Systematic study of $\alpha$-decay half-lives of super-heavy nuclei with 106$\leq$Z$\leq$118

M.Hassanzad; O.N.Ghodsi

REVIEW 2 major objections 5 minor 97 references

Systematic study of $\alpha$-decay half-lives of super-heavy nuclei with 106$\leq$Z$\leq$118

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Among 28 proximity-potential versions, Ngô 80 reproduces alpha-decay half-lives of superheavy nuclei best.

desk verdict A useful systematic benchmark of proximity potentials for superheavy alpha decay, but the ranking metric is wrong and the predictions rest on unquantified WS4 energies. read the letter →

arxiv 1908.02070 v1 pith:6EG23WUT submitted 2019-08-06 nucl-th

O.N.Ghodsi , M.Hassanzad This is my paper · ORCID

classification nucl-th PACS 23.60.+e27.90.+b

keywords alpha-decaysuperheavynucleiproximitypotentialNgo80WKBapproximationdoublefoldingmodelQ_WS4half-lifepredictions

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

This paper tests 28 versions of the nuclear proximity potential against measured $\alpha$-decay half-lives for 70 superheavy nuclei with $106\le Z\le 118$. It combines each proximity potential with an exact double-folding Coulomb potential for a spherical $\alpha$ particle and a deformed daughter nucleus, and computes the barrier penetrability with the WKB approximation. The authors find that the Ngô 80 version gives the smallest scatter, a standard deviation of $4.6053$ s, slightly better than the next-best full-coverage version. Using Ngô 80 with WS4 $\alpha$-decay energies, they predict half-lives for unmeasured superheavy isotopes and identify some with half-lives near 100 seconds, which are unusually stable for nuclei outside the known stability islands. The payoff is a recommended potential for superheavy $\alpha$-decay estimates and a concrete list of candidate relatively stable superheavy nuclei.

What carries the argument

The central object is the total interaction potential $V_T(r)=V_N(r)+V_C(r)+V_l(r)$ between the $\alpha$ particle and the deformed daughter nucleus. The nuclear part is a proximity potential; the winning version, Ngô 80, uses a universal function of the surface separation that is parabolic on one side of $s_0=-1.6$ fm and exponential on the other. The Coulomb part is computed by double folding the charge densities of a spherical $\alpha$ and a deformed daughter, using Fermi distributions with deformation parameters $\beta_2$ and $\beta_4$. The half-life follows from the WKB penetrability $P$ averaged over daughter orientation, $T_{1/2}=\ln 2/(\nu_0 P)$, and the 28 versions are ranked by the standard deviation of their computed half-lives against the experimental values.

What would settle it

Measure the $\alpha$-decay energy of a predicted long-lived isotope, for example the $A=291$, $Z=114$ nucleus with predicted half-life $3.61\times10^2$ s and $Q_{WS4}=9.245$ MeV, and compare the measured value with the WS4 value; a discrepancy of about 0.2 MeV would move the half-life by roughly a factor of 10. A cheaper check is to recompute the paper's Table V half-lives with two independent mass models and see whether the roughly 100-second nuclei stay in the same half-life band.

Watch

Extended reading notes

Core claim

The paper claims that, for $\alpha$ decay of superheavy nuclei in the range $Z=106$ to $118$, the Ngô 80 version of the proximity potential is the most reliable among the 28 versions examined. With experimental $Q_\alpha$ values for 70 nuclei, Ngô 80 yields $SD=4.6053$ s, the smallest standard deviation of any version that covers all 70 nuclei, ahead of γ-MS 1966 at $4.7238$ s and clearly ahead of the remaining versions. For isotopes without measured data, the same potential is combined with $Q_{WS4}$ $\alpha$-decay energies to predict half-lives; several of these predictions fall near 100 seconds, and the paper reports that they agree well with the VSS, Royer, and UDL semi-empirical formulas for the same nuclei.

Load-bearing premise

The predictive half of the paper stands on the assumption that WS4 $\alpha$-decay energies are accurate to roughly 0.1 to 0.2 MeV for unmeasured superheavy nuclei, because the WKB penetration probability depends exponentially on $Q_\alpha$ and a 0.2 MeV error would change a predicted half-life by roughly an order of magnitude.

