom-ph
keywords bound-statebetadecayheavy-ionstorageringhighlychargedionscharge-changingreactionsdifferentialequationmodel205Tlhalf-life
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper claims that the decay curves of several ion species stored simultaneously in a heavy-ion storage ring can be described by a small set of coupled linear differential equations that include bound-state $\beta$ decay, electron capture, and electron ionization. Using the recent $^{205}\mathrm{Tl}^{81+}$ bound-state $\beta$ decay experiment at the ESR, the authors show that fitting these equations to the well-sampled decay curve of the co-circulating $^{200}\mathrm{Hg}^{80+}$ ions, and scaling the resulting rates to the $^{205}\mathrm{Pb}$ system by known $Z$-dependences, reproduces all measured parent and daughter curves. The fit implies that radiative recombination with cooler electrons dominates the storage-stage loss of $^{205}\mathrm{Pb}^{81+}$, that the argon gas jet strips 97% of the $^{205}\mathrm{Pb}^{81+}$ daughters to the 82+ charge state, and that the fully ionized 82+ ions never overlapped with the gas jet. With these background processes under control, the paper re-derives the bound-state $\beta$ decay rate $\lambda^{\mathrm{c.m.}}_{\beta_b} = 2.76(28)\times10^{-8}$ s$^{-1}$, corresponding to a half-life of $T_{1/2} = 291^{+33}_{-27}$ days. The wider claim is that this framework makes mechanical scraping of the storage ring unnecessary for such measurements, simplifying future half-life studies of highly charged ions.

What carries the argument

The central object is a system of five coupled linear ordinary differential equations (equations (2)–(6)) for the ion numbers $N(t_s)$ of $^{205}\mathrm{Tl}^{81+}$, $^{205}\mathrm{Pb}^{81+}$, $^{205}\mathrm{Pb}^{82+}$, $^{205}\mathrm{Tl}^{80+}$, and $^{205}\mathrm{Pb}^{80+}$, with rate parameters for $\beta$ decay ($\lambda_{\beta_b}$), electron capture (recombination, $\lambda_{\mathrm{cap}}$), and electron ionization (stripping, $\lambda_{\mathrm{str}}$). The system is solved analytically and numerically, and its power comes from closure with the co-circulating mercury ions: the far better-sampled decay curve of $^{200}\mathrm{Hg}^{80+}$ fixes the free parameters, and the scaling relations $\sigma_{\mathrm{REC,NRC}} \propto Z^5$ and $\sigma_{\mathrm{str}} \propto Z^2$, together with the measured capture-to-stripping ratio $C_R = 1.425(14)$, convert those mercury rates into $^{205}\mathrm{Pb}$ rates. A time-delay shift for daughter ions, taken from the $^{200}\mathrm{Hg}^{80+}$ curve, aligns the simulation with the data before the $\beta$ decay rate is extracted.

What would settle it

A dedicated measurement of the charge-changing cross sections of $^{200}\mathrm{Hg}^{79+}$ and $^{205}\mathrm{Pb}^{81+}$ ions passing through an argon gas jet at the same energy (400 MeV/u), with a charge-state-resolved detector downstream of the target, would directly test the $Z^5$ and $Z^2$ scalings of equations (11)–(13) and the transfer of $C_R = 1.425(14)$ from a $^{206}\mathrm{Pb}^{81+}$ beam. If the measured capture-to-stripping ratios for the two species disagree with the scaled predictions by more than the assigned 10% systematic uncertainty, the inferred 97% stripping efficiency, the non-overlap of the 82+ ions with the gas jet, and consequently the 291-day half-life would have to be revised.

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Extended reading notes

Core claim

The paper's central claim is that the coupled differential equations (2)–(6) accurately simulate the decay curves of the simultaneously stored ions $^{205}\mathrm{Tl}^{81+}$, $^{205}\mathrm{Pb}^{81+}$, $^{205}\mathrm{Pb}^{82+}$, $^{200}\mathrm{Hg}^{79+}$, and $^{200}\mathrm{Hg}^{80+}$, including the feeding and depleting effects of bound-state $\beta$ decay, electron capture, and electron ionization. By fitting the well-populated $^{200}\mathrm{Hg}^{80+}$ curve and transferring the fitted rates to the $^{205}\mathrm{Pb}$/$^{205}\mathrm{Tl}$ system via $Z^5$ scaling for electron capture and $Z^2$ scaling for ionization (equations (11)–(13)), with the capture-to-stripping ratio $C_R = 1.425(14)$ measured on a $^{206}\mathrm{Pb}^{81+}$ beam, the simulations reproduce the experimental curves over the full storage and stripping stages. The author's conclusion is that radiative recombination is the primary loss mechanism of $^{205}\mathrm{Pb}^{81+}$ during storage ($\lambda^A_{\mathrm{cap}}(\mathrm{^{205}Pb^{81+}}) = 3.99(10)\times10^{-5}$ s$^{-1}$ while stripping is only $\lambda^A_{\mathrm{str}}(\mathrm{^{205}Pb^{81+}}) = 1.52(15)\times10^{-6}$ s$^{-1}$), that the gas jet strips about 97% of the $^{205}\mathrm{Pb}^{81+}$ ions to the 82+ charge state, and that the fully ionized $^{205}\mathrm{Pb}^{82+}$ and $^{200}\mathrm{Hg}^{80+}$ ions do not overlap with the gas jet, since their capture rates track the electron cooler current rather than the gas target density. Applying these validated parameters to the parent/daughter ratio at the end of storage yields a center-of-mass $\beta$ decay rate $\lambda^{\mathrm{c.m.}}_{\beta_b} = 2.76(28)\times10^{-8}$ s$^{-1}$ and a half-life $T_{1/2} = 291^{+33}_{-27}$ days, establishing that a stable neutral $^{205}\mathrm{Tl}$ atom becomes radioactive when fully stripped of its electrons.

