arxiv: 2604.21784 · v2 · submitted 2026-04-23 · ⚛️ nucl-th

Recognition: 2 theorem links

· Lean Theorem

Ground-state properties of superheavy Z=122 isotopes within the deformed relativistic Hartree-Bogoliubov theory in continuum

Jin-Hong Zhuang , Zhen-Hua Zhang , Yuan-Yuan Wang , Cong Pan , Kai-Yuan Zhang , Huan-Yu Zhang , Yu Sun

Authors on Pith no claims yet

Pith reviewed 2026-05-12 03:38 UTC · model grok-4.3

classification ⚛️ nucl-th

keywords superheavy nucleiZ=122drip linesmagic numbersrelativistic Hartree-Bogoliubovnuclear deformationground-state propertiescontinuum effects

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The pith

The deformed relativistic Hartree-Bogoliubov theory in continuum determines the proton and neutron drip lines for Z=122 superheavy isotopes and suggests magic numbers at N=184, 258, and 350.

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

The paper applies the deformed relativistic Hartree-Bogoliubov theory in continuum to calculate ground-state properties of nuclei with 122 protons across many neutron numbers. It obtains binding energies, separation energies, deformations, and radii while comparing results to the spherical relativistic continuum Hartree-Bogoliubov approach. Analysis of Fermi energies and nucleon separation energies then locates the points at which additional protons or neutrons become unbound. The same data sets identify neutron counts where shell effects appear to create extra stability.

Core claim

Ground-state properties of Z=122 isotopes are computed in the deformed relativistic Hartree-Bogoliubov theory in continuum and compared with relativistic continuum Hartree-Bogoliubov results. This yields the proton and neutron drip lines within both frameworks from the behavior of Fermi and separation energies, together with the identification of possible magic numbers N=184, 258, and 350.

What carries the argument

Deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), which incorporates axial deformation, pairing, and continuum coupling to obtain self-consistent solutions for heavy nuclei.

If this is right

The proton drip line marks the last bound Z=122 isotope on the proton-rich side.
The neutron drip line marks the last bound Z=122 isotope on the neutron-rich side.
Nuclei with N=184, 258, or 350 are expected to exhibit enhanced stability against particle emission.
Single-particle energies, radii, and pairing gaps change smoothly with neutron number except near the suggested magic values.

Where Pith is reading between the lines

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

Confirmation of the magic numbers would narrow the search window for longer-lived superheavy elements in experiments.
The same computational strategy can be repeated for nearby proton numbers to chart the full superheavy stability region.
Including triaxial or octupole shapes more systematically could shift the exact drip-line locations in future calculations.

Load-bearing premise

The density functional and its treatment of continuum and pairing effects remain reliable for nuclei with 122 protons whose deformation and neutron excess lie far beyond the region where the functional was originally calibrated.

What would settle it

A measured two-neutron separation energy for a Z=122 nucleus with neutron number near 258 that shows no local maximum relative to neighboring isotopes would falsify the suggested magic number at N=258.

Figures

Figures reproduced from arXiv: 2604.21784 by Cong Pan, Huan-Yu Zhang, Jin-Hong Zhuang, Kai-Yuan Zhang, Yuan-Yuan Wang, Yu Sun, Zhen-Hua Zhang.

**Figure 1.** Figure 1: FIG. 1. The evolution of PECs for the view at source ↗

**Figure 2.** Figure 2: FIG. 2. The PECs of view at source ↗

**Figure 3.** Figure 3: FIG. 3. The PECs of view at source ↗

**Figure 4.** Figure 4: FIG. 4. The binding energy per nucleon view at source ↗

**Figure 6.** Figure 6: FIG. 6. The two-proton separation energy view at source ↗

**Figure 5.** Figure 5: FIG. 5. The (a) proton Fermi surface view at source ↗

**Figure 7.** Figure 7: FIG. 7. The same as Fig view at source ↗

**Figure 8.** Figure 8: FIG. 8. Single-particle energy levels for spherical states view at source ↗

**Figure 9.** Figure 9: FIG. 9. The quadrupole deformation view at source ↗

**Figure 11.** Figure 11: FIG. 11. The proton and neutron pairing gap, ∆ view at source ↗

read the original abstract

The ground-state properties of superheavy $Z = 122$ isotopes are investigated using the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc). Bulk properties, including binding energies, Fermi energies, nucleon separation energies, quadrupole deformations, and root-mean-square radii, are calculated. The results are compared with those obtained from the relativistic continuum Hartree-Bogoliubov (RCHB) theory. By examining the dependence on the angular-momentum cutoff and the effects of triaxial and octupole deformations, a strategy for determining the ground states is suggested. Furthermore, based on an analysis of the Fermi and nucleon separation energies, the proton and neutron drip lines for $Z = 122$ isotopes are determined within both the DRHBc and RCHB frameworks. The possible magic numbers $N=184$, 258, and 350 are also suggested. Finally, the evolution of single-particle levels, deformation, charge and neutron radii as well as average pairing gaps with increasing neutron number, is discussed.

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.

