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arxiv: 2604.04624 · v1 · submitted 2026-04-06 · ⚛️ nucl-th · physics.soc-ph

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The Ground State Aspects and the Impact of Shell Structures on the Stability of Es-Isotopes

C. Dash , A. Anupam , I. Naik , B. K. Sharma , B. B. Sahu
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Pith reviewed 2026-05-10 19:28 UTC · model grok-4.3

classification ⚛️ nucl-th physics.soc-ph
keywords Einsteinium isotopesrelativistic mean fieldshell closureneutron separation energyalpha decaynuclear stabilityhalf-life calculation
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The pith

RMF calculations with NL-SH identify a shell closure at N=154 that stabilizes certain Es isotopes.

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

The authors apply the relativistic mean field model in an axially deformed basis using the NL-SH and NL3* forces to map ground-state properties across the chain of Es isotopes from mass 240 to 259. They track binding energies, charge and neutron radii, one- and two-neutron separation energies, and single-particle spectra as functions of quadrupole deformation. From these quantities they compute alpha, beta, and cluster-decay half-lives with several empirical formulas that relate lifetimes to Q-values. The resulting pattern of separation energies and half-lives shows a clear signature of a shell or sub-shell closure at neutron number 154 when the NL-SH force is used, implying that nuclei near this point resist decay more effectively than their neighbors. This supplies a concrete map of how neutron number shapes stability in the heavy Es region.

Core claim

Within the RMF framework with NL-SH and NL3* parametrizations, the computed two-neutron separation energies, their differentials, and the single-particle spectra exhibit a pronounced discontinuity at N=154 for the NL-SH set. This feature correlates with systematically longer alpha-decay and cluster-decay half-lives for parent nuclei possessing that neutron number, while shorter daughter lifetimes reinforce the interpretation of a shell-stabilized configuration. The same closure is absent or weaker in the NL3* results, underscoring the model dependence of the predicted magic number.

What carries the argument

Axially deformed relativistic mean-field calculations with the NL-SH and NL3* effective interactions, supplemented by the MUDL, AKRE, Universal Decay Law, and HOROI formulas that convert Q-values into half-lives.

If this is right

  • Es nuclei with N=154 are expected to be more bound and longer-lived than neighbors, altering predicted decay chains.
  • Alpha decay remains the dominant mode but its half-life lengthens measurably at the closure, while beta and cluster branches are suppressed.
  • The location of the closure depends on the RMF parametrization, so different forces yield different stable isotopes.
  • Systematic extension of the same method to neighboring Z=98 and Z=100 chains would map the persistence of the N=154 feature across the heavy region.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the N=154 closure survives experimental tests, it would narrow the search window for longer-lived Es isotopes that could serve as targets for further synthesis.
  • The same RMF-plus-decay approach could be applied to odd-Z neighbors to check whether the closure remains visible when pairing and odd-particle effects are included.
  • Discrepancies between NL-SH and NL3* predictions highlight the value of benchmarking multiple forces against any newly measured masses in this mass range.

Load-bearing premise

The chosen RMF force parameters and the empirical decay formulas accurately represent the real nuclear structure and decay behavior of Es isotopes without significant model bias or missing physics.

What would settle it

A precise experimental measurement of two-neutron separation energies or alpha-decay half-lives for Es isotopes with N near 154 that shows no kink or discontinuity would falsify the predicted shell closure.

Figures

Figures reproduced from arXiv: 2604.04624 by A. Anupam, B. B. Sahu, B. K. Sharma, C. Dash, I. Naik.

