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High-resolution conversion electron spectroscopy of the 125I electron-capture decay

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Pith's one-line read High-resolution spectroscopy of the 125I decay finds a 50% shake probability for its conversion electrons, 2.5 times the single-configuration prediction, and yields nuclear parameters $\lambda=-1.2(6)$ and $|\delta|=0.015(2)$ for the…

desk verdict A careful new measurement that credibly updates λ and |δ| for 125Te; the 50% shake fraction is a rough estimate that needs an error budget. read the letter →

arxiv 1909.01523 v1 pith:YYK3RDT7 submitted 2019-09-04 nucl-ex physics.atom-ph

B.P.E. Tee , A.E. Stuchbery , M. Vos , J.T.H. Dowie , B.Q. Lee , M. Alotiby , I. Greguric , T. Kibedi This is my paper · ORCID
classification nucl-exphysics.atom-ph
keywords 125Ielectron-capturedecayconversionelectronspectroscopypenetrationparameterinternalcoefficientsE2/M1mixingratioshakeprobability125Teparticle-vibrationalmodel
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 reports high-resolution measurements of the conversion electrons emitted when the 35.5-keV excited state of $^{125}$Te is populated by electron capture in $^{125}$I. By fitting the measured $L$, $M$, and $N$ sub-shell intensities together with literature values, it extracts a penetration parameter $\lambda = -1.2(6)$ and an E2/M1 mixing ratio $|\delta| = 0.015(2)$ for the 35.5-keV transition. The small negative $\lambda$ means the nuclear-penetration correction to the internal conversion coefficients is under 4%. The line-shape analysis also finds that about 50% of the conversion-electron intensity sits in low-energy shake tails, more than twice the 20% single-configuration prediction. A sympathetic reader would care because the result sharpens a long-standing test of how nuclear currents enter internal conversion and because $^{125}$I is a widely used medical isotope whose Auger and conversion-electron yields are needed for dosimetry.

What carries the argument

The argument runs through two identities. First, the conversion coefficient of each sub-shell is written as $\alpha_i = \alpha_i(M1)(1+b_1(i)\lambda+b_2(i)\lambda^2)$ for the $M1$ part, combined with the $E2$ part through $|\delta|$; the coefficients $b_1,b_2$ come from Dirac-Hartree-Fock-Slater wavefunctions. Second, every conversion line is fitted with a Lorentzian core plus four Gaussians, with the three low-energy tail components' shifts, widths, and intensities fixed from the high-resolution $L_1$ line and then applied to all other lines. The tail areas are identified with shake electrons, whose energy distribution is tied to outer-shell binding energies by the Krause-Carlson relation. The fit uses the measured sub-shell intensity ratios plus literature conversion coefficients to constrain $\lambda$ and $\delta$ in a least-squares sense.

What would settle it

A coincidence experiment that detects a shake electron at the same time as the 35.5-keV conversion electron would separate true shake from surface-plasmon energy loss: if the low-energy tail does not require a second electron, the 50% shake assignment collapses. Likewise, if high-resolution spectra of the $L_1$, $M_1$, and $N_1$ lines, recorded with better statistics, demand different tail parameters for different shells, the common-tail assumption, and with it the fitted $\lambda$ and $|\delta|$, would need revision.

Watch

Extended reading notes

Core claim

The paper's central claim is that the high-resolution conversion-electron spectrum of the 35.5-keV $M1+E2$ transition in $^{125}$Te can be described by a common line shape whose low-energy tail is mostly atomic shake, and that with this line shape the measured sub-shell ratios, combined with earlier data, determine $\lambda = -1.2(6)$ and $|\delta| = 0.015(2)$. The fitted tail intensity corresponds to a shake probability of about 50%, which is 2.5 times the predicted value of 20% from single-configuration calculations. The magnitude of $\lambda$ is close to the value obtained by combining the particle-vibrational model's allowed penetration matrix elements with the experimental forbidden $M1$ gamma matrix element, while its negative sign contradicts the positive sign predicted by core-polarization theory.

