New shell-model calculations of the $\delta_C$ correction to superallowed $0^+\rightarrow0^+$ nuclear $\beta$ decay and standard-model implications

F. Nowacki; L. Xayavong; N. A. Smirnova

REVIEW 3 major objections 3 minor 59 references

New shell-model calculations of the $\delta_C$ correction to superallowed $0^+\rightarrow0^+$ nuclear $\beta$ decay and standard-model implications

T0 review · 3 major / 3 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Improved shell-model correction gives |V_ud| = 0.97359(33)

desk verdict A serious refinement of the δ_C2 shell-model correction with useful new numbers, but the final |V_ud| claim leans on an understated δ_C1 problem that the abstract itself flags. read the letter →

arxiv 2508.18189 v1 pith:KBVCRA6P submitted 2025-08-25 nucl-th

L. Xayavong , N. A. Smirnova , F. Nowacki This is my paper

classification nucl-th

keywords superallowedbetadecayV_udCKMunitarityshellmodelradialmismatchcorrectionWoods-Saxonpotentialchargeradiiisospinsymmetrybreaking

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 presents refined shell-model calculations of the radial mismatch correction δ_C2 in superallowed 0+→0+ nuclear beta decay. By calibrating Woods-Saxon radial wave functions to measured separation energies and to charge radii through a generalized formula using spectroscopic factors, the authors obtain a new average ℱt value of 3073.11 s and a corresponding |V_ud| of 0.97359(33). The main exception to earlier results is ¹⁸Ne, where δ_C2 is about a factor of two smaller; reductions also appear for A≥38 but within the new error bars. If correct, this shifts the Cabibbo-Kobayashi-Maskawa matrix element relevant to unitarity tests.

What carries the argument

The load-bearing device is the radial mismatch correction δ_C2, computed from shell-model wave functions built on realistic Woods-Saxon radial orbitals. Its two calibration handles are: (i) the potential depth is adjusted so that the single-particle energies reproduce separation energies to the (A−1) intermediate states, and (ii) the potential length is fixed by charge radii evaluated through a generalized formula in which proton occupation numbers are replaced by sums of spectroscopic factors. A surface diffuseness uncertainty of ±0.1 fm is propagated into the error budget.

What would settle it

Measure the ¹⁸Ne superallowed ft value precisely and compute its radial mismatch with an independent method (e.g., ab initio nuclear structure); if the independent result disagrees with this paper's factor-of-two smaller δ_C2, the calibration procedure fails.

Watch

Extended reading notes

Core claim

The central claim is that the radial mismatch correction δ_C2 can be computed more reliably by treating the Woods-Saxon single-particle well as the source of radial wave functions, with its depth matched to the measured separation energies of the intermediate (A−1) states and its length parameter constrained by charge radii evaluated from sums of spectroscopic factors rather than simple occupation numbers. This calibration, combined with untruncated configuration-mixing shell-model calculations, yields a new averaged ℱt value of 3073.11(99)_stat(36)_δ_R'(173)_δ_NS s and |V_ud| = 0.97359(33). The result for ¹⁸Ne, where δ_C2 is halved, is the most striking consequence of the updated charge-rad

Load-bearing premise

The whole result rests on the assumption that the Woods-Saxon well, calibrated to separation energies and to charge radii via the generalized spectroscopic-factor formula, produces radial wave functions accurate enough for the mismatch correction; if that calibration is wrong, the central numbers shift.

Editorial extensions

If this is right

A new recommended average ℱt value of 3073.11(99)(36)(173) s for superallowed 0+→0+ decays.
A shift in |V_ud| to 0.97359(33), which feeds directly into Cabibbo-Kobayashi-Maskawa unitarity tests.
For ¹⁸Ne, the radial mismatch correction is reduced by roughly a factor of two, changing its measured ℱt.
For most nuclides with A≥38, δ_C2 is reduced, though the changes stay inside the newly assigned errors.
The isospin-mixing correction δ_C1 is shown to follow an approximate inverse-square law in the energy separation of the lowest admixed levels, indicating that isobaric displacement energies need independent calibration.

Reading between the lines

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

The factor-of-two change in ¹⁸Ne signals that other superallowed emitters with poorly constrained charge radii or spectroscopic-factor sums could see similarly large revisions; the paper's own error bars may understate this sensitivity.
The inverse-square law identified for δ_C1 could, if confirmed, be used to predict isospin-mixing corrections for superallowed emitters where the relevant admixed levels are not directly measurable.
The method's dependence on spectroscopic factors suggests a natural cross-check: compare its predicted single-particle occupancies against transfer-reaction data.
A new experimental measurement of the ¹⁸Ne ft value would directly discriminate between the old and new δ_C2.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The paper does real work on the radial mismatch correction δ_C2 for superallowed beta decay. The improvements are concrete: charge radii are constrained through a generalized formula using spectroscopic factors, Woods–Saxon depths are matched to separation energies, the diagonalizations are truncation-free, and diffuseness is now varied as an uncertainty. That is a credible way to tighten the radial wave functions, and the resulting δ_C2 values for most nuclei land close to earlier studies, which is a good sanity check. The 18Ne factor-of-two change is the one outlier and is tied to the charge-radius treatment; it is the kind of thing you want explained in the text before you trust the rest.