Editorial extensions

If this is right

Ngô 80 can be treated as the recommended proximity version for alpha-decay half-life estimates in the superheavy region whenever an experimental $Q_\alpha$ is available.
The unmeasured isotopes listed in the paper with predicted half-lives near 100 seconds become concrete candidate nuclei for future synthesis and decay-chain identification.
The agreement among Ngô 80, VSS, Royer, and UDL for the same predicted nuclei indicates that the roughly 100-second half-lives are not an artifact of one particular potential.
The same potential-plus-$Q_{WS4}$ procedure can be rerun for neighbouring isotopes to map where the relatively stable pockets of superheavy nuclei sit.

Reading between the lines

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

Because the paper does not quote uncertainties on $Q_{WS4}$, the predicted half-lives are best read as central values; recomputing them with two or three independent mass models would show whether the roughly 100-second nuclei survive as a band rather than a single-model point.
The standard-deviation margin between Ngô 80 and γ-MS 1966 is small, so a different Coulomb treatment or deformation set could reorder the top two versions; the ranking should be checked outside $Z=106$ to $118$ before being treated as universal.
A natural extension is to apply the same method to decay chains beyond $Z=118$ or to very neutron-rich superheavy isotopes, where the WS4 mass model has not yet been benchmarked against data.

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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 is a systematic benchmark of 28 proximity potentials for alpha-decay half-lives of Z=106-118, and it builds a plausible case that Ngo80 reproduces the measured data best. The case is not yet solid: the ranking metric is standard deviation in linear seconds, which on a dataset spanning eight orders of magnitude is dominated by a few long-lived nuclei. The predictive section also depends on WS4 Q_alpha values with no quoted uncertainty.

What is actually new: the same group already covered Z=52-107 with 28 potentials; here they extend to the superheavy region, add a deformed double-folding Coulomb potential, and compare Ngo80 against 27 other proximity versions. They also produce a table of half-life predictions for unmeasured isotopes using WS4 energies, with comparisons to VSS, Royer, and UDL. The reproduction of measured half-lives by Ngo80 in Table III is genuinely decent; many values land within a factor of 2-5, and the WKB treatment with orientation averaging is standard. The paper is reproducible in principle; formulas and references are sufficient for an expert re-implementation.

The load-bearing soft spot is Eq. (26). A linear-seconds SD is the wrong loss function for half-lives spanning 1e-6 to 1e2 s. The stress-test example is right: 278113 with T_exp=1.4e-3 s is underpredicted by a factor of 88, but its linear residual is below 0.0014 s, while 285112 with T_exp=34 s contributes about 10 s of residual. The margin between Ngo80 (4.6053 s) and gamma-MS1966 (4.7238 s) is 0.12 s, smaller than the long-lived residuals. If you re-rank on log10 half-life residuals, the ordering may change, and the paper's central recommendation is unsupported until that check is done. The authors' own Ref. [35] used RMS on log10; they should do the same here. A related minor issue is that the SD comparison mixes versions with different numbers of nuclei (e.g., gamma-RR1984 has SD 0.1056 for 27 nuclei), so the comparison table is not apples-to-apples.

The predictive half is fragile. The WS4 Q_alpha values enter the WKB exponent, and a 0.2 MeV error changes half-lives by an order of magnitude. The paper gives no uncertainty estimate or propagation, so the claimed agreement with VSS/Royer/UDL is at best indicative. They also never state the implicit alpha preformation factor of unity, nor do they test its sensitivity.

Who this is for: people working in superheavy alpha-decay systematics who want a quick comparison of proximity potential versions, and experimental groups looking for candidate isotopes. It deserves a serious referee, but with a request for major revision: redo the ranking on a log10 scale, propagate the WS4 uncertainties, and state the preformation assumption. As is, the benchmark claim is not established, but the underlying calculation and data collection are solid enough to be worth engaging with.

Referee Report

2 major / 5 minor

Summary. The paper reports a systematic comparison of 28 versions of the proximity potential for the alpha-decay half-lives of 70 superheavy nuclei with 106<=Z<=118. The calculation uses experimental Q_alpha values, a double-folding Coulomb potential for a spherical alpha particle and a deformed daughter, WKB penetration probabilities with orientation averaging, and the standard assault-frequency formula. The authors find that the Ngo 80 version yields the smallest standard deviation, in linear seconds, from the experimental half-lives (SD = 4.6053 s versus 4.7238 s for the next full-coverage version). Using Ngo 80 and the WS4 mass-model Q_alpha values, they then predict half-lives for unmeasured isotopes, including several with half-lives around 100 s, and compare these predictions with the VSS, Royer, and UDL semi-empirical formulas.