Load-bearing premise

The analysis assumes that all conversion-electron lines share exactly the same low-energy tail shape, fixed from the $L_1$ line, and that this tail is mostly atomic shake rather than electrons that lost energy while leaving the source.

Editorial extensions

If this is right

  • The 35.5-keV transition's conversion coefficients deviate from the no-penetration values by less than 4%, so the earlier evaluation with a larger positive penetration anomaly is not supported.
  • The measured $|\delta|=0.015(2)$ agrees with the Kisslinger-Sörensen-model prediction, while the sign of $\delta$ remains undetermined by conversion-coefficient data alone.
  • The measured $L_1:M_1$ and $M_1:N_1$ ratios agree with theoretical internal conversion coefficients, confirming that the electrostatic spectrometer's transmission is effectively energy-independent over the measured range.
  • A shake probability near 50% means the low-energy tails carry as much intensity as the main conversion lines, so any absolute conversion-electron or Auger-yield determination for $^{125}$I must include this tail intensity.
  • For l-forbidden $M1$ transitions generally, the paper's analysis suggests that the magnitude of the penetration parameter can be estimated by combining a theoretical calculation of the allowed penetration matrix elements with the experimental forbidden $M1$ gamma matrix element.

Reading between the lines

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

  • If the common-tail assumption is checked and survives, the 50% shake fraction would be a direct experimental benchmark for correlation-inclusive shake calculations on open-shell atoms, not just for Te.
  • The negative sign of $\lambda$ in $^{125}$Te, taken with the signs reported for $^{121}$Te and $^{123}$Te, suggests that core-polarization theories giving a positive sign for these $\nu d_{3/2}\to\nu s_{1/2}$ transitions should be revisited; a high-resolution remeasurement of the other two isotopes at similar precision would test that pattern.
  • Because the published Auger yields for $^{125}$I are normalized through the conversion-electron intensities used in this paper, the shift from the older $\lambda=+2.4$, $|\delta|=0.029$ evaluation to the new values changes those absolute yields at the few-percent level, which matters for dosimetry models of this medical isotope.
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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

3 major / 5 minor

Summary. The paper reports high-resolution conversion-electron spectroscopy of the electron-capture decay of 125I, using an electrostatic spectrometer, to determine nuclear parameters of the 35.5-keV M1+E2 transition in 125Te and to study electron shake. The authors fit the present L1:L2:L3, M1:M2:M3, and M1:N1 intensity ratios together with literature ICC data and angular-correlation data using Eqs. (7)-(9), obtaining λ = -1.2(6) and |δ| = 0.015(2) with reduced χ² = 1.2. They also estimate the shake probability from the tail intensity of the conversion lines as about 50%, roughly 2.5 times the calculated value of about 20%, and compare the measured λ with particle-vibrational and other nuclear models.

Significance. If correct, the results provide a precise, small negative penetration parameter for an l-forbidden M1 transition, which is in tension with core-polarization predictions, and they suggest a large enhancement of shake probability in an open-shell atom. The work also underpins Auger-yield determinations for the medical isotope 125I. The paper is commendable for a transparent fitting procedure, a reduced χ² of 1.2, a transmission check using the L1:M1 ratio that is insensitive to λ and δ, and for exploring the effect of different natural-width databases in the line-shape fits. However, the central claims rest on two assumptions that need further scrutiny: the common-tail line-shape model and the post-hoc rejection of discrepant literature data.