The soft spot is the one the abstract itself exposes. δ_C1 is strongly interaction-dependent, and the authors say an additional procedure to enforce isobaric displacements is indispensable. But the headline average Ft and |V_ud| are presented as resulting from the δ_C2 calculation. If the quoted numbers use δ_C1 from somewhere else without the indispensable procedure, then the central |V_ud| and its uncertainty are not actually supported by this paper. That is a load-bearing gap, and it is self-identified rather than an external quibble. The calibration to charge radii and separation energies also means the correction is not fully independent of fitted inputs, though that is normal for this kind of nuclear-structure work and does not by itself sink the method.

I have not seen the full text, only the abstract, so I cannot say whether the gap is closed there. The right move is to referee the full paper and explicitly check: (1) what was done for δ_C1 and whether the averaged Ft uses it, (2) the 18Ne deviation, and (3) whether the new error bars cover model choices like the diffuseness variation and the deep potential matching. The abstract alone is not enough to trust the final |V_ud|, but the methodological refinements are worth taking seriously and the implications for CKM unitarity are relevant.

I would send this to a nuclear-structure referee with a request to focus on the δ_C1 handling and the outlier. The paper is not a paradigm shift, but it is an honest, useful increment to an active precision measurement. If the full text resolves the δ_C1 issue, the numbers will deserve citation.

Referee Report

3 major / 3 minor

Summary. The paper reports refined shell-model calculations of the radial-mismatch correction δ_C2 to superallowed 0+→0+ beta decay, using Woods-Saxon radial wave functions constrained by charge radii and separation energies, with full configuration-interaction diagonalizations. It then uses these δ_C2 values to update the world average of the corrected Ft value and the extracted |V_ud|, giving Ftbar = 3073.11(99)_stat(36)_delta_R'(173)_delta_NS s and |V_ud| = 0.97359(33). The abstract reports general agreement with previous calculations except for a factor-of-two change in 18Ne and reductions for A >= 38, and it explicitly notes that the smaller isospin-mixing correction δ_C1 is strongly interaction-dependent and requires an additional isobaric-displacement procedure.

Significance. If the calculations are correct, this paper would update the superallowed-decay correction set and shift |V_ud| by about 0.0002 to 0.0003, which is important for CKM unitarity tests. The methodological improvements—using spectroscopic-factor-weighted charge radii, enforcing separation-energy constraints on the potential, and performing untruncated shell-model diagonalizations—are substantive and deserve credit. The addition of a diffuseness uncertainty is also a useful step. However, the central claim cannot be fully evaluated from the abstract alone: the final |V_ud| depends on the total δ_C = δ_C1 + δ_C2, and the abstract explicitly identifies δ_C1 as problematic without showing that the indispensable procedure was actually applied and validated.

major comments (3)

[Abstract] The quoted Ftbar and |V_ud| are presented as resulting from δ_C2 calculations, but |V_ud| requires the total nuclear-structure correction δ_C = δ_C1 + δ_C2. The abstract itself states that δ_C1 is strongly interaction-dependent and that an additional isobaric-displacement procedure appears indispensable, yet it gives no indication of which δ_C1 values were used, whether this procedure was applied, or how its uncertainty was incorporated. Without this, the central |V_ud| value and its uncertainty are unsupported. The paper must specify the provenance of δ_C1, the applied isobaric-displacement correction, and a test of its validity.
[Abstract] The abstract reports that δ_C2 for 18Ne is smaller by approximately a factor of two relative to previous studies, principally due to the updated charge-radius treatment, but offers no quantitative explanation. This is the largest deviation and is the most direct manifestation of the new calibration procedure. A load-bearing claim of this kind needs a discussion of which spectroscopic factors and radius contributions drove the change, and why the assigned uncertainty covers this effect.
[Abstract] The uncertainty budget quoted for Ftbar and |V_ud| lists statistical, δ_R', and δ_NS errors, but the only explicitly mentioned model-related uncertainty is the ±0.1 fm variation in surface diffuseness. The paper must state whether the uncertainties in the Woods-Saxon depth, the charge-radius-to-spectroscopic-factor mapping, and the separation-energy matching are included. If these calibration choices are not propagated, the new total uncertainty is likely underestimated, which directly affects the quoted 0.33 uncertainty on |V_ud|.

minor comments (3)