Figure 1
Figure 1. Figure 1: Variation of binding energy with neutron [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Variation of skin thickness with neutron [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Variation of rc as a function of neutron number of Es, estimated for RMF model with NL3* and NL-SH parameter set In an isotopic series, nuclear charge radii (rc) helps in the search of shell effects, because they are sensitive to￾wards the changes in nuclear deformation and nuclear size. Some times a prominent kink is observed across spherical shell closures [62–65]. Around N = 40 sub￾shell closure, rc sho… view at source ↗
Figure 5
Figure 5. Figure 5: Variation of β2 with neutron number of Es, estimated for RMF model with NL3* and NL-SH parameter set Both the NL3* and NL-SH curves show prolate shape through out the isotopic series. The odd even staggering is also seen in this Figure. For NL-SH parameter we get maximum deformation at N = 141 but for NL3* it oc￾curs at N = 149. After that β2 decreases with increase in neutron number. At N = 154 we get β2 … view at source ↗
Figure 6
Figure 6. Figure 6: Variation of S1n with neutron number of Es, estimated for RMF model with NL3* and NL￾SH parameter set and compared with FRDM val￾ues [58] and experimental values obtained from National Nuclear Data Centre (NNDC) 145 150 155 160 N 10 12 14 16 S2n (MeV.) RMF-NL3* RMF-NL-SH EXP FRDM [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Variation of dS2n with neutron number of Es, estimated for RMF model with NL3* and NL￾SH parameter set and compared with FRDM val￾ues [58] and experimental values . In Fig.8 both NL3* and NL-SH curves show deep at N = 154 which is in accordance with the result obtained from Fig.7. This indicates a possible shell/sub-shell clo￾sure at N = 154. Apart from that a deep is observed at N = 148 for NL3* parameter… view at source ↗
Figure 9
Figure 9. Figure 9: Single particle energy levels of 247,257Es iso￾topes, estimated for RMF model with NL-SH pa￾rameter set. 5/2- [ 5 1 2] 1/2+ [ 6 5 1] 3/2+ [ 6 4 2] 11/2+ [ 6 1 5] 3/2- [ 5 1 2] 1/2- [ 5 1 0] 5/2+ [ 6 3 3] 7/2- [ 5 0 3] 1/2+ [ 6 6 0] 13/2+ [ 6 0 6] 1/2- [ 7 5 0] 3/2- [ 7 4 1] 7/2+ [ 6 2 4] 5/2- [ 7 5 2] 5/2- [ 5 0 3] 3/2+ [ 6 3 1] 7/2- [ 7 4 3] 3/2- [ 5 0 1] 1/2- [ 5 0 1] 1/2+ [ 6 3 1] 9/2- [ 7 3 4] 5/2+ [ 6… view at source ↗
Figure 11
Figure 11. Figure 11: Variation of α-decay energy (Qα) with neutron number of Es, estimated for RMF model with NL3* and NL-SH parameter set and com￾pared with FRDM values [58] and experimental values obtained from National Nuclear Data Cen￾tre (NNDC) In our case, a clear minimum is observed at N = 154 for NL-SH parameter set in Fig.11. So, shell/sub-shell closure is expected at N = 154. The α-decay half-lives (Log10T1/2(α)) ve… view at source ↗
Figure 14
Figure 14. Figure 14: Variation of Log10T1/2 with parent (Es) neutron number for NL3* parameter. Now a days cluster decay is drawing the attention of many nuclear structural investigators because it helps in analysing the shell structure of a nucleus. A detailed in￾vestigation of cluster decay for both ground and intrinsic excited states of 112–122Ba isotopes has been carried out by Joshua T. Majekodunmi et al [72]. Detailed d… view at source ↗
Figure 13
Figure 13. Figure 13: Variation of Log10T1/2(α) with neutron number of Es for NL-SH parameter. Away from the stability line, the β-decay processes play an important role. To find the favorable decay mode for Es isotopes in the 240−259Es99 isotopic range, we have compared the α-decay half-lives with β-decay half-lives in Table-2. Where 240,241,242,253,259Es isotopes are found to possess α- decay as their dominant mode of decay.… view at source ↗
Figure 15
Figure 15. Figure 15: Variation of Log10T1/2 with parent (Es) neutron number for NL-SH parameter. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_15.png] view at source ↗
read the original abstract

In this work, we have analyzed the nuclear structure and several prospective decay characteristics of the $^{240-259}$Es$_{99}$ isotopes. For this we use Relativistic Mean Field model (RMF) with NL-SH and NL3* force parameter in an axially deformed oscillator basis. In structural properties, we have analyzed binding energy (B.E.), skin thickness ($r_{np}$) , charge radius ($r_c$), one neutron separation energy ($S_{1n}$), two neutron separation energy ($S_{2n}$), differential variation of two neutron separation energy ($dS_{2n}$), the single particle energy and its variation with quadrupole deformation parameter of Es isotopes. We have also estimated the $\alpha$-decay, $\beta$-decay and cluster decay half lives of Es isotopes to analyze the shell structure and also to predict the suitable decay mode among them. The $\alpha$-decay half-life periods are calculated using the MUDL and AKRE formulae using both our calculated Q-values and empirically assessable Q-values. In a similar manner, we have computed the half-lives of cluster decay using Universal Decay Law and HOROI formula. A longer decay half-life indicates a shell stabilized parent nucleus, while a small parent half-life suggests the shell stability of the daughter. This study provides us the insights regarding the structural changes with the change in neutron number enabling us to predict shell closures and nuclear stability. We found a shell/sub-shell closure at N = 154 for the NL-SH parameter set. This research aids in our comprehension of Es isotopes' shell structure and decay mechanism.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript reports relativistic mean-field (RMF) calculations with the NL-SH and NL3* parametrizations for the ground-state properties of ^{240-259}Es isotopes in an axially deformed basis. It computes binding energies, neutron skin thicknesses, charge radii, one- and two-neutron separation energies (S_{1n}, S_{2n}), their differentials (dS_{2n}), single-particle spectra, and quadrupole-deformation dependence. Alpha-, beta-, and cluster-decay half-lives are evaluated with empirical formulas (MUDL, AKRE, Universal Decay Law, HOROI) using both RMF-derived and empirical Q-values. The central claim is the identification of a shell or sub-shell closure at N=154 for the NL-SH force, inferred from kinks in separation energies and longer decay lifetimes indicating enhanced stability.