major comments (3)
  1. [Section V.A, Table III, Eq. (9)] The least-squares fit excludes all literature values that are "more than two standard deviations away from the corresponding fitted values," including the four most precise angular-correlation determinations of δ (rows marked "c": +0.09(1), +0.095(25), +0.078(12), +0.08(3)). Because the fit is itself used to define the reference values, this exclusion is post-hoc and circular; it removes precisely the data that disagree with the fitted |δ| = 0.015(2). The paper should report the fit with these points included, or apply a pre-defined robust rejection criterion, and should discuss the physical tension between the ICC ratios and the angular-correlation δ values. This is load-bearing because |δ| is a central claimed result.
  2. [Section III, Table I, Section V.B, Eq. (8)] All conversion-electron lines are fitted with tail parameters fixed to the L1 line, based on the assumption that all conversion lines share the same tail distribution. The extracted peak areas for L2, L3, M2, M3, and N1 therefore depend on the L1 tail shape and on the assumption that shake probabilities are equal across subshells. These areas enter the determination of λ and |δ| via Eq. (8). The paper varies the natural-width database but never varies the tail shape or relaxes the common-tail constraint. A test that fits the tail parameters for at least the stronger lines independently, or a systematic variation of the tail shape (e.g., an asymmetric tail), is needed to bracket this systematic. Without it, the quoted uncertainties on λ and |δ| are not complete.
  3. [Section V.B] The 50% shake probability has no uncertainty and no systematic budget. It is computed directly as (0.4+0.5+0.2)/(1+0.4+0.5+0.2) from the fixed tail intensities. The paper itself acknowledges that (i) the large overlap between the broad tails and the main peak may overestimate the tail intensity and (ii) the symmetric Gaussian tail shape is not the expected asymmetric shake distribution (Ref. [57]). These caveats need to be quantified. In addition, the comparison value of about 20% is taken from Ref. [23], a co-author's PhD thesis; the prediction should be documented in a peer-reviewed source or reproduced in the paper, and the measured shake probability should be quoted with an error bar.
minor comments (5)
  1. [Section V.A] The reduced χ² = 1.2 is quoted without the number of degrees of freedom; please provide it to allow the reader to judge the fit quality.
  2. [Fig. 3 caption] The caption states "The reduced χ2 of the this fit is 1.9"; "the this" is a typo.
  3. [Section V.B] The text compares the tail shifts in Table I with the outer-shell binding energies, but tail #2 at -18 eV does not correspond directly to any of the listed N4/N5/O1/O2/O3 binding energies; a brief discussion of how the three discrete tail components map onto the expected shake distribution would be helpful.
  4. [Table III] The column headers "Calculated λ=+2.4a |δ|=0.029|δ|=0.015" are visually ambiguous; please clarify which column corresponds to which parameter set.
  5. [Section II] The phrase "the deviation was fairy constant" should read "fairly constant".

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: lambda and delta are least-squares fit parameters, and the 50% shake fraction is an empirical estimate compared with an independent benchmark, not derived from it.

full rationale

The central nuclear quantities are obtained by a standard least-squares fit: Eq. (7) and Eq. (8) combine experimental sub-shell ratios with theoretical alpha0(M1) and alpha0(E2) from BrIcc [25] and b1,b2 coefficients from CATAR [32], and MINUIT minimizes the chi-squared of Eq. (9). These theoretical coefficients are fixed external inputs; the fit returns lambda and |delta|. Nothing in these equations defines a target in terms of the fitting parameter; the experimental ratios are data, not outputs of the fit. The 50% 'measured shake probability' is read from the freely fitted tail intensities in Table I (0.4+0.5+0.2 fraction), after attributing the tails to intrinsic shake. It is not constrained to the 20% value of [23]; [23] is a single-configuration calculation used for comparison, and the paper explicitly notes that it omits electron-electron correlations and may underestimate the shake. The common-tail assumption for all conversion lines is an empirical modeling choice supported by the high-resolution L1 fit and by the similarity of calculated shake probabilities in [23]; even if this assumption is uncertain, as Section V.B concedes, uncertainty is not circularity. No equation in the paper reduces a predicted quantity to a fitted input or to a self-citation. The only self-citations ([10,11,23]) are methodological or comparative and do not carry the derivation of lambda, |delta|, or the 50% value.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The reported λ and |δ| are fitted outputs, not derived constants; the theoretical conversion coefficients and the assumed common tail shape are external inputs. No new particles, forces, or dimensions are introduced.