[Abstract] The notation '3073.11(99)_stat(36)_δ_R'(173)_δ_NS s' is visually cramped; separate the subscripts and the unit, and define δ_R' and δ_NS explicitly in the abstract or in a table.
[Abstract] The phrase 'large configuration spaces without truncation' is vague. Specify the model spaces and the number of determinants for the nuclei studied; this will help readers judge the convergence.
[Abstract] In the sentence 'A reduction is also observed in most cases with A>=38, through the deviations generally remain...', 'through' should be 'though'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: δ_C2 is calibrated to independent separation energies and charge radii, not to the Ft value it predicts.

full rationale

The paper's central derivation is a shell-model calculation of the radial mismatch correction δ_C2. The radial wave functions are constrained by external data—measured separation energies and charge radii—and the many-body wave functions come from diagonalization of effective interactions. The output δ_C2 values are then combined with other corrections to produce an averaged Ft value and |V_ud|. No step in this chain defines the target quantity in terms of itself or fits a parameter to the final observable. The charge-radius constraint uses spectroscopic factors from the shell-model wave functions, but the charge radii themselves are independent experimental inputs; using them to calibrate a potential is a standard, non-circular procedure. The abstract's caveat about δ_C1 being strongly interaction-dependent and requiring an additional isobaric-displacement procedure is a self-identified limitation or completeness issue, not a circularity: it indicates that the total correction may be incomplete, but it does not make the δ_C2 derivation depend on the final Ft value. No load-bearing self-citation chain is visible in the provided text. Therefore the derivation is self-contained with respect to its target predictions, and no circularity is present.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

All entries are inferred from the abstract; the full text was not reviewed. The main calibration inputs are the Woods-Saxon parameters, and the main external anchors are measured charge radii and separation energies.

free parameters (4)

Woods-Saxon potential depth = not stated
Adjusted to reproduce separation energies to intermediate (A-1) states (abstract, improvement i); changes radial wave functions used for delta_C2.
Radial length parameter (radius) = not stated
Constrained by charge radii via generalized formula with sums of spectroscopic factors (abstract, improvement i); determines the scale of the Woods-Saxon wave functions.
Surface diffuseness = not stated, +/-0.1 fm variation assigned as uncertainty
An input choice; the paper adds a +/-0.1 fm variation as a new uncertainty, but the central value is not derived in the abstract.
Isobaric displacement adjustment = not stated
The abstract says an additional procedure to ensure isobaric displacements within isospin multiplets appears indispensable, implying an energy or Coulomb correction is tuned or applied; no parameter value is given.

assumptions (4)

domain assumption The shell-model effective interactions used are valid for the studied nuclei.
The abstract says diagonalization of well-established effective interactions; their accuracy is assumed from prior work.
domain assumption Woods-Saxon radial wave functions with adjusted parameters faithfully represent radial densities.
The central delta_C2 calculation depends on these wave functions, but no validation of the tails is shown in the abstract.
domain assumption Experimental charge radii and separation energies used as constraints are accurate.
These are external inputs from measurement; their errors are not propagated in the abstract except for the diffuseness variation.
domain assumption The standard decomposition of delta_C into delta_C1 and delta_C2 and the definition of delta_C2 as a radial-overlap mismatch are accepted.
The paper relies on this prior framework without deriving it.

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Cite this review

Pith. "Pith review of New shell-model calculations of the $\delta_C$ correction to superallowed $0^+\rightarrow0^+$ nuclear $\beta$ decay and standard-model implications." pith.science (2026). https://pith.science/paper/KBVCRA6P

@misc{pith2026250818189,
  author       = {Pith},
  title        = {Pith review of: New shell-model calculations of the $\delta_C$ correction to superallowed $0^+\rightarrow0^+$ nuclear $\beta$ decay and standard-model implications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KBVCRA6P}},
  note         = {Machine review of arXiv:2508.18189}
}

abstract

Refined calculations of the radial mismatch correction, $\delta_{C2}$, to superallowed $0^+\rightarrow0^+$ nuclear $\beta$ decay are performed using the shell model with realistic Woods-Saxon radial wave functions. Two important improvements are introduced: i) charge radii used to constrain the length parameter are evaluated within a generalized formula, where proton occupation numbers are substituted by sums of spectroscopic factors, while radial wave functions are required to match separation energies with respect to the intermediate $(A-1)$-nucleon states by adjusting parameters such as the potential depth; ii) configuration mixing wave functions and energies for many-particle states are obtained through the diagonalization of well-established effective interactions in large configuration spaces without truncation. Furthermore, a variation of $\pm0.1$\,fm in the surface diffuseness parameter is now incorporated as a source of uncertainty. The present results are generally in fairly good agreement with those from previous studies. As an exception, the $\delta_{C2}$ value obtained for $^{18}$Ne is smaller by approximately a factor of two, principally due to the updated charge-radius treatment. A reduction is also observed in most cases with $A\ge38$, through the deviations generally remain within the newly assigned error bars. The smaller isospin-mixing counterpart, $\delta_{C1}$, is strongly interaction-dependent, roughly following an inverse-square law with respect to the energy separation between the lowest admixed levels. Therefore, an additional procedure to ensure isobaric displacements within the isospin multiplets appears to be indispensable. Our results for $\delta_{C2}$ lead to a new averaged $\overline{\mathcal{F}t}$ value of $3073.11(99)_{stat}(36)_{\delta_R'}(173)_{\delta_{NS}}$~s with $\chi^2/\nu=0.624$. The corresponding $|V_{ud}|$ value is 0.97359(33).