Significance. Should the ranking be robust, the paper would provide a concrete recommendation among proximity interactions for practical estimates of superheavy-nucleus alpha-decay half-lives and a set of candidate alpha-decaying isotopes for future experiments. The comparison is useful as an external benchmark: none of the model parameters is fitted to the 70 half-lives, the Coulomb potential is treated with sphericity-deformation coupling, and 28 versions are tested on a common data set. The two main components of the paper are, however, load-bearing: the ranking in Table II is based on a linear-seconds standard deviation that is dominated by a few long-lived nuclei, and the predictive section rests on WS4 Q_alpha values whose uncertainties are not quantified. Both need to be addressed before the conclusions can be accepted.

major comments (2)

[Section III, Eq. (26), Table II] The ranking of the 28 proximity potentials is made with the linear-seconds standard deviation of Eq. (26). Because the half-lives in Table III span roughly seven orders of magnitude (from about 10^-6 s to about 10^2 s), this metric is numerically controlled by the few longest-lived nuclei. For instance, for 278113 (T_exp = 1.4e-3 s) the Ngo 80 value is 1.59e-5 s, an underestimate by a factor of about 88, yet its linear contribution to the SD is below 1.4e-3 s; in contrast, 285112 (T_exp = 34 s) contributes a linear residual of order 10 s. The reported winning margin over gamma-MS 1966 is only 0.12 s, far smaller than the contribution of a single long-lived nucleus. Since the remainder of the paper, including the predictive section, is built on the choice of Ngo 80, the authors must repeat the ranking with a log10-based metric (as in their own Ref. [35]) and show that the conclusion is stable; as it stands, the central claim that Ngo 80 is the best version is not established.
[Section III, Table V, Eq. (15)] The predicted half-lives in Table V are obtained by combining the Ngo 80 potential with the WS4 Q_alpha values of Ref. [46]. Because the WKB penetrability in Eq. (15) depends exponentially on Q_alpha, an uncertainty of only 0.1-0.2 MeV in the WS4 Q_alpha changes a predicted half-life by roughly an order of magnitude. The paper cites Ref. [92] for the overall quality of WS4 in this mass region but gives no numerical uncertainty for Q_alpha and no propagation of that uncertainty into Table V. Consequently, the specific ~100 s candidates and the claimed agreement with VSS, Royer, and UDL are not yet quantitatively supported. The authors should state the accuracy of Q_WS4 for these superheavy nuclei and provide a sensitivity analysis (for example, shifting Q_alpha by +/-0.1 and +/-0.2 MeV and reporting the resulting half-life ranges).

minor comments (5)

[Section II A, Eq. (13)] The last equality in Eq. (13) appears to omit the factor hbar that is present in the preceding expression; please state the units or convention used so that the assault frequency is dimensionally correct.
[Section II A, Eq. (14)] The equation is printed as G = 2nr + 1 but the accompanying text defines G as 2nr + l; these must be reconciled, since Eq. (13) uses G + 3/2.
[Section III, Table II] The criterion for excluding versions with partial coverage is stated only as 'less than the others'; for example, Prox.00 has 60 of the 70 nuclei. Please define the inclusion threshold explicitly, since comparing SDs over different sample sizes is otherwise misleading.
[Section III, Table IV] Table IV is labeled 'continued Table III' instead of having its own caption and number; the same columns should be described in a standalone caption.
[Abstract and Section II] The abstract says 'a exact method' and should read 'an exact method'; in addition, the word 'exact' for the Coulomb potential should be qualified, since Eq. (19) truncates the deformation expansion and the integrations in Eq. (18) are performed numerically.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: all computed half-lives follow from external inputs and are compared as benchmarks, not fitted to the target data.