free parameters (3)
  • λ (penetration parameter) = -1.2(6)
    Output of least-squares fit to present and literature conversion-coefficient ratios via Eqs. (7)-(9); central reported result.
  • |δ| (E2/M1 mixing ratio) = 0.015(2)
    Fitted simultaneously with λ; only magnitude is constrained by conversion-electron data.
  • Tail component parameters (shift, relative intensity, width) = Tail1: -5 eV, 0.4, 8 eV; Tail2: -18 eV, 0.5, 24 eV; Tail3: -42 eV, 0.2, 55 eV
    Fitted to high-resolution L1 line and imposed on all conversion lines (Table I); these control extracted peak areas and the 50% shake estimate.
assumptions (5)
  • domain assumption BrIcc theoretical ICCs and CATAR penetration coefficients b1, b2 are correct.
    Eqs. (7)-(8) use these as fixed inputs to convert measured ratios into λ and δ; errors would shift the fitted values.
  • ad hoc to paper All conversion electron lines share the same tail distribution, taken from L1.
    Stated in Section III to minimize free parameters; underpins peak areas of weak L2, L3, M3, and N1 lines.
  • domain assumption The low-energy tails are dominated by intrinsic shake rather than extrinsic inelastic scattering.
    Section III expects surface plasmon probability of about 3%, so it treats tails as shake; Section V.B uses tail areas to estimate 50% shake probability.
  • domain assumption Signs of the calculated E2 and penetration matrix elements in the PV model are reliable.
    Used in Section V.A to deduce that the negative sign of λ is compatible with the positive mixing ratio; wrong signs would weaken the sign conclusion.
  • domain assumption PV model with ξ=3.0 and g_s^b = 0.6 g_s^free describes the 125Te states.
    Used for the theoretical λ comparison in Table IV; the model under-predicts B(M1) by about 50 times, so only the semi-empirical |λ|=0.8 is used for magnitude.

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Cite this review

Pith. "Pith review of High-resolution conversion electron spectroscopy of the 125I electron-capture decay." pith.science (2026). https://pith.science/paper/YYK3RDT7

@misc{pith2026190901523,
  author       = {Pith},
  title        = {Pith review of: High-resolution conversion electron spectroscopy of the 125I electron-capture decay},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YYK3RDT7}},
  note         = {Machine review of arXiv:1909.01523}
}
read the original abstract

The conversion electrons from the decay of the 35.5-keV excited state of 125Te following the electron capture decay of 125I have been investigated at high resolution using an electrostatic spectrometer. The penetration parameter lambda = -1.2(6) and mixing ratio |delta| = 0.015(2) were deduced by fitting to literature values and present data. The shake probability of the conversion electrons is estimated to be 0.5, more than two times larger than the predicted value of 0.2.

Figures

Figures reproduced from arXiv: 1909.01523 by the authors.

Figure 1
Figure 1. The 5/2 + ground state of 125I decays with an allowed EC transition to the 35.5-keV 3/2 + excited state in the 125Te daughter nucleus. The direct EC decay to the 1/2 + ground state of 125Te with a second forbidden ∆J = 2 transition is highly retarded; its probability is less than 1% of the total decay intensity [5]. To EC decay to the second excited state in 125Te at 144.775 keV and J π = 11/2 − would require a thir… view at source ↗
Figure 2
Figure 2. FIG. 2. Top panel: Layout of the electrostatic spectrometer [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Lower panel: The L1-CE spectrum measured at high resolution (200 eV fft ld)d ith fit btid entering into a decelerating lens system (close to ground [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: The spectrum of L1,L2 and L3 conversion lines recorded at low resolu￾tion (main power supply scanned and 1000 eV pass energy). The fit (red) of the L1 to L3-CE spectrum uses the line shape parameters of [PITH_FULL_IMAGE:figures/full_fig_p003_5.png]
Figure 3
Figure 3. Figure 3: FIG. 3. (a) The [PITH_FULL_IMAGE:figures/full_fig_p004_3.png]
Figure 4
Figure 4. Figure 4: FIG. 4. Spectra from three separate measurements in low-resolution mode: (a) [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Ratios of the experimental conversion coefficients to [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

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