Load-bearing premise

The whole analysis hinges on the assumption that the electron capture and ionization rates for the $^{205}\mathrm{Pb}$ ions are obtained from the fitted $^{200}\mathrm{Hg}$ rates by simple $Z^5$ and $Z^2$ scaling, with the capture-to-stripping ratio measured on a $^{206}\mathrm{Pb}^{81+}$ beam ($C_R = 1.425$) applying unchanged to $^{205}\mathrm{Pb}^{81+}$ and $^{200}\mathrm{Hg}^{79+}$; if those scalings are wrong, the 97% stripping efficiency, the no-overlap conclusion, and the extracted half-life all lose support.

Editorial extensions

If this is right

  • Radiative recombination with cooler electrons is the dominant loss for $^{205}\mathrm{Pb}^{81+}$ during storage ($\lambda^A_{\mathrm{cap}} = 3.99(10)\times10^{-5}$ s$^{-1}$ versus stripping at $1.52(15)\times10^{-6}$ s$^{-1}$), so the simplified ratio method of Eq. (1) is adequate for the half-life analysis of this experiment.
  • The argon gas jet strips about 97% of the $^{205}\mathrm{Pb}^{81+}$ daughters to the resolvable $^{205}\mathrm{Pb}^{82+}$ charge state, confirming that the stripping-stage counting of daughters is efficient.
  • Because the capture rates of the fully ionized $^{205}\mathrm{Pb}^{82+}$ and $^{200}\mathrm{Hg}^{80+}$ track the electron cooler current (ratio of capture rates across stages $\approx 5.13$ for a tenfold current increase), the gas jet did not overlap with the 82+ ion orbits, so the stripping stage did not deplete the ions it was designed to count.
  • The framework removes the need for mechanical scrapers in future electron-capture and beta-decay experiments in storage rings, providing a simpler path to half-life measurements at facilities such as FAIR's ILIMA programme.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The strategy of using a co-circulating stable contaminant as an in-situ calibrant could be generalized: intentionally co-storing a well-understood ion species with a similar mass-to-charge ratio would map the ring's gas density, cooler current, and target overlap for every run without extra detectors.
  • The $Z^5/Z^2$ scaling transfer is only tested indirectly through the global fit; a dedicated cross-section measurement of $^{200}\mathrm{Hg}^{79+}$ and $^{205}\mathrm{Pb}^{81+}$ on argon at 400 MeV/u would either harden the quoted half-life or reveal that its systematic uncertainty is larger than reported.
  • A physical model of the observed cooling-time delays (449 s in storage, 37 s in stripping) as a function of velocity offset and cooler current would improve the extraction of beta decay rates for shorter-lived ions, where the time delay is a larger fraction of the lifetime.
  • Because the equations are linear in ion numbers, the same framework can incorporate additional charge states and other atomic processes (for example dielectronic recombination) without changing its structure, which would be useful for denser gas targets or heavier ions.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 7 minor

Summary. This manuscript presents a coupled linear ODE model (Eqs. 2–6) for the populations of 205Tl81+, 205Pb81+, 205Pb82+, 205Tl80+, and 205Pb80+ ions stored simultaneously in the ESR during the recent 205Tl81+ bound-state β-decay experiment, including βb decay, electron capture (recombination), and ionization (stripping). Analytical solutions are given in Appendix A and a SymPy code in Appendix B. Because 200Hg79+/80+ contaminants are stored at similar m/q, the authors fit the free charge-changing rates of the 200Hg system to the measured decay curves (Fig. 6), transfer them to 205Tl/205Pb via Z^5 (capture) and Z^2 (ionization) scaling (Eqs. 11–16), and compare the simulated curves with data after applying per-dataset daughter-ion time delays (Sec. 5.1). The paper claims accurate simulation of the decay curves, a 97% stripping efficiency for 205Pb81+ during the gas-jet stage, and that the Ar gas jet did not overlap the fully ionized 205Pb82+ and 200Hg80+ beams. In Sec. 5.3 it quotes λc.m.βb = 2.76(28)×10^-8 s^-1 (T1/2 = 291+33−27 d), obtained with the simplified formula Eq. (1).