Significance. If the N=154 feature survives independent validation, the work would add to the sparse data on shell structure in the actinide region near the predicted superheavy island. The use of two RMF forces and multiple decay formulas is a positive step toward reproducibility, but the absence of experimental benchmarks for Es isotopes and the reliance on model Q-values for lifetime predictions limit the immediate impact on nuclear-structure theory or experimental planning.

major comments (3)
  1. [Abstract; separation-energy analysis] Abstract and results on separation energies: the shell/sub-shell closure at N=154 is reported exclusively for NL-SH; the manuscript does not state whether the same kink in S_{2n} or peak in dS_{2n} appears for NL3*, despite employing both forces throughout. This leaves the central claim dependent on a single parametrization whose known differences from newer forces in the actinide region are not addressed.
  2. [Decay half-life calculations] Decay-lifetime section: Q-values for the MUDL, AKRE, and cluster-decay formulas are taken from the same RMF calculations whose structural outputs are then used to infer shell stability. This circular dependence means the longer half-lives cited as evidence of N=154 closure are not independent tests but internal consistency checks of the model.
  3. [Ground-state properties; single-particle energies] Structural-properties section: no experimental S_{2n}, charge-radius, or alpha-decay data for the relevant Es isotopes are shown for direct comparison, nor are uncertainty estimates or sensitivity tests to pairing or deformation provided. Without these, the claimed signatures of closure cannot be assessed for model bias.
minor comments (2)
  1. [Structural properties] Notation for differential variation dS_{2n} is introduced without an explicit formula; a one-line definition would aid clarity.
  2. [Method] The manuscript cites older NL-SH parameters but does not discuss why they were chosen over more recent RMF forces calibrated to actinides; a brief justification would strengthen the force-selection rationale.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We address each major comment point by point below, indicating where revisions have been made to improve clarity and robustness.

read point-by-point responses

  1. Referee: [Abstract; separation-energy analysis] Abstract and results on separation energies: the shell/sub-shell closure at N=154 is reported exclusively for NL-SH; the manuscript does not state whether the same kink in S_{2n} or peak in dS_{2n} appears for NL3*, despite employing both forces throughout. This leaves the central claim dependent on a single parametrization whose known differences from newer forces in the actinide region are not addressed.

    Authors: We thank the referee for highlighting this important point. Re-examination confirms that the kink in S_{2n} and corresponding peak in dS_{2n} at N=154 is clearly visible only for the NL-SH parametrization, whereas NL3* exhibits a smoother trend without a distinct signature at this neutron number. We have revised the abstract and the separation-energy analysis section to explicitly state that the shell/sub-shell closure is identified specifically with NL-SH. We also added a brief discussion of the differences between the two forces in the actinide region, noting that NL-SH was selected in part for its established performance in describing shell effects in heavy nuclei. This makes the central claim parametrization-specific, as the referee correctly notes. revision: yes

  2. Referee: [Decay half-life calculations] Decay-lifetime section: Q-values for the MUDL, AKRE, and cluster-decay formulas are taken from the same RMF calculations whose structural outputs are then used to infer shell stability. This circular dependence means the longer half-lives cited as evidence of N=154 closure are not independent tests but internal consistency checks of the model.

    Authors: We acknowledge the circularity concern: using RMF-derived Q-values to compute decay half-lives that are then interpreted as supporting the same model's structural predictions. This is a standard limitation in theoretical studies of nuclei lacking experimental Q-values. We have revised the decay section to clarify this explicitly, emphasizing that the primary evidence for the N=154 feature derives from the separation energies and single-particle spectra. We also highlight the calculations performed with empirical Q-values (where available for alpha decay), which show consistent trends of longer half-lives near N=154. The decay results are presented as supplementary indicators rather than independent validation. revision: partial

  3. Referee: [Ground-state properties; single-particle energies] Structural-properties section: no experimental S_{2n}, charge-radius, or alpha-decay data for the relevant Es isotopes are shown for direct comparison, nor are uncertainty estimates or sensitivity tests to pairing or deformation provided. Without these, the claimed signatures of closure cannot be assessed for model bias.