full rationale

The paper's derivation chain is self-contained in the relevant sense. The half-life formula (Eqs. 12-15) uses external model inputs: a chosen proximity potential, a double-folding Coulomb potential, WKB penetration, and an empirical global quantum number G. The experimental Q_alpha values used in the benchmark section are inputs, not outputs, and no parameter is fitted to the experimental half-lives listed in Table III. The selection of Ngo80 as the best version is a model-selection judgment based on the standard deviation defined in Eq. (26), computed after all versions are evaluated on the same 70-nucleus data set; this is benchmarking, not prediction-from-fit. The predictive section uses Q_WS4 values from Ref. [46], an external mass model, to compute half-lives for unmeasured nuclei, and the agreement with VSS, Royer, and UDL is an external comparison, not a circular reuse of the paper's own outputs. The only prior self-citation, Ref. [35], appears in the introduction as background and is not load-bearing for the present claim. The use of a linear-seconds standard deviation could be questioned on statistical or log-scale grounds, but that is a metric/correctness concern, not a circularity reduction: it does not make any computed quantity equal to its input by construction. Therefore no circular step is present.

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

The paper introduces no new entities or forces; it imports the proximity potential family, deformed Coulomb treatment, and mass model predictions from the literature. The main chosen inputs are the empirical global quantum number G, the Fermi density parameters r0 and a, and the implicit unit preformation factor. The Q_WS4 energies are external predictions with unknown uncertainty in this region.

free parameters (3)

Global quantum number G = 22, 20, 18
Dimensionless empirical values entering the assault frequency in Eq. (13); taken from Ref. [14] based on neutron number, not derived in this paper. Choice affects the overall half-life scale.
Fermi density diffuseness and radius parameters (r0, a) = r0 = 1.07 fm, a = 0.54 fm
Parameters for the deformed charge density in Eq. (19), taken from Bohr-Mottelson (Ref. [82]) without a sensitivity study; they influence the Coulomb barrier and half-lives.
Alpha preformation factor = 1 (implicit)
Eq. (12) omits an explicit preformation probability, effectively assuming unit probability; any preformation factor below 1 lengthens all computed half-lives.

assumptions (5)

standard math WKB approximation (Eq. 15) gives an accurate barrier penetration probability.
Used for the tunneling integral; standard semi-classical result.
domain assumption Alpha particle is preformed with unit probability.
Implicit in Eq. (12); no preformation factor included.
domain assumption Centrifugal potential can be neglected because spin-parities of the SHN are unknown.
Stated in Section II.A; affects the barrier and half-lives for odd and odd-odd nuclei.
domain assumption The daughter nucleus charge density is a deformed Fermi distribution with beta2, beta4 from Moller et al. (Ref. [81]) and the alpha particle is spherical.
Used in the double-folding Coulomb potential, Eq. (19).
domain assumption WS4 mass model Q_alpha predictions are reliable for unmeasured superheavy nuclei.
Q_WS4 values from Ref. [46] with a prior comparison (Ref. [92]) invoked, but no uncertainty is given for this region.

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Cite this review

Pith. "Pith review of Systematic study of $\alpha$-decay half-lives of super-heavy nuclei with 106$\leq$Z$\leq$118." pith.science (2026). https://pith.science/paper/6EG23WUT

@misc{pith2026190802070,
  author       = {Pith},
  title        = {Pith review of: Systematic study of $\alpha$-decay half-lives of super-heavy nuclei with 106$\leq$Z$\leq$118},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6EG23WUT}},
  note         = {Machine review of arXiv:1908.02070}
}

abstract

The $\alpha$- decay half-lives of the superheavy nuclei are systematically studied using different versions of proximity potential and a exact method to calculate Coulomb potential between spherical and deformed nuclei in the framework of the double folding model. To reproduce the $\alpha$-decay half-life, the experimental $\alpha$-decay energy and Wentzel-Kramers-Brillouin approximation have been used. It is found that the computed values by the Ng$\hat{o}$ 80 are in good compromise with the experimental half-lives in comparison with other versions. Also, by using this version and within $Q_{WS4}$ for determination $\alpha$-decay energies for superheavy elements, we had predicted the $\alpha$-decay half-lives for superheavy nuclei which have not been reported yet. The long half-lives with magnitude about $100$ seconds are predicted for the superheavy nuclei which are not in stability islands which indicating remarkable stability in comparison with their neighbors. These results are also in good agreement with the predictions of other semi-empirical formulas.