Significance. If the claims were fully supported, the paper would provide a valuable, reusable framework: a closed set of ODEs with analytical solutions and machine-readable code, the use of stable co-stored contaminants as rate calibrants, and a cross-check of the approximations underlying the simplified ratio formula Eq. (1) used in earlier storage-ring βb analyses. The calibrant idea is genuinely useful for future ILIMA/FAIR decay experiments, and the 205Pb82+ curves in Fig. 6(c,d) are, in part, predictions from the scaled 200Hg parameters rather than direct fits, which is a strength. Credit is due for shipping the code, presenting analytical solutions, and giving a physically sensible description of the dominant atomic processes. The load-bearing steps, however, are weaker than the text implies: the agreement is visual only, the free parameters are fitted to the same 200Hg curves, the no-overlap conclusion is an interpretation of a single ratio that the model cannot actually test, Table 1 and the text contain several mutually inconsistent rate values, and the quoted half-life is an input of the simulation obtained with the same simplified formula as in refs.

major comments (4)
  1. [§5.3 (no-overlap claim)] The conclusion that the Ar gas jet did not overlap the fully ionized 205Pb82+ and 200Hg80+ beams is based on λB_cap205Pb82+/λA_cap205Pb82+ ≈ 5.1 'showing the same trend' as the cooler-current ratio IB/IA = 10. This inference is underdetermined. Writing the storage-stage rate as λA = x + r (20-mA cooler plus residual-gas terms) and the stripping-stage rate as λB = 10x + r + g (200-mA cooler, same residual gas, gas-jet contribution g), the observed ratio 5.1 is consistent with g = 0 only if the residual-gas contribution is comparable to the 20-mA cooler contribution (r ≈ x), and it is equally consistent with substantial positive g for other (x, r) combinations; the factor-of-2 gap between 5.1 and 10 is never explained. Equations (2)–(6) contain no gas-jet-overlap parameter for the fully ionized species, so the no-overlap statement is not a fitted or tested result of the model. Because this assumption justifies neglecting the recapture of 205Pb82+ to 205Pb81+ during the stripping stage (which directly affects the daughter count entering the λβb analysis), the claim needs an explicit test — e.g., fitting an overlap parameter and showing it is consistent with zero, or a quantitative bound from the measured gas-jet density — or it should be explicitly downgraded to a consistency argument with stated residual-gas assumptions.
  2. [Table 1 vs. §5.3 text] The numbers supporting the central claims are internally inconsistent. The text quotes λB_cap205Pb82+ = 2.26(23)×10^-4 s^-1 twice, while Table 1 lists 2.43(24)×10^-4 s^-1; the stated ratio λB/λA ≈ 5.13 is reproduced by neither (2.26/4.45 = 5.08; 2.43/4.45 = 5.46). Similarly, λB_str205Pb81+ = 6.32(63)×10^-3 s^-1 in the text is consistent with Eq. (12) applied to Table 1's λB_str200Hg79+ = 6.01(60)×10^-3 s^-1, but Table 1 lists 6.80(68)×10^-3 s^-1, and λA_str205Pb81+ appears as 1.52(15)×10^-6 s^-1 in the text versus 1.64(16)×10^-6 s^-1 in Table 1. Also, Table 1's λB_cap205Pb81+ = 2.65(27)×10^-3 s^-1 does not equal (82/80)^5 × λB_cap200Hg79+ = 2.86×10^-3 s^-1 from Eq. (11). Since the ≈5.1 ratio and the 97% stripping efficiency are derived from these values, the table and text must be reconciled before the quantitative claims can be assessed.
  3. [§5.3, Fig. 6 (validation quality)] The central claim that the equations 'accurately simulate the decay curves' rests on a single dataset with a purely visual comparison. The parameters λA_str200Hg79+, λB_cap200Hg79+, and λB_cap200Hg80+ are free parameters fitted to the 200Hg80+ curve; no residuals or goodness-of-fit quantities are reported; the daughter-ion time delays of 449 s and 37 s are hand-calibrated per dataset for 200Hg80+ and transferred to 205Pb82+ without uncertainties; and a uniform 10% systematic error is attached to the remaining parameters. With this much freedom, agreement with one dataset cannot discriminate between the model and alternatives such as a model with gas-jet overlap of the fully ionized species. The manuscript should report the fit procedure, parameter uncertainties, residuals, and ideally a comparison on an independent dataset, or consistently describe the comparison as illustrative rather than quantitative (the abstract currently says 'quantitative comparison').
  4. [§5.3, Appendix B (role of λβb)] The λβb value quoted in the paper is an input of the simulation, not an output. The code in Appendix B and the analytical solutions use the previously published laboratory-frame λβb = 1.93×10^-8 s^-1 from refs. [6,7,25] to compute the 205Tl81+ and 205Pb81+ curves, and the 'determination' in §5.3 recomputes λc.m.βb = 2.76(28)×10^-8 s^-1 using the simplified formula Eq. (1) — the same method and value as the original analysis. The agreement in Fig. 6 is therefore a consistency check of the charge-changing rates given the published decay constant, not an independent validation or determination of that constant. The title and abstract should be aligned with this (for example, 'validating the background model used for the half-life determination'), and the text should state explicitly which quantities are input and which are fitted.
minor comments (7)
  1. [§4] The 200Hg79+/80+ rate equations are never written out, although the abstract and §4 claim the framework simulates these ions and they are the calibrants on which the fits are based; writing them out would allow the reader to verify the boundary conditions and to see explicitly that no gas-jet-overlap parameter appears.
  2. [Eqs. (3) and (26)] Equation (3) contains a typo, 'λcap 205Pb82+ × N205Pb82 (ts)', which is missing the charge subscript '+', and Eq. (26) contains a formatting artifact, 'N205textTl 81+ (0)'.
  3. [Fig. 6 caption] The caption reads 'string stages' where it should read 'stripping stages'.
  4. [§5.2, Eqs. (7) and (11)] The stage label 'A/B' in Eqs. (11)–(13) is misleading: λA_cap205Pb81+ = 3.99(10)×10^-5 s^-1 is obtained in Eq. (7) from the RR ratio, whereas Eq. (11) would give 4.30×10^-5 s^-1 from λA_cap200Hg79+ with Z^5 scaling; if Eqs. (11)–(13) are intended only for the stripping stage, say so explicitly.
  5. [§5.1] The daughter-ion delay times (449 s and 37 s) are stated without uncertainties and without a discussion of how an uncertainty of, say, 10% in the 449 s delay propagates into the fitted rates and into the final ratio 5.1; an estimate of this systematic effect is needed.
  6. [References [21] and [39]] Reference [21] is an incomplete citation (URL only, no publication details), and reference [39] contains a corrupted fragment in the author list ('Yu.A. Leta decay of highly charged ions.nd P. Moritz'); both should be corrected.
  7. [Appendix B] The hard-coded values in the code (e.g., 4.33×10^-5, 4.44×10^-5, 1.52×10^-6) do not exactly match Table 1 (4.34(6)×10^-5, 4.45(6)×10^-5, 1.64(16)×10^-6), and the snippet uses ROOT's TF1 without importing it; the code should be updated to the final Table 1 values so it reproduces the figures as published.