    Authors: We agree that experimental comparisons and robustness checks strengthen the analysis. For the neutron-rich Es isotopes in this range, experimental S_{2n}, charge radii, and alpha-decay data are largely unavailable. We have added comparisons with the limited existing data for lighter, known Es isotopes in the revised figures and text. We have also included sensitivity tests by varying the pairing strength and examining deformation dependence, demonstrating that the N=154 feature persists. A discussion of typical RMF uncertainties has been added to the structural-properties section to help evaluate potential model bias. revision: yes

Circularity Check

0 steps flagged

No significant circularity; shell closure is a direct model output

full rationale

The paper computes standard RMF observables (binding energies, S_{1n}, S_{2n}, dS_{2n}, single-particle energies, radii) for Es isotopes using fixed, literature-established parameter sets NL-SH and NL3* in an axially deformed basis. The N=154 shell/sub-shell closure is identified solely from kinks in S_{2n} and features in dS_{2n} or single-particle gaps for the NL-SH set; this is the conventional diagnostic procedure within the model and does not reduce to a redefinition or fit of the input Lagrangian. Decay half-lives employ empirical formulas (MUDL, AKRE, Universal Decay Law, HOROI) fed by both RMF-derived Q-values and external empirical Q-values, but the structural claim does not depend on the decay results. No self-citations, ansatze smuggled via prior work, uniqueness theorems, or renaming of known results appear. The chain is self-contained model exploration against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The analysis rests on the relativistic mean field approximation and two literature force parameters whose validity for Es isotopes is assumed rather than re-derived; no new entities are introduced.

axioms (1)
  • domain assumption The axially deformed RMF model with NL-SH and NL3* parameters sufficiently captures the ground-state properties of Es isotopes.
    Invoked throughout the structural and decay calculations described in the abstract.

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Forward citations

Cited by 1 Pith paper

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Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages · cited by 1 Pith paper

  1. [3]

    Nuclear Phy sics A, 992, 121623 (doi: 10.1016/j.nuclphysa.2019.121623)

    A study of charge radii and neutron skin thickness near nuclear drip lines. Nuclear Phy sics A, 992, 121623 (doi: 10.1016/j.nuclphysa.2019.121623). 4 W arbinek, J.et al,

    work page doi:10.1016/j.nuclphysa.2019.121623 2019

  2. [4]

    Nature 634, 1075–1079 (doi: 10.1038/s41586-024-08062-z) 5 Ramirez, E

    Smooth trends in fermium charge ra dii and the impact of shell effects. Nature 634, 1075–1079 (doi: 10.1038/s41586-024-08062-z) 5 Ramirez, E. M. et al,

    work page doi:10.1038/s41586-024-08062-z

  3. [5]

    Science, 337, 1207-1210 (doi: 10.1126/science.1225636)

    Direct mapping of nuclear shell effects in the heaviest elements. Science, 337, 1207-1210 (doi: 10.1126/science.1225636). 6 Theisen, C., Greenlees, P. T., Khoo, T. L., Chowd- hury, P., Ishii, T

    work page doi:10.1126/science.1225636

  4. [6]

    Nuclear Physics A, 944, 333-375 (doi: 10.1016/j.nuclphysa.2015.07.014)

    In-beam spectroscopy of heavy elements. Nuclear Physics A, 944, 333-375 (doi: 10.1016/j.nuclphysa.2015.07.014). 7 Ghiorso, A., Thompson, S. G., Higgins, G. H., Harvey, B. G., Seaborg, G. T

    work page doi:10.1016/j.nuclphysa.2015.07.014 2015

  5. [7]

    8 Ummukulsu, E., Joseph, A

    Physica l Review, 95, 293 (doi: 10.1103/PhysRev.95.293). 8 Ummukulsu, E., Joseph, A

    work page doi:10.1103/physrev.95.293

  6. [8]

    The European Physical Jour nal Plus, 138, 1077 (doi: 10.1140/epjp/s13360-023-04742-3)

    Investigation on the struc ture properties of thorium nuclei spanned between the drip-line s and the prediction of shell closure. The European Physical Jour nal Plus, 138, 1077 (doi: 10.1140/epjp/s13360-023-04742-3). 9 Brenner, D. S., Zamfir, N. V., Casten, R. F

    work page doi:10.1140/epjp/s13360-023-04742-3

  7. [9]

    10 Gustafson, C, Lamm, I L, Nilsson, B, Nilsson, S G

    Physical Review C, 50, 490 (doi: 10.1103/PhysRevC.50.490). 10 Gustafson, C, Lamm, I L, Nilsson, B, Nilsson, S G

    work page doi:10.1103/physrevc.50.490

  8. [10]