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Works this paper leans on

59 extracted references · 42 canonical work pages

[1]

author author J. C. \ Hardy \ and\ author I. S. \ Towner ,\ https://doi.org/10.1103/PhysRevC.102.045501 journal journal Phys. Rev. C \ volume 102 ,\ pages 045501 ( year 2020 ) NoStop

doi:10.1103/physrevc.102.045501 2020
[2]

Czarnecki , author W

author author A. Czarnecki , author W. J. \ Marciano ,\ and\ author A. Sirlin ,\ https://doi.org/10.1103/PhysRevD.100.073008 journal journal Phys. Rev. D \ volume 100 ,\ pages 073008 ( year 2019 ) NoStop

doi:10.1103/physrevd.100.073008 2019
[3]

\ Ma , author X

author author P.-X. \ Ma , author X. Feng , author M. Gorchtein , author L.-C. \ Jin , author K.-F. \ Liu , author C.-Y. \ Seng , author B.-G. \ Wang ,\ and\ author Z.-L. \ Zhang ,\ https://doi.org/10.1103/PhysRevLett.132.191901 journal journal Phys. Rev. Lett. \ volume 132 ,\ pages 191901 ( year 2024 ) NoStop

doi:10.1103/physrevlett.132.191901 2024
[4]

\ Seng , author M

author author C.-Y. \ Seng , author M. Gorchtein , author H. H. \ Patel ,\ and\ author M. J. \ Ramsey-Musolf ,\ https://doi.org/10.1103/PhysRevLett.121.241804 journal journal Phys. Rev. Lett. \ volume 121 ,\ pages 241804 ( year 2018 ) NoStop

doi:10.1103/physrevlett.121.241804 2018
[5]

Cirigliano , author W

author author V. Cirigliano , author W. Dekens , author J. de Vries , author S. Gandolfi , author M. Hoferichter ,\ and\ author E. Mereghetti ,\ https://doi.org/10.1103/PhysRevLett.133.211801 journal journal Phys. Rev. Lett. \ volume 133 ,\ pages 211801 ( year 2024 ) NoStop

work page doi:10.1103/physrevlett.133.211801 2024
[6]

Gennari , author M

author author M. Gennari , author M. Drissi , author M. Gorchtein , author P. Navr\'atil ,\ and\ author C.-Y. \ Seng ,\ https://doi.org/10.1103/PhysRevLett.134.012501 journal journal Phys. Rev. Lett. \ volume 134 ,\ pages 012501 ( year 2025 ) NoStop

doi:10.1103/physrevlett.134.012501 2025
[7]

\ Seng \ and\ author M

author author C.-Y. \ Seng \ and\ author M. Gorchtein ,\ https://doi.org/10.1103/PhysRevC.107.035503 journal journal Phys. Rev. C \ volume 107 ,\ pages 035503 ( year 2023 ) NoStop

doi:10.1103/physrevc.107.035503 2023
[8]

Towner ,\ https://doi.org/https://doi.org/10.1016/0375-9474(92)90170-O journal journal Nucl

author author I. Towner ,\ https://doi.org/https://doi.org/10.1016/0375-9474(92)90170-O journal journal Nucl. Phys. A \ volume 540 ,\ pages 478 ( year 1992 ) NoStop

doi:10.1016/0375-9474(92)90170-o 1992

Show all 59 references

[9]

Tishchenko , author S

author author V. Tishchenko , author S. Battu , author R. M. \ Carey , author D. B. \ Chitwood , author J. Crnkovic , author P. T. \ Debevec , author S. Dhamija , author W. Earle , author A. Gafarov , author K. Giovanetti , author T. P. \ Gorringe , author F. E. \ Gray , autho...