Circularity Check

1 steps flagged · score 4.0 of 10

The half-life reported in Sec. 5.3 is the already-published value hard-coded into the Appendix B simulations; the differential-equation framework itself is not circular.

  1. self citation load bearing [Section 5.3 and Appendix B]
    "Finally, for the determination of the βb decay constant for fully ionized 205Tl ions, the ratio of the parent (205Tl81+) and daughter (205Pb82+) ions was evaluated at the end of the storage stage. Using equation 1, βb decay rate in the center of mass frame was determined to be λc.m.βb = γλβb = 2.76(28)×10−8 s−1 ... More details on the data analysis can be found in [6,7,25,45,50]."

    The ODE code in Appendix B hard-codes λβb = 1.93e-8 s−1, which is exactly 2.76e-8/γ for the 400 MeV/u beam (γ≈1.43). The half-life 'determined' in Sec. 5.3 is therefore the same value that was inserted as an input to the model used for the simulations. The extraction formula, Eq. (1), is taken from the old simplified analysis, and the detailed data analysis is referred to the same authors' earlier papers [6,7,25,45,50]. Thus the claimed half-life output is not produced by the new differential-equation framework; it is a restatement of the already-published value, which the simulations had already assumed.

full rationale

The new content of the paper—the coupled ODE system (2)-(6) and the comparison of its solutions with the measured 200Hg and 205Pb decay curves—is not circular. The equations are a genuine model, and the 200Hg fit plus Z-scaling to 205Pb is a testable physical assumption rather than a by-construction identity: the 205Pb82+ data could in principle disagree with the scaled rates. I therefore do not treat the stripping efficiency or the no-gas-jet-overlap inference as circular, although they are model-dependent and rest on the fitted 200Hg rates and the CR transfer. The one clear self-referential step is the half-life. Appendix B supplies the published λβb as an input to the simulation, and Section 5.3 then reports the same value (converted to the center-of-mass frame) as a determination, with the actual analysis deferred to the same authors' prior papers. This is a presentation-of-known-result issue rather than a mathematical derivation of the half-life from the new framework; the independent measurement lives in [6,7]. Hence the central modeling claim retains independent content, but the 'determination' is a self-citation-restated output. Score 4.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The model relies on scaling factors and theory estimates to convert measured rates for one species into rates for another. The central conclusions (97% stripping, no gas-jet overlap, half-life support) depend on these assumptions and on the free parameters fitted to the 200Hg curves. No new particles or physical entities are introduced.