Figures

Figures reproduced from arXiv: 1908.02070 by the authors.

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This proximity model was labeled as Proximity 1977( P rox.77)

75 ) for ξ ≥ 1.2511, (7) where ξ = s/b is the minimum separation distance, which only depends on separation distance s = r − C1 − C2 fm. This proximity model was labeled as Proximity 1977( P rox.77). Diﬀerent modiﬁcations values on the surface asymmetry constant and surface energy constant that leads to diﬀerent versions of Prox.77 shown in Table I. Using...

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[3]

The Viola-Seaborg-Sobiczewski (VSS) semi-empirical re lationship One of the most famous formulae for calculating alpha decay half-live s is the ﬁve parameter formula oﬀered by Viola and Seaborg [83]. log10(T 1 2 ) = ( aZ + B)Q− 1 2 + cZ + D + hlog, (20) where Z is the atomic number of the parent nucleus and a, b, c and d a re 1 .66175, − 8.5166, − 0.20228...
[4]

The analytical formula for α -decay half-life An analytical formula for α-decay half-lives has been developed by Royer [28] and is given by log10(T 1 2 ) = a + bA 1 6 √ Z + cZ√ Qα , (22) where A and Z represent the mass and charge number of parent nu clei. The constant a, b, and c are hlog =      a = − 25.31 b = − 1.1629 c = 1.5864 for Z = even, N = ...
[5]

The universal decay law New universal decay law (UDL) for α and cluster decay modes was introduced by Qi et al. [85]. log10(T 1 2 ) = aZcZd √ A Qc + b √ AZcZd(A 1 3 d + A 1 3 c ) + c, (24) where A = AcAd Ac+Ad and the constant a = 0 .4314, b = − 0.4087 and c = − 25.7725 are determined by ﬁtting to experimental of both α and cluster decays [85]. III. RESUL...

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Pith tools

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[4] [1]

This proximity model was labeled as Proximity 1977( P rox.77)

75 ) for ξ ≥ 1.2511, (7) where ξ = s/b is the minimum separation distance, which only depends on separation distance s = r − C1 − C2 fm. This proximity model was labeled as Proximity 1977( P rox.77). Diﬀerent modiﬁcations values on the surface asymmetry constant and surface energy constant that leads to diﬀerent versions of Prox.77 shown in Table I. Using...

1977

[5] [2]

, (13) where R2 n = 3 5 R2 0 [58] and G = 2nr + l is the global quantum number [14]: G = 2nr + 1 =    22 for N > 126 20 for 82 < N ≤ 126. 18 for N ≤ 82 (14) The α-decay penetration probability Pα using the WKB semi classical approximation deﬁned as: P = exp{− 2 ℏ ∫ rb ra √ 2µ(VT (r) − Qα ) dr}, (15) 4 Where µ = m Aα +Ad Aα Ad is the reduced mass which ...

[6] [3]

The Viola-Seaborg-Sobiczewski (VSS) semi-empirical re lationship One of the most famous formulae for calculating alpha decay half-live s is the ﬁve parameter formula oﬀered by Viola and Seaborg [83]. log10(T 1 2 ) = ( aZ + B)Q− 1 2 + cZ + D + hlog, (20) where Z is the atomic number of the parent nucleus and a, b, c and d a re 1 .66175, − 8.5166, − 0.20228...

[7] [4]

The analytical formula for α -decay half-life An analytical formula for α-decay half-lives has been developed by Royer [28] and is given by log10(T 1 2 ) = a + bA 1 6 √ Z + cZ√ Qα , (22) where A and Z represent the mass and charge number of parent nu clei. The constant a, b, and c are hlog =      a = − 25.31 b = − 1.1629 c = 1.5864 for Z = even, N = ...

[8] [5]

The universal decay law New universal decay law (UDL) for α and cluster decay modes was introduced by Qi et al. [85]. log10(T 1 2 ) = aZcZd √ A Qc + b √ AZcZd(A 1 3 d + A 1 3 c ) + c, (24) where A = AcAd Ac+Ad and the constant a = 0 .4314, b = − 0.4087 and c = − 25.7725 are determined by ﬁtting to experimental of both α and cluster decays [85]. III. RESUL...

1966