2013
[10]

author author I. S. \ Towner \ and\ author J. C. \ Hardy ,\ https://doi.org/10.1103/PhysRevC.66.035501 journal journal Phys. Rev. C \ volume 66 ,\ pages 035501 ( year 2002 ) NoStop

2002 doi
[11]

author author I. S. \ Towner \ and\ author J. C. \ Hardy ,\ https://doi.org/10.1103/PhysRevC.77.025501 journal journal Phys. Rev. C \ volume 77 ,\ pages 025501 ( year 2008 ) NoStop

2008 doi
[12]

Cohen \ and\ author D

author author S. Cohen \ and\ author D. Kurath ,\ https://doi.org/https://doi.org/10.1016/0375-9474(67)90285-0 journal journal Nucl. Phys. A \ volume 101 ,\ pages 1 ( year 1967 ) NoStop

1967 doi
[13]

Cohen \ and\ author D

author author S. Cohen \ and\ author D. Kurath ,\ https://doi.org/https://doi.org/10.1016/0029-5582(65)90148-3 journal journal Nucl. Phys. \ volume 73 ,\ pages 1 ( year 1965 ) NoStop

1965 doi
[14]

author author E. K. \ Warburton \ and\ author B. A. \ Brown ,\ https://doi.org/10.1103/PhysRevC.46.923 journal journal Phys. Rev. C \ volume 46 ,\ pages 923 ( year 1992 ) NoStop

1992 doi
[15]

Ormand \ and\ author B

author author W. Ormand \ and\ author B. Brown ,\ https://doi.org/https://doi.org/10.1016/0375-9474(89)90203-0 journal journal Nucl. Phys. A \ volume 491 ,\ pages 1 ( year 1989 ) NoStop

1989 doi
[16]

author author J. B. \ McGrory \ and\ author B. H. \ Wildenthal ,\ https://doi.org/10.1103/PhysRevC.7.974 journal journal Phys. Rev. C \ volume 7 ,\ pages 974 ( year 1973 ) NoStop

1973 doi
[17]

author author A. P. \ Zuker , author B. Buck ,\ and\ author J. B. \ McGrory ,\ https://doi.org/10.1103/PhysRevLett.21.39 journal journal Phys. Rev. Lett. \ volume 21 ,\ pages 39 ( year 1968 ) NoStop

1968 doi
[18]

Wildenthal ,\ https://doi.org/https://doi.org/10.1016/0146-6410(84)90011-5 journal journal Progress in Particle and Nuclear Physics \ volume 11 ,\ pages 5 ( year 1984 ) NoStop

author author B. Wildenthal ,\ https://doi.org/https://doi.org/10.1016/0146-6410(84)90011-5 journal journal Progress in Particle and Nuclear Physics \ volume 11 ,\ pages 5 ( year 1984 ) NoStop

1984 doi
[19]

author author B. A. \ Brown \ and\ author W. A. \ Richter ,\ https://doi.org/10.1103/PhysRevC.74.034315 journal journal Phys. Rev. C \ volume 74 ,\ pages 034315 ( year 2006 ) NoStop

2006 doi
[20]

ortersh\

author author M. L. \ Bissell , author J. Papuga , author H. Na\" dja , author K. Kreim , author K. Blaum , author M. De Rydt , author R. F. \ Garcia Ruiz , author H. Heylen , author M. Kowalska , author R. Neugart , author G. Neyens , author W. N\"ortersh\"auser , author F. N...

2014 doi
[21]

Honma , author T

author author M. Honma , author T. Otsuka , author B. A. \ Brown ,\ and\ author T. Mizusaki ,\ https://doi.org/10.1103/PhysRevC.69.034335 journal journal Phys. Rev. C \ volume 69 ,\ pages 034335 ( year 2004 ) NoStop

2004 doi
[22]

Poves , author J

author author A. Poves , author J. Sánchez-Solano , author E. Caurier ,\ and\ author F. Nowacki ,\ https://doi.org/https://doi.org/10.1016/S0375-9474(01)00967-8 journal journal Nucl. Phys. A \ volume 694 ,\ pages 157 ( year 2001 ) NoStop

2001 doi
[23]

Richter , author M

author author W. Richter , author M. Van Der Merwe , author R. Julies ,\ and\ author B. Brown ,\ https://doi.org/https://doi.org/10.1016/0375-9474(91)90007-S journal journal Nuclear Physics A \ volume 523 ,\ pages 325 ( year 1991 ) NoStop

1991 doi
[24]

Honma , author T

author author M. Honma , author T. Otsuka , author T. Mizusaki ,\ and\ author M. Hjorth-Jensen ,\ https://doi.org/10.1103/PhysRevC.80.064323 journal journal Phys. Rev. C \ volume 80 ,\ pages 064323 ( year 2009 ) NoStop

2009 doi
[25]

Caurier , author F

author author E. Caurier , author F. Nowacki , author A. Poves ,\ and\ author J. Retamosa ,\ https://doi.org/10.1103/PhysRevLett.77.1954 journal journal Phys. Rev. Lett. \ volume 77 ,\ pages 1954 ( year 1996 ) NoStop

1954 doi
[26]

Millener \ and\ author D

author author D. Millener \ and\ author D. Kurath ,\ https://doi.org/https://doi.org/10.1016/0375-9474(75)90683-1 journal journal Nucl. Phys. A \ volume 255 ,\ pages 315 ( year 1975 ) NoStop