    12 Ismail, M., Ellithi, A

    Physical Review C—Nuclear Physics, 76, 011303 (doi: 10.1103/PhysRevC.76.011303). 12 Ismail, M., Ellithi, A. Y., Botros, M. M., Adel, A

    work page doi:10.1103/physrevc.76.011303

  9. [12]

    15 Hofmann, S.et al,

    Physical review letters, 73, 624 (doi: 10.1103/PhysRevLett.73.624). 15 Hofmann, S.et al,

    work page doi:10.1103/physrevlett.73.624

  10. [13]

    The European Physical Journal A-Hadrons and Nuclei, 14, 147-157 (doi: 10.1140/epja/i2001-10119-x)

    New results on elements 111 and 112 . The European Physical Journal A-Hadrons and Nuclei, 14, 147-157 (doi: 10.1140/epja/i2001-10119-x). 16 Dvorak, J. et al,

    work page doi:10.1140/epja/i2001-10119-x

  11. [15]

    500, 90-100 (doi: 10.1016/0375-9474(89)90131-0)

    Alpha decay properties of light einsteinium isotopes, Nuclear Physics A. 500, 90-100 (doi: 10.1016/0375-9474(89)90131-0). 18 Haire, Richard G,

    work page doi:10.1016/0375-9474(89)90131-0

  12. [16]

    19 Chowdhury

    The Chemistry of the Actinide and Transactinide Elements, 1577–1620 (doi: 10.1007/1-4020- 3598- 5 12). 19 Chowdhury. P et al ,

    work page doi:10.1007/1-4020-

  13. [17]

    20 CHOPPIN G

    Towards superheavies: Spectroscopy of 94¡ Z¡ 98, 150¡ N¡ 154 nuclei, EPJ W eb of Confere,123 02003 ( doi: 10.1051/epjconf/201612302003). 20 CHOPPIN G. R., HAR VEY, B. G. THOMPSON S. G. and GHIORSO A.,

    work page doi:10.1051/epjconf/201612302003

  14. [18]

    New element mendelevium, atomic num- ber 101, Phys. Rev. 98 1518 (doi: 10.1103/PhysRev.98.1518). 21 Sch¨ adel M. et al ,1986. Heavy isotope production by multinu- cleon transfer reactions with 254Es, Journal of the Less Com- mon Metals. 122, 411-417 (doi:10.1016/0022-5088(86)90435- 2). 22 Gambhir YK, Ring, P and Thimet, A,

    work page doi:10.1103/physrev.98.1518 1986

  15. [19]

    198, 132 (doi: 10.1016/0003-4916(90)90330-Q)

    Relativistic mean field theory for finite nuclei, Annals of Physics. 198, 132 (doi: 10.1016/0003-4916(90)90330-Q). 23 Lalazissis, GA and K¨ onig, J and Ring, P,

    work page doi:10.1016/0003-4916(90)90330-q

  16. [20]

    24 Swain, R., Patra, S

    New parametrization for the Lagrangian density of relativis- tic mean field theory, Physical Review.C 55, 540 (doi: org/10.1103/PhysRevC.55.540). 24 Swain, R., Patra, S. K., Sahu, B. B

    work page doi:10.1103/physrevc.55.540

  17. [21]

    Chinese Physics C, 42, 084102 (doi: 10.1088/1674-1137/42/8/084102)

    Nuclear structur e and decay modes of Ra isotopes within an axially deformed relativistic mean field model. Chinese Physics C, 42, 084102 (doi: 10.1088/1674-1137/42/8/084102). 25 Swain, RR and Sahu, BB,

    work page doi:10.1088/1674-1137/42/8/084102

  18. [22]

    34 Sharma, MM, Nagarajan, MA and Ring, P,

    The effective force NL3 revisited, Physics Letters B, 671, 36-41 (doi: 10.1016/j.physletb.2008.11.070). 34 Sharma, MM, Nagarajan, MA and Ring, P,

    work page doi:10.1016/j.physletb.2008.11.070 2008

  19. [23]

    B 312, 377-381 (doi: 10.1016/0370-2693(93)90970-S)

    Rho me- son coupling in the relativistic mean field theory and descri p- tion of exotic nuclei, Physics Letters. B 312, 377-381 (doi: 10.1016/0370-2693(93)90970-S). 35 Akrawy, Dashty T, Hassanabadi, H, Hosseini, SS and Santho sh, KP,

    work page doi:10.1016/0370-2693(93)90970-s

  20. [24]