free parameters (5)
  • λA_str200Hg79+ (storage-stage stripping rate of 200Hg79+) = 1.45(15)×10^-6 s^-1
    Free parameter fitted to the 200Hg80+ decay curve; anchors the stripping rate that is then scaled to 205Pb81+ via (82/80)^2.
  • λB_cap200Hg79+ (stripping-stage capture rate of 200Hg79+) = 2.53(25)×10^-3 s^-1
    Free parameter fitted to the 200Hg80+ curve; via eqs (11) and (14) sets λB_cap205Pb81+ and λB_str200Hg79+.
  • λB_cap200Hg80+ (stripping-stage capture rate of 200Hg80+) = 2.15(22)×10^-4 s^-1
    Free parameter fitted to the 200Hg80+ curve; via eq (13) sets λB_cap205Pb82+, which underpins the no-gas-jet-overlap conclusion.
  • Daughter-ion time delay (storage stage) = 449 s
    Calibrated from the 200Hg80+ curve and applied to 205Pb82+; time alignment affects the visual comparison in Fig. 6.
  • Daughter-ion time delay (stripping stage) = 37 s
    Same calibration approach; applied to 205Pb82+ in the stripping stage.
assumptions (6)
  • domain assumption Electron-capture (recombination) rate scales as Z^5 and ionization rate scales as Z^2 for interactions with the Ar gas jet (eqs 11-13).
    Scaling laws from [31,47,48] are assumed to transfer measured 200Hg rates to 205Pb without in-paper validation for these relativistic ions.
  • domain assumption The RR recombination-rate ratio for 205Pb81+ to 205Tl81+ is given by theory (RR ratio 0.92(2)) (eq 7).
    The absolute storage-stage loss rate of the daughter is anchored to this theoretical ratio rather than to a direct measurement.
  • domain assumption The capture-to-stripping cross-section ratio CR = 1.425(14) measured with a 206Pb81+ beam applies to 205Pb81+ and 200Hg79+ (eqs 14-16).
    The key parametrization of the stripping stage is transferred from a neighboring isotope without direct measurement for the species of interest.
  • domain assumption The beam consists of the stated species with 205Pb81+ contamination at the quoted level (Sec. 3).
    Initial conditions of the ODEs; text states 0.1% but the code in Appendix B uses 1.73e-3 (0.173%).
  • domain assumption Electron cooling equalizes velocities so that orbits are determined by m/q and charge-changed ions either drift to new orbits or leave the acceptance (Sec. 2, Sec. 5.1).
    This is the basis for the time-delay treatment and for which species are considered stored or lost.
  • domain assumption The only nuclear decay of 205Tl81+ considered is βb to 205Pb81+; continuum β- decay to 205Pb82+ is neglected (eqs 2-6).
    The equations have no 205Tl81+ -> 205Pb82+ branch; the paper does not assess the continuum branch quantitatively here, which is consistent with its small Q-value but is not explicitly justified.

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Cite this review

Pith. "Pith review of Half-life determination of heavy ions in a storage ring considering feeding and depleting background processes." pith.science (2026). https://pith.science/paper/P7WYTTZ2

@misc{pith2026250604784,
  author       = {Pith},
  title        = {Pith review of: Half-life determination of heavy ions in a storage ring considering feeding and depleting background processes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/P7WYTTZ2}},
  note         = {Machine review of arXiv:2506.04784}
}
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.

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Works this paper leans on

51 extracted references · 41 canonical work pages

  1. [1]

    Litvinov, F

    Yu.A. Litvinov, F. Bosch, Beta decay of highly charged ions. Reports on Progress in Physics 74(1), 016301 (2011). https://doi. org/10.1088/0034-4885/74/1/016301

    work page doi:10.1088/0034-4885/74/1/016301 2011

  2. [2]

    Litvinov, Thomas Stöhlker, Nuclear physics with unstable ions at storage rings

    Fritz Bosch, Yuri A. Litvinov, Thomas Stöhlker, Nuclear physics with unstable ions at storage rings. Prog. Part. Nucl. Phys. 73, 84–140 (2013). https://doi.org/10.1016/j.ppnp.2013. 07.002.U R L http://www.sciencedirect.com/science/article/pii/ S0146641013000744

    work page doi:10.1016/j.ppnp.2013 2013

  3. [4]

    Najafi, I

    M.A. Najafi, I. Dillmann, F. Bosch, T. Faestermann, B. Gao, R. Gernhäuser, C. Kozhuharov, S.A. Litvinov, Yu.A. Litvinov, L. Maier, F. Nolden, U. Popp, M.S. Sanjari, U. Spillmann, M. Steck, T. Stöhlker, H. Weick, CsI-Silicon Particle detector for Heavy ions Orbiting in Storage rings (CsISiPHOS). Nuclear Instruments and Methods in Physics Research Section A:...

    work page doi:10.1016/j.nima.2016.08.040 2016

  4. [6]

    Sidhu, G

    R.S. Sidhu, G. Leckenby, R.J. Chen, R. Mancino, et al. Bound- state beta decay of 205Tl81+ ions and the LOREX project. Physical Review Letters, (2024). URLhttps://journals.aps.org/prl/accepted/ 3307eY92Fff1599711197443b14781dbdec3b8d06. accepted

    work page 2024

  5. [7]

    Leckenby, R.S

    G. Leckenby, R.S. Sidhu, R.J. Chen, R. Mancino et al., High- temperature 205Tl decay clarifies 205Pb dating in early Solar Sys- tem. Nature (2024). https://doi.org/10.1038/s41586-024-08130-4

    work page doi:10.1038/s41586-024-08130-4 2024

  6. [8]