1975 doi
[27]

Xayavong \ and\ author N

author author L. Xayavong \ and\ author N. A. \ Smirnova ,\ https://doi.org/10.1103/PhysRevC.97.024324 journal journal Phys. Rev. C \ volume 97 ,\ pages 024324 ( year 2018 ) NoStop

2018 doi
[28]

Xayavong \ and\ author N

author author L. Xayavong \ and\ author N. A. \ Smirnova ,\ https://doi.org/10.1103/PhysRevC.105.044308 journal journal Phys. Rev. C \ volume 105 ,\ pages 044308 ( year 2022 ) NoStop

2022 doi
[29]

Xayavong \ and\ author N

author author L. Xayavong \ and\ author N. A. \ Smirnova ,\ https://doi.org/10.1103/PhysRevC.109.014317 journal journal Phys. Rev. C \ volume 109 ,\ pages 014317 ( year 2024 ) NoStop

2024 doi
[30]

Ormand \ and\ author B

author author W. Ormand \ and\ author B. Brown ,\ https://doi.org/https://doi.org/10.1016/0375-9474(85)90341-0 journal journal Nucl. Phys. A \ volume 440 ,\ pages 274 ( year 1985 ) NoStop

1985 doi
[31]

Liang , author N

author author H. Liang , author N. V. \ Giai ,\ and\ author J. Meng ,\ https://doi.org/10.1103/PhysRevC.79.064316 journal journal Phys. Rev. C \ volume 79 ,\ pages 064316 ( year 2009 ) NoStop

2009 doi
[32]

Satu a , author J

author author W. Satu a , author J. Dobaczewski , author W. Nazarewicz ,\ and\ author M. Rafalski ,\ https://doi.org/10.1103/PhysRevLett.106.132502 journal journal Phys. Rev. Lett. \ volume 106 ,\ pages 132502 ( year 2011 ) NoStop

2011 doi
[33]

Auerbach ,\ https://doi.org/10.1103/PhysRevC.79.035502 journal journal Phys

author author N. Auerbach ,\ https://doi.org/10.1103/PhysRevC.79.035502 journal journal Phys. Rev. C \ volume 79 ,\ pages 035502 ( year 2009 ) NoStop

2009 doi
[34]

Damgaard ,\ https://doi.org/https://doi.org/10.1016/0375-9474(69)90974-9 journal journal Nucl

author author J. Damgaard ,\ https://doi.org/https://doi.org/10.1016/0375-9474(69)90974-9 journal journal Nucl. Phys. A \ volume 130 ,\ pages 233 ( year 1969 ) NoStop

1969 doi
[35]

author author J. C. \ Hardy \ and\ author I. S. \ Towner ,\ https://doi.org/10.1103/PhysRevC.91.025501 journal journal Phys. Rev. C \ volume 91 ,\ pages 025501 ( year 2015 ) NoStop

2015 doi
[36]

Melconian , author S

author author D. Melconian , author S. Triambak , author C. Bordeanu , author A. Garc\' a , author J. C. \ Hardy , author V. E. \ Iacob , author N. Nica , author H. I. \ Park , author G. Tabacaru , author L. Trache , author I. S. \ Towner , author R. E. \ Tribble ,\ and\ autho...

2011 doi
[37]

Hagberg , author V

author author E. Hagberg , author V. T. \ Koslowsky , author J. C. \ Hardy , author I. S. \ Towner , author J. G. \ Hykawy , author G. Savard ,\ and\ author T. Shinozuka ,\ https://doi.org/10.1103/PhysRevLett.73.396 journal journal Phys. Rev. Lett. \ volume 73 ,\ pages 396 ( y...

1994 doi
[38]

author author A. D. \ MacLean , author A. T. \ Laffoley , author C. E. \ Svensson , author G. C. \ Ball , author J. R. \ Leslie , author C. Andreoiu , author A. Babu , author S. S. \ Bhattacharjee , author H. Bidaman , author V. Bildstein , author C. Burbadge , author M. Bowry...

2020
[39]

author author K. G. \ Leach , author P. E. \ Garrett , author I. S. \ Towner , author G. C. \ Ball , author V. Bildstein , author B. A. \ Brown , author G. A. \ Demand , author T. Faestermann , author P. Finlay , author K. L. \ Green , author R. Hertenberger , author R. Kr\"uc...

2013 doi
[40]

author author H. I. \ Park , author J. C. \ Hardy , author V. E. \ Iacob , author M. Bencomo , author L. Chen , author V. Horvat , author N. Nica , author B. T. \ Roeder , author E. Simmons , author R. E. \ Tribble ,\ and\ author I. S. \ Towner ,\ https://doi.org/10.1103/PhysR...