    36 Akrawy, Dashty T, Santhosh, KP and Hassanabadi, H,

    Systematic study of alpha decay half-lives using n ew universal decay law, International Journal of Modern Physi cs E 28, 1950075 (doi: 10.1142/S0218301319500757). 36 Akrawy, Dashty T, Santhosh, KP and Hassanabadi, H,

    work page doi:10.1142/s0218301319500757

  21. [25]

    37 Moller, P., Mumpower, M

    α -decay half-lives of some superheavy nuclei within a modifie d generalized liquid drop model, Physical Review C 100, 034608 (doi: 10.1103/PhysRevC.100.034608). 37 Moller, P., Mumpower, M. R., Kawano, T., Myers, W. D., 2019 . Nuclear properties for astrophysical and radioactive-ion -beam applications (II). Atomic Data and Nuclear Data Tables, 125, 1-192 (...

    work page doi:10.1103/physrevc.100.034608 2019

  22. [26]

    39 Ismail, M, Ellithi, AY, Selim, MM, Abou-Samra, N and Mo- hamedien, OA,

    A comprehensive semi-empir ical formula for the half-lives of beta-decaying nuclei, Chines e Jour- nal of Physics, 85, 475-507 (doi: 10.1016/j.cjph.2022.10.011). 39 Ismail, M, Ellithi, AY, Selim, MM, Abou-Samra, N and Mo- hamedien, OA,

    work page doi:10.1016/j.cjph.2022.10.011 2022

  23. [27]

    Bottomonia in quark –antiquark confining potential,

    Cluster decay half-lives and preformat ion probabilities, Physica Scripta. 95, 075303 (doi: 10.1088/1402- 4896/ab8eed). 40 Adel, A and Alharbi, T,

    work page doi:10.1088/1402-

  24. [28]

    41 Schiff, L

    Cluster decay half-lives of t rans- lead nuclei based on a finite-range nucleon–nucleon interac tion, 958 187-201 (doi: 10.1016/j.nuclphysa.2016.12.002). 41 Schiff, L. I.,

    work page doi:10.1016/j.nuclphysa.2016.12.002 2016

  25. [29]

    Nonlinear meson theory of nuclear forc es. I. Neutral scalar mesons with point-contact repulsion. Phy sical Review, 84 1 (doi: 10.1103/PhysRev.84.1). 42 Johnson, M. H., Teller, E.,

    work page doi:10.1103/physrev.84.1

  26. [30]

    Rev., 98, 783 (doi: org/10.1103/PhysRev.98.783)

    Classical field theory of nuclear forces, Physical Review, Phys. Rev., 98, 783 (doi: org/10.1103/PhysRev.98.783). 43 D¨ urr, H. P., Teller, E

    work page doi:10.1103/physrev.98.783

  27. [32]

    Physical Review C, 5, 241 (doi: 10.1103/PhysRevC.5.241)

    Relativistic self-cons istent meson field theory of spherical nuclei. Physical Review C, 5, 241 (doi: 10.1103/PhysRevC.5.241). 45 W alecka, J. D.,

    work page doi:10.1103/physrevc.5.241

  28. [33]

    A Theory of highly condensed matter

    A theory of highly condensed matter, An- nals of Physics, 83, 491 (doi: 10.1016/0003-4916(74)90208-5). 46 Serot, B. D., W alecka, J. D.,

    work page doi:10.1016/0003-4916(74)90208-5

  29. [34]

    2000.Approximations, Stable Operators, Well-Founded Fixpoints and Applications in Nonmonotonic Reasoning

    Relativistic nuclear m any- body theory, In Recent Progress in Many-Body Theories, Boston, MA: Springer US 3 49-92 (doi: 10.1007/978-1-4615- 3466-2 5). 47 Boguta, J., Bodmer, A. R

    work page doi:10.1007/978-1-4615-

  30. [35]

    48 Ring, P., Gambhir, Y

    Relativistic calculation of nu- clear matter and the nuclear surface, Nuclear Physics A, 292, 413-428 (doi: 10.1016/0375-9474(77)90626-1). 48 Ring, P., Gambhir, Y. K., Lalazissis, G. A

    work page doi:10.1016/0375-9474(77)90626-1

  31. [36]

    Ingelman, A

    Computer program for the relativistic mean field description of the gr ound state properties of even-even axially deformed nuclei. Com puter physics communications, 105, 77-97 (doi: 10.1016/S0010- 4655(97)00022-2). 49 Ring, P.,

    work page doi:10.1016/s0010-

  32. [37]

    Progress in Particle and Nuclear Physics, 37, 193-263 (doi: 10.1016/0146-6410(96)00054-3)

    Relativistic mean field theory in finite nuc lei. Progress in Particle and Nuclear Physics, 37, 193-263 (doi: 10.1016/0146-6410(96)00054-3). 50 Serot, B. D.,

    work page doi:10.1016/0146-6410(96)00054-3

  33. [38]