    Sidhu, Yu.A

    R.S. Sidhu, Yu.A. Litvinov, et al. Influence of hyperfine interaction on the nuclear electron capture decay in 111Sn, (2022). Proposal for GSI Program Advisory Committee

    work page 2022

  7. [9]

    Griffin, I

    C. Griffin, I. Dillmann, et al. Symbiotic measurement of masses, half-lives, and neutron branching ratios of 137,138Ia tt h eE S R (2022). Proposal for GSI Program Advisory Committee

    work page 2022

  8. [10]

    Litvinov et al

    Yu.A. Litvinov et al. Nuclear excitation by electron capture (NEEC) measurements using the ESR electron cooler as a target for free electrons (2020). Proposal for GSI Program Advisory Committee

    work page 2020

Show all 51 references
  1. [11]

    Korten et al

    W. Korten et al. Nuclear two-photon decay and bound-state pair conversion, (2022). Proposal for GSI Program Advisory Commit- tee

    2022

  2. [12]

    Brandau et al

    C. Brandau et al. Laser excitation of the 229Th nucleus using nuclear hyperfine mixing, (2020). Proposal for GSI Program Advisory Committee

    2020

  3. [13]

    Daudel, M

    R. Daudel, M. Jean, M. Lecoin, Sur la possibilité d’existence d’un type particulier de radioactivité phénomène de création e. Journal de Physique et Le Radium 8(8), 238–243 (1947). https://doi.org/ 10.1051/jphysrad:0194700808023800

    1947 doi

  4. [14]

    Bahcall, Theory of Bound-State Beta Decay

    John N. Bahcall, Theory of Bound-State Beta Decay. Physical Review 124, 495–499 (1961). https://doi.org/10.1103/PhysRev. 124.495

    1961 doi

  5. [15]

    Litvinov, R.J

    Yu.A. Litvinov, R.J. Chen, Radioactive decays of stored highly charged ions. The European Physical Journal A59(5), 102 (2023). https://doi.org/10.1140/epja/s10050-023-00978-w

    2023 doi

  6. [16]

    M. Jung, F. Bosch, K. Beckert, H. Eickhoff, H. Folger, B. Franzke, A. Gruber, P. Kienle, O. Klepper, W. Koenig et al., First observation of bound-state β − decay. Physical Review Letters 69, 2164–2167 (1992). https://doi.org/10.1103/PhysRevLett.69.2164

    1992 doi

  7. [17]

    Bosch, T

    F. Bosch, T. Faestermann, J. Friese, F. Heine, P. Kienle, E. Wefers, K. Zeitelhack, K. Beckert, B. Franzke, O. Klepper et al., Obser- vation of Bound-State β − Decay of Fully Ionized 187Re: 187Re- 187Os Cosmochronometry. Physical Review Letters77, 5190–5193 (1996). https://doi...

    1996 doi

  8. [18]

    URLhttps://www.nndc.bnl

    National Nuclear Data Center: NNDC. URLhttps://www.nndc.bnl. gov/

  9. [19]

    Ohtsubo, F

    T. Ohtsubo, F. Bosch, H. Geissel, L. Maier, C. Scheidenberger, F. Attallah, K. Beckert, P. Beller, D. Boutin, T. Faestermann et al., Simultaneous Measurement of β − Decay to Bound and Contin- uum Electron States. Physical Review Letters 95, 052501 (2005). https://doi.org/10.11...

    2005 doi

  10. [20]

    Bambynek, H

    W. Bambynek, H. Behrens, M.H. Chen, B. Crasemann, M.L. Fitz- patrick, K.W.D. Ledingham, H. Genz, M. Mutterer, R.L. Intemann, Orbital electron capture by the nucleus. Reviews of Modern Physics 49(1), 77 (1977). https://doi.org/10.1103/RevModPhys.49.77

    1977 doi

  11. [21]

    Kurcewicz, F

    J. Kurcewicz, F. Bosch, H. Geissel, Yu.A. Litvinov, K. Beck- ert, P. Beller, D. Boutin, C. Brandau, L. Chen, T. Faestermann, et al. Direct Observation of Bound-State β- Decay of Fully Ionized 205Hg. URL https://www.mll-muenchen.de/forschung/ kernspektroskopie/kurcewicz_gsi_205hg.pdf

  12. [22]

    Freedman, C.M

    M.S. Freedman, C.M. Stevens, E.P. Horwitz et al., Solar Neutrinos: Proposal for a New Test. Science 193(4258), 1117–1119 (1976). https://doi.org/10.1126/science.193.4258.1117

    1976

  13. [23]

    Pavi´cevi´c, G

    M.K. Pavi´cevi´c, G. Amthauer, V . Cvetkovi´c et al., Lorandite from Allchar as geochemical detector for pp-solar neutrinos. Nuclear Instruments and Methods in Physics Research Section A: Accel- erators, Spectrometers, Detectors and Associated Equipment 895, 62–73 (2018). http...