2014 doi
[41]

Xayavong ,\ @noop journal journal Ph.D

author author L. Xayavong ,\ @noop journal journal Ph.D. thesis, University of Bordeaux \ ( year 2016 ) NoStop

2016
[42]

author author N. A. \ Smirnova ,\ https://doi.org/10.3390/physics5020026 journal journal Physics \ volume 5 ,\ pages 352 ( year 2023 ) NoStop

2023 doi
[43]

Xayavong , author Y

author author L. Xayavong , author Y. Lim , author N. A. \ Smirnova ,\ and\ author C. W. \ Johnson ,\ https://arxiv.org/abs/2505.20587 title Radial excitations and their potential impact on fermi -decay rates ( year 2025 ),\ https://arxiv.org/abs/2505.20587 arXiv:2505.20587 [n...

2025 arXiv
[44]

French \ and\ author M

author author J. French \ and\ author M. MacFarlane ,\ https://doi.org/https://doi.org/10.1016/0029-5582(61)90128-6 journal journal Nucl. Phys. \ volume 26 ,\ pages 168 ( year 1961 ) NoStop

1961 doi
[45]

Brown \ and\ author W

author author B. Brown \ and\ author W. Rae ,\ https://doi.org/https://doi.org/10.1016/j.nds.2014.07.022 journal journal Nuclear Data Sheets \ volume 120 ,\ pages 115 ( year 2014 ) NoStop

2014 doi
[46]

author author I. S. \ Towner \ and\ author J. C. \ Hardy ,\ https://doi.org/10.1103/PhysRevC.92.055505 journal journal Phys. Rev. C \ volume 92 ,\ pages 055505 ( year 2015 ) NoStop

2015 doi
[47]

Audi , author F

author author G. Audi , author F. G. \ Kondev , author M. Wang , author B. Pfeiffer , author X. Sun , author J. Blachot ,\ and\ author M. MacCormick ,\ https://doi.org/10.1088/1674-1137/36/12/001 journal journal Chinese Physics C \ volume 36 ,\ pages 1157 ( year 2012 ) NoStop

2012 doi
[48]

\ Seng \ and\ author M

author author C.-Y. \ Seng \ and\ author M. Gorchtein ,\ https://doi.org/10.1103/PhysRevC.109.045501 journal journal Phys. Rev. C \ volume 109 ,\ pages 045501 ( year 2024 ) NoStop

2024 doi
[49]

Ohayon ,\ https://arxiv.org/abs/2409.08193 https://arxiv.org/abs/2409.08193 arXiv:2409.08193 [nucl-ex] NoStop

author author B. Ohayon ,\ https://arxiv.org/abs/2409.08193 https://arxiv.org/abs/2409.08193 arXiv:2409.08193 [nucl-ex] NoStop

arXiv
[50]

amer , author K. Kreim , author A. Krieger , author P. Lievens , author T. Neff , author R. Neugart , author G. Neyens , author W. N\

author author D. T. \ Yordanov , author M. L. \ Bissell , author K. Blaum , author M. De Rydt , author C. Geppert , author M. Kowalska , author J. Kr\"amer , author K. Kreim , author A. Krieger , author P. Lievens , author T. Neff , author R. Neugart , author G. Neyens , autho...

2012 doi
[51]

onig , author J. D. \ Lantis , author Y. Liu , author B. Maa , author A. J. \ Miller , author W. N\

author author B. A. \ Brown , author K. Minamisono , author J. Piekarewicz , author H. Hergert , author D. Garand , author A. Klose , author K. K\"onig , author J. D. \ Lantis , author Y. Liu , author B. Maa , author A. J. \ Miller , author W. N\"ortersh\"auser , author S. V. ...

2020 doi
[52]

onig , author D. M. \ Rossi , author B. A. \ Brown , author A. Incorvati , author J. Lantis , author K. Minamisono , author W. N\

author author S. V. \ Pineda , author K. K\"onig , author D. M. \ Rossi , author B. A. \ Brown , author A. Incorvati , author J. Lantis , author K. Minamisono , author W. N\"ortersh\"auser , author J. Piekarewicz , author R. Powel ,\ and\ author F. Sommer ,\ https://doi.org/10...

2021 doi
[53]

onig , author A. Koszor\'us , author S. Kujanp\

author author P. Plattner , author E. Wood , author L. Al Ayoubi , author O. Beliuskina , author M. L. \ Bissell , author K. Blaum , author P. Campbell , author B. Cheal , author R. P. \ de Groote , author C. S. \ Devlin , author T. Eronen , author L. Filippin , author R. F. \...