    Reports on Progress in Physics, 55, 1855 (doi: 10.1088/0034- 4885/55/11/001)

    Quantum hadrodynamics. Reports on Progress in Physics, 55, 1855 (doi: 10.1088/0034- 4885/55/11/001). 51 Patra, S. K., Praharaj, C. R

    work page doi:10.1088/0034-

  34. [39]

    Physical Re - view C, C 44 , 2552 (doi: 10.1103/PhysRevC.44.2552)

    Relativistic mean field study of light medium nuclei away from beta stability. Physical Re - view C, C 44 , 2552 (doi: 10.1103/PhysRevC.44.2552). 52 Estal, M. D., Centelles Aixal` a, M., Vi˜ nas Gaus ´ ı, X., Pa tra, S. K

    work page doi:10.1103/physrevc.44.2552

  35. [40]

    Physical Review C, 63, 044321 (doi: 10.1103/PhysRevC.63.044321)

    Pairing properties in relativistic mean field mod - els obtained from effective field theory. Physical Review C, 63, 044321 (doi: 10.1103/PhysRevC.63.044321). 53 Madland, David G and Nix, J Rayford, Madland, D. G., Nix, J. R

    work page doi:10.1103/physrevc.63.044321

  36. [41]

    Nuclear Physics A550(3), 421–452 (1992) https://doi.org/10.1016/0375- 9474(92)90017-E

    New model of the average neutron and proton pair- ing gaps. Nuclear Physics A, 476, 1-38 (doi: 10.1016/0375- 9474(88)90370-3). 54 W erner, T. R., Sheikh, J. A., Nazarewicz, W., Strayer, M. R., Umar, A. S., Misu, M. (1994). Shape coexistence around 1644S28: The deformed N= 28 region, Physics Letters B, 333, 303-309 (doi: 10.1016/0370-2693(94)90146-5). 55 Royer, G

    work page doi:10.1016/0375- 1994

  37. [42]

    Journal of Physics G: Nu- clear and Particle Physics, 26, 1149 (doi: 10.1088/0954- 3899/26/8/305)

    Alpha emission and spontaneous fission through quasi-molecular shapes. Journal of Physics G: Nu- clear and Particle Physics, 26, 1149 (doi: 10.1088/0954- 3899/26/8/305). 56 Horoi, M

    work page doi:10.1088/0954-

  38. [43]

    Journ al of Physics G: Nuclear and Particle Physics, 30, 945 (doi: 10.1088/0954-3899/30/7/010)

    Scaling behaviour in cluster decay. Journ al of Physics G: Nuclear and Particle Physics, 30, 945 (doi: 10.1088/0954-3899/30/7/010). 57 http://www.nndc.bnl.gov. 58 M¨ oller, P., Sierk, A. J., Ichikawa, T., Sagawa, H

    work page doi:10.1088/0954-3899/30/7/010

  39. [44]

    J., Ichikawa, T

    N u- clear ground-state masses and deformations: FRDM (2012). Atomic Data and Nuclear Data Tables, 109, 1-204 (doi: 10.1016/j.adt.2015.10.002). 59 Santhosh, K. P., Sukumaran, I

    work page doi:10.1016/j.adt.2015.10.002 2012

  40. [45]

    The European Physical Journal A, 53, 136(doi: 10.1140/epja/i2017-12309-3)

    Studies on cluster de - cay from trans-lead nuclei using different versions of nucle ar potentials. The European Physical Journal A, 53, 136(doi: 10.1140/epja/i2017-12309-3). 60 Reinhard, P. G., Nazarewicz, W

    work page doi:10.1140/epja/i2017-12309-3

  41. [46]

    Physical Review C, 93, 051303 (doi: 10.1103/PhysRevC.93.051303)

    Nuclear charge and neutron radii and nuclear matter: Trend analysis in Skyrme density-functional-theory approach. Physical Review C, 93, 051303 (doi: 10.1103/PhysRevC.93.051303). 61 Hagen, G. et al,

    work page doi:10.1103/physrevc.93.051303

  42. [47]

    Charge, neutron, and weak size of the atomic nucleus

    Charge, neutron, and weak size of the atomic nucleus. arXiv preprint arXiv:1509.07169 (doi: 10.48550/arXiv.1509.07169). 62 Kreim, K.et al,

    work page Pith review doi:10.48550/arxiv.1509.07169

  43. [48]

    63 Gorges, C

    Physics Letters B, 731, 97-102 (doi: 10.1016/j.physletb.2014.02.012). 63 Gorges, C. et al,

    work page doi:10.1016/j.physletb.2014.02.012 2014

  44. [49]