    2018 doi

  14. [24]

    Meyer, D.D

    B.S. Meyer, D.D. Clayton, Short-Lived Radioactivities and the Birth of the sun. Space Science Reviews 92(1), 133–152 (2000). https://doi.org/10.1023/A:1005282825778

    2000 doi

  15. [25]

    R.S. Sidhu. Thesis, Ruprecht-Karls-Universität Heidelberg, (2021). URL https://archiv.ub.uni-heidelberg.de/volltextserver/ 30275/

    2021

  16. [27]

    D. Möhl, G. Petrucci, L. Thorndahl, S. van der Meer, Physics and technique of stochastic cooling. Physics Reports 58(2), 73–102 (1980). ISSN 0370-1573. URL https://www.sciencedirect.com/ science/article/pii/0370157380901404

    1980

  17. [28]

    Pajek, R

    M. Pajek, R. Schuch, Total radiative recombination rates for ions interacting with electrons from an electron cooler. Nuclear Instru- ments and Methods in Physics Research Section B: Beam Inter- actions with Materials and Atoms 93(3), 241–248 (1994). ISSN 0168-583X. URL https:...

    1994

  18. [29]

    Yu Tolstikhina, V .P

    I. Yu Tolstikhina, V .P. Shevelko, Collision processes involving heavy many-electron ions interacting with neutral atoms. Physics- Uspekhi 56(3), 213 (2013). https://doi.org/10.3367/UFNe.0183. 201303a.0225

    2013 doi

  19. [30]

    Y .L. Xue, X. Cai, D. Yu, J. Shao, F.F. Ruan, D.J. Qi, M.W. Zhang, W. Wang, Loss mechanisms and lifetimes of heavy ion beams in HIRFL-CSRe. Journal of Physics: Conference Series 163(1), 012075 (2009). https://doi.org/10.1088/1742-6596/163/1/012075

    2009 doi

  20. [31]

    Eichler, Th

    J. Eichler, Th. Stöhlker, Radiative electron capture in relativis- tic ion-atom collisions and the photoelectric effect in hydrogen- like high-Z systems. Physics Reports 439(1), 1–99 (2007). ISSN 0370-1573. URL https://www.sciencedirect.com/science/article/ pii/S037015730600442X

    2007

  21. [32]

    Litvinov, F

    Yu.A. Litvinov, F. Bosch, H. Geissel, J. Kurcewicz, Z. Patyk, N. Winckler, L. Batist, K. Beckert, D. Boutin, C. Brandau et al., Mea- surement of the β + and Orbital Electron-Capture Decay Rates in Fully Ionized, Hydrogenlike, and Heliumlike 140Pr Ions. Physi- 123 Eur. Phys. J....

    2025

  22. [33]

    Winckler, H

    N. Winckler, H. Geissel, Yu.A. Litvinov, K. Beckert, F. Bosch, D. Boutin, C. Brandau, L. Chen, C. Dimopoulou, H.G. Essel et al., Orbital electron capture decay of hydrogen- and helium-like 142Pm ions. Physics Letters B 679(1), 36–40 (2009). https://doi.org/10. 1016/j.physletb....

    2009

  23. [34]

    Glorius, C

    J. Glorius, C. Langer, Z. Slavkovská, L. Bott, C. Brandau, B. Brück- ner, K. Blaum, X. Chen, S. Dababneh, T. Davinson et al., Approach- ing the Gamow Window with Stored Ions: Direct Measurement of 124Xe(p,γ ) in the ESR Storage Ring. Physical Review Letters 122(9), 092701 (201...

    2019 doi

  24. [35]

    Kienle, F

    P. Kienle, F. Bosch, P. Bühler, T. Faestermann, Yu.A. Litvinov, N. Winckler, M.S. Sanjari, D.B. Shubina, D. Atanasov, H. Geissel et al., High-resolution measurement of the time-modulated orbital electron capture and of the β + decay of hydrogen-like 142Pm60+ ions. Physics Lett...

    2013 doi

  25. [36]

    Litvinov, F

    Yu.A. Litvinov, F. Bosch, N. Winckler, D. Boutin, H.G. Essel, T. Faestermann, H. Geissel, S. Hess, P. Kienle, R. Knöbel et al., Observation of non-exponential orbital electron capture decays of hydrogen-like 140Pr and142Pm ions. Physics Letters B664(3), 162– 168 (2008). https:...

    2008 doi

  26. [37]

    Geissel, K

    H. Geissel, K. Beckert, F. Bosch, H. Eickhoff, B. Franczak, B. Franzke, M. Jung, O. Klepper, R. Moshammer, G. Münzenberg, F. Nickel, F. Nolden, U. Schaaf, C. Scheidenberger, P. Spädtke, M. Steck, K. Sümmerer, A. Magel, First storage and cooling of secondary heavy-ion beams at ...

    1992

  27. [38]

    Meshkov, Storage and cooling of ion beams

    I. Meshkov, Storage and cooling of ion beams. Physica Scripta 2015(T166), 014037 (2015). https://doi.org/10.1088/0031-8949/ 2015/T166/014037

    2015 doi

  28. [39]

    Nolden, P

    F. Nolden, P. Hülsmann, Yu.A. Leta decay of highly charged ions.nd P. Moritz, C. Peschke, P. Petri, M.S. Sanjari, M. Steck, H. Weick, J.X. Wu, Y .D. Zang, S.H. Zhang, T.C. Zhao. A fast and sensitive resonant Schottky pick-up for heavy ion storage rings. Nuclear Instruments and...