2023
[54]

Katyal , author A

author author V. Katyal , author A. Chakraborty , author B. K. \ Sahoo , author B. Ohayon , author C.-Y. \ Seng , author M. Gorchtein ,\ and\ author J. Behr ,\ https://doi.org/10.1103/PhysRevA.111.042813 journal journal Phys. Rev. A \ volume 111 ,\ pages 042813 ( year 2025 ) NoStop

2025 doi
[55]

amer , author V. Lagaki , author B. Maa , author S. Malbrunot-Ettenauer , author T. Miyagi , author K. K\

author author S. W. \ Bai , author X. F. \ Yang , author A. Koszor\'us , author J. C. \ Berengut , author J. Billowes , author M. L. \ Bissell , author K. Blaum , author A. Borschevsky , author P. Campbell , author B. Cheal , author C. S. \ Devlin , author K. T. \ Flanagan , a...

2025
[56]

Bohr \ and\ author B

author author A. Bohr \ and\ author B. R. \ Mottelson ,\ @noop journal journal Nuclear structure Vol.I: Single-Particle Motion \ ( year 1969 ) NoStop

1969
[57]

Schwierz , author I

author author N. Schwierz , author I. Wiedenhover ,\ and\ author A. Volya ,\ https://arxiv.org/abs/0709.3525 title Parameterization of the woods-saxon potential for shell-model calculations ( year 2007 ),\ https://arxiv.org/abs/0709.3525 arXiv:0709.3525 [nucl-th] NoStop

2007 arXiv
[58]

author author L. R. B. \ Elton ,\ @noop journal journal Nuclear sizes (Oxford University Press) \ ( year 1961 ) NoStop

1961
[59]

author author A. P. \ Zuker , author A. Poves , author F. Nowacki ,\ and\ author S. M. \ Lenzi ,\ https://doi.org/10.1103/PhysRevC.92.024320 journal journal Phys. Rev. C \ volume 92 ,\ pages 024320 ( year 2015 ) NoStop

2015 doi

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [1]

author author J. C. \ Hardy \ and\ author I. S. \ Towner ,\ https://doi.org/10.1103/PhysRevC.102.045501 journal journal Phys. Rev. C \ volume 102 ,\ pages 045501 ( year 2020 ) NoStop

doi:10.1103/physrevc.102.045501 2020

[2] [2]

Czarnecki , author W

author author A. Czarnecki , author W. J. \ Marciano ,\ and\ author A. Sirlin ,\ https://doi.org/10.1103/PhysRevD.100.073008 journal journal Phys. Rev. D \ volume 100 ,\ pages 073008 ( year 2019 ) NoStop

doi:10.1103/physrevd.100.073008 2019

[3] [3]

\ Ma , author X

author author P.-X. \ Ma , author X. Feng , author M. Gorchtein , author L.-C. \ Jin , author K.-F. \ Liu , author C.-Y. \ Seng , author B.-G. \ Wang ,\ and\ author Z.-L. \ Zhang ,\ https://doi.org/10.1103/PhysRevLett.132.191901 journal journal Phys. Rev. Lett. \ volume 132 ,\ pages 191901 ( year 2024 ) NoStop

doi:10.1103/physrevlett.132.191901 2024

[4] [4]

\ Seng , author M

author author C.-Y. \ Seng , author M. Gorchtein , author H. H. \ Patel ,\ and\ author M. J. \ Ramsey-Musolf ,\ https://doi.org/10.1103/PhysRevLett.121.241804 journal journal Phys. Rev. Lett. \ volume 121 ,\ pages 241804 ( year 2018 ) NoStop

doi:10.1103/physrevlett.121.241804 2018

[5] [5]

Cirigliano , author W

author author V. Cirigliano , author W. Dekens , author J. de Vries , author S. Gandolfi , author M. Hoferichter ,\ and\ author E. Mereghetti ,\ https://doi.org/10.1103/PhysRevLett.133.211801 journal journal Phys. Rev. Lett. \ volume 133 ,\ pages 211801 ( year 2024 ) NoStop

work page doi:10.1103/physrevlett.133.211801 2024

[6] [6]

Gennari , author M

author author M. Gennari , author M. Drissi , author M. Gorchtein , author P. Navr\'atil ,\ and\ author C.-Y. \ Seng ,\ https://doi.org/10.1103/PhysRevLett.134.012501 journal journal Phys. Rev. Lett. \ volume 134 ,\ pages 012501 ( year 2025 ) NoStop

doi:10.1103/physrevlett.134.012501 2025

[7] [7]

\ Seng \ and\ author M

author author C.-Y. \ Seng \ and\ author M. Gorchtein ,\ https://doi.org/10.1103/PhysRevC.107.035503 journal journal Phys. Rev. C \ volume 107 ,\ pages 035503 ( year 2023 ) NoStop

doi:10.1103/physrevc.107.035503 2023

[8] [8]

Towner ,\ https://doi.org/https://doi.org/10.1016/0375-9474(92)90170-O journal journal Nucl

author author I. Towner ,\ https://doi.org/https://doi.org/10.1016/0375-9474(92)90170-O journal journal Nucl. Phys. A \ volume 540 ,\ pages 478 ( year 1992 ) NoStop

doi:10.1016/0375-9474(92)90170-o 1992