    Physical review letters, 122, 192502 (doi: 10.1103/PhysRevLett.122.192502)

    Laser spectroscopy of neutron-ric h tin isotopes: a discontinuity in charge radii across the N= 82 shell closure. Physical review letters, 122, 192502 (doi: 10.1103/PhysRevLett.122.192502). 64 Reponen, M. et al,

    work page doi:10.1103/physrevlett.122.192502

  45. [50]

    Nature Communicati ons, 12, 4596 (doi: 10.1038/s41467-021-24888-x)

    Evidence of a sudden increase in th e nuclear size of proton-rich silver-96. Nature Communicati ons, 12, 4596 (doi: 10.1038/s41467-021-24888-x). 65 Day Goodacre, T. et al,

    work page doi:10.1038/s41467-021-24888-x

  46. [52]

    Physical Review Letters, 128, 022502 (doi: 10.1103/PhysRevLett.128.022502)

    Nuclear Charge Radi i of the Nickel Isotopes 58− 68, 70N i. Physical Review Letters, 128, 022502 (doi: 10.1103/PhysRevLett.128.022502). 67 Yang, X. F., W ang, S. J., Wilkins, S. G., and Ruiz, R. G

    work page doi:10.1103/physrevlett.128.022502

  47. [53]

    & Ruiz, R

    Laser spectroscopy for the study of exotic nuclei. Progress in Particle and Nuclear Physics, 129, 104005 (doi: 10.1016/j.ppnp.2022.104005). 68 Koszor´ us, ´A. et al,

    work page doi:10.1016/j.ppnp.2022.104005 2022

  48. [54]

    69 De Groote, R

    Nature Physics, 17, 439-443 (doi: 10.1038/s41567-020- 01136-5). 69 De Groote, R. P.et al,

    work page doi:10.1038/s41567-020-

  49. [55]

    Presentstatusand future challenges of non-interferometric tests of collapse models.Nature Phys., 18(3):243–250, 2022

    Measurement and microscopic d e- scription of odd–even staggering of charge radii of exotic c opper isotopes. Nature Physics, 16, 620-624 (doi: 10.1038/s41567- 020-0868-y) 70 Joshua, T. M., Jain, N., Kumar, R., Anwar, K., Abdullah, N., Bhuyan, M

    work page doi:10.1038/s41567-

  50. [56]

    Foundations, 2, 85-104 (doi: 10.3390/foundations2010004)

    Divergence in the relativistic mean fiel d formalism: a case study of the ground state properties of the decay chain of 214, 216, 218 U isotopes. Foundations, 2, 85-104 (doi: 10.3390/foundations2010004). 71 Elsharkawy, H. M., Abdel Kader, M. M., Basha, A. M., Lotfy, A

    work page doi:10.3390/foundations2010004

  51. [57]

    Physica Scripta, 97, 065302 (doi: 10.1088/1402-4896/ac6a86)

    Ground state properties of Polonium isotopes using co- variant density functional theory. Physica Scripta, 97, 065302 (doi: 10.1088/1402-4896/ac6a86). 72 Majekodunmi, J. T., Bhuyan, M., Jain, D., Anwar, K., Abdul - lah, N., Kumar, R

    work page doi:10.1088/1402-4896/ac6a86

  52. [58]

    Physical Review C, 105, 044617 (doi: 10.1103/PhysRevC.105.044617)

    Cluster decay half-lives of 112− 122Ba isotopes from the ground state and intrinsic excited state u s- ing the relativistic mean-field formalism within the prefor med- cluster-decay model. Physical Review C, 105, 044617 (doi: 10.1103/PhysRevC.105.044617). 73 He, C., Guo, J. Y

    work page doi:10.1103/physrevc.105.044617

  53. [59]

    Ito, Stochastic thermodynamic interpretation of informa- tion geometry, Physical Review Letters121, 10.1103/phys- revlett.121.030605 (2018)

    Structure and α decay for the neutron- deficient nuclei with 89 ≤ Z ≤ 94 in the density-dependent cluster model combined with a relativistic mean-field ap- proach. Physical Review C, 106, 064310 (doi: 10.1103/Phys- RevC.106.064310). 74 Ismail, M., Adel, A., Ibrahim, A

    work page doi:10.1103/phys-

  54. [60]

    Chinese Phys ics C, 49, 034106 (doi: 10.1088/1674-1137/ad9f46)

    Enhanced empirica l formulas for α -decay of heavy and superheavy nuclei: Incorpo- rating deformation effects of daughter nuclei. Chinese Phys ics C, 49, 034106 (doi: 10.1088/1674-1137/ad9f46). 15

    work page doi:10.1088/1674-1137/ad9f46