    2011

  29. [40]

    Sanjari, P

    M.S. Sanjari, P. Hülsmann, F. Nolden, A. Schempp, J.X. Wu, D. Atanasov, F. Bosch, C. Kozhuharov, Yu.A. Litvinov et al., A reso- nant Schottky pickup for the study of highly charged ions in storage rings. Physica Scripta2013(T156), 014088 (2013).https://doi.org/ 10.1088/0031-89...

    2013 doi

  30. [41]

    Klepper, C

    O. Klepper, C. Kozhuharov, Particle detectors for beam diag- nosis and for experiments with stable and radioactive ions in the storage-cooler ring ESR. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Mate- rials and Atoms 204, 553–556 (200...

    2003

  31. [42]

    Wang, W.J

    M. Wang, W.J. Huang, F.G. Kondev, G. Audi, S. Naimi, The AME 2020 atomic mass evaluation (II). Tables, graphs and references. Chinese Physics C 45(3), 030003 (2021). https://doi.org/10.1088/ 1674-1137/abddaf

    2021

  32. [43]

    Kondev, M

    F.G. Kondev, M. Wang, W.J. Huang, S. Naimi, G. Audi, The NUBASE2020 evaluation of nuclear physics properties. Chi- nese Physics C 45(3), 030001 (2021). https://doi.org/10.1088/ 1674-1137/abddae/meta

    2021

  33. [44]

    Kramida, Yu

    A. Kramida, Yu. Ralchenko, J. Reader. Atomic Spectra Database. National Institute of Standards and Technology, Gaithersburg, MD, (2023). URL https://physics.nist.gov/asd

    2023

  34. [45]

    Leckenby, R.S

    G. Leckenby, R.S. Sidhu, R.J. Chen, Yu.A. Litvinov, J. Glorius, C. Griffin, I. Dillmann, and the E121 Collaboration. Analysis methods to determine the bound-state beta-decay half-life of Thallium-205. EPJ Web of Conferences 279, 06010 (2023). https://doi.org/10. 1051/epjconf/20...

    2023

  35. [46]

    Reeg et al

    H. Reeg et al. The beam current transformers at SIS and ESR. GSI Scientific Report, pp. 392 (1991). URL https://repository.gsi.de/ record/53540

    1991

  36. [47]

    Kaganovich, Edward A

    Igor D. Kaganovich, Edward A. Startsev, Ronald C. Davidson, Steve R. Kecskemeti, Amitai Bin-Nun, Dennis Mueller, Larry Grisham, Rand L. Watson, Vladimir Horvat, Konstantinos E. Zaharakis et al., Ionization cross-sections for ion–atom collisions in high-energy ion beams. Nuclea...

    2005 doi

  37. [48]

    Kaganovich, Edward Startsev, Ronald C

    Igor D. Kaganovich, Edward Startsev, Ronald C. Davidson, Scaling and formulary of cross-sections for ion–atom impact ionization. New Journal of Physics8(11), 278 (2006).https://doi.org/10.1088/ 1367-2630/8/11/278

    2006

  38. [49]

    Trageser

    C. Trageser. Thesis, der Justus-Liebig-Universität Gießen, (2018). doi:https://doi.org/10.22029/jlupub-9788

    2018 doi

  39. [50]

    Leckenby

    G. Leckenby. Thesis (in preparation), (2024)

    2024

  40. [51]

    Atanasov, N

    D.R. Atanasov, N. Winckler, D. Balabanski, L. Batist, F. Bosch, D. Boutin, C. Brandau, C. Dimopoulou, H.G. Essel, T. Faestermann et al., Half-life measurements of stored fully ionized and hydrogen- like 122I ions. Eur. Phys. J. A48, 22 (2012).https://doi.org/10.1140/ epja/i201...

    2012

  41. [52]

    Ozturk, B

    F.C. Ozturk, B. Akkus, D. Atanasov, H. Beyer, F. Bosch, D. Boutin, C. Brandau, P. Bühler, R.B. Cakirli, R.J. Chen et al., New test of modulated electron capture decay of hydrogen-like 142Pm ions: Precision measurement of purely exponential decay. Phys. Lett. B 797, 134800 (201...

    2019

  42. [53]

    Steck, Yu.A

    M. Steck, Yu.A. Litvinov, Heavy-ion storage rings and their use in precision experiments with highly charged ions. Progress in Par- ticle and Nuclear Physics 115, 103811 (2020). https://doi.org/10. 1016/j.ppnp.2020.103811

    2020

  43. [54]

    Walker, Yu.A

    P.M. Walker, Yu.A. Litvinov, H. Geissel, The ILIMA project at F A I R .I n t .J .M a s sS p e c t r o m .349–350, 247–254 (2013).https://doi. org/10.1016/j.ijms.2013.04.007.U R L http://www.sciencedirect. com/science/article/pii/S1387380613001334 123

    2013 doi

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