Desk Editor's Note private letter to a colleague

DRHBc calculation for the Z=122 chain supplies concrete drip-line and magic-number estimates but rests on unvalidated extrapolation of a functional calibrated far from this region.

read the letter

The main takeaway is that this paper runs the deformed relativistic Hartree-Bogoliubov in continuum (DRHBc) on the full Z=122 isotopic chain and extracts proton and neutron drip lines plus candidate magic numbers at N=184, 258, and 350. It also compares those results to the spherical RCHB version and checks sensitivity to angular-momentum cutoff and higher-order deformations. That is the concrete new output: specific numbers for an uncalculated superheavy chain that experimental groups can use as targets or benchmarks. The work is competent at what it sets out to do. The authors lay out the numerical strategy clearly, show how they locate the ground states, and track the evolution of radii, deformations, and pairing gaps with neutron number. Those plots and tables are the parts that will actually get used. The soft spot is the lack of any anchor to measured data. The functional parameters come from fits to lighter nuclei, and the manuscript only compares DRHBc to RCHB (same functional family). There are no direct checks against known binding energies, radii, or deformations for the synthesized superheavy nuclei around Z=114–118. That leaves the drip-line locations and the magic-number claims as model-dependent extrapolations whose uncertainty at extreme N/Z is not quantified. The continuum treatment and pairing are standard, but without those benchmarks it is hard to judge how much the results shift if the functional is adjusted. This paper is for nuclear theorists who run or compare density-functional calculations in the superheavy region and for experimentalists who need order-of-magnitude guidance on where the drip lines sit. It is not a foundational advance, but it fills a specific gap with reproducible numbers. It deserves a serious referee because the calculations are systematic and the results are falsifiable once new data appear. I would send it for review with the expectation that the authors add at least a short section comparing to existing superheavy measurements and stating the estimated uncertainty on the drip lines.

Referee Report

1 major / 1 minor

Summary. The manuscript applies the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) to compute ground-state properties (binding energies, Fermi energies, separation energies, quadrupole deformations, rms radii) of Z=122 superheavy isotopes. It compares results to the spherical RCHB framework, examines convergence with angular-momentum cutoff and higher-order deformations, determines proton and neutron drip lines from separation energies, and identifies candidate magic numbers at N=184, 258, and 350. Evolution of single-particle levels, deformations, radii, and pairing gaps with neutron number is also discussed.

Significance. If the numerical results are robust, the work supplies concrete predictions for drip-line locations and possible shell closures in an experimentally inaccessible region, using a deformed continuum treatment that is well-suited to the physics. The systematic checks on cutoff and multipole deformations are a positive feature of the implementation.

major comments (1)

The drip-line and magic-number conclusions rest on separation energies and Fermi energies obtained from a density functional whose parameters were fitted to lighter nuclei. No direct comparison is made to measured binding energies, radii, or deformations of synthesized superheavy nuclei (Z=114–118), leaving the reliability of the extrapolation at Z=122 untested; this is load-bearing for the central claims about drip lines and N=184/258/350 closures.

minor comments (1)

The strategy for selecting ground states after checking angular-momentum cutoff, triaxiality, and octupole deformation is mentioned in the abstract but would benefit from a concise summary table or flowchart in the methods/results section.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of the work's significance and for the constructive major comment. We respond point by point below.

read point-by-point responses

Referee: The drip-line and magic-number conclusions rest on a density functional whose parameters were fitted to lighter nuclei. No direct comparison is made to measured binding energies, radii, or deformations of synthesized superheavy nuclei (Z=114–118), leaving the reliability of the extrapolation at Z=122 untested; this is load-bearing for the central claims about drip lines and N=184/258/350 closures.

Authors: We agree that the density functional parameters were fitted primarily to lighter nuclei and that the present manuscript contains no direct comparisons to the available experimental data on binding energies, radii, or deformations for the synthesized superheavy nuclei with Z=114–118. This is a genuine limitation when assessing the absolute accuracy of the extrapolation to Z=122. The manuscript instead focuses on the methodological advantages of the deformed continuum treatment, the systematic convergence checks with angular-momentum cutoff and higher multipoles, and the differences relative to spherical RCHB results. These internal consistency tests support the reported drip-line locations and candidate shell closures. We will add a concise paragraph in the revised manuscript that references prior applications of the same DRHBc framework to known superheavy systems, thereby placing the Z=122 predictions in the context of existing model validations without performing new calculations. revision: partial

Circularity Check

0 steps flagged

No circularity: standard model application with independent outputs

full rationale

The manuscript applies the established DRHBc framework to compute binding energies, separation energies, deformations, and radii for Z=122 isotopes, then reads off drip lines and candidate magic numbers directly from those computed quantities. No equation or claim reduces the reported results to the inputs by definition, no fitted parameter is relabeled as a prediction, and no load-bearing premise rests on a self-citation chain whose validity is presupposed. The calculations constitute an extrapolation whose reliability is an open question, but the derivation chain itself remains self-contained and non-circular.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central results rest on the DRHBc density functional whose parameters were determined by fits to known nuclei, plus standard assumptions of relativistic mean-field theory.

free parameters (1)

relativistic density-functional parameters
The effective interaction (typically PC-PK1 or similar) contains several coupling constants fitted to binding energies and radii of lighter nuclei.

axioms (1)

domain assumption The deformed relativistic Hartree-Bogoliubov equations in continuum accurately capture ground-state properties of Z=122 nuclei.
Invoked throughout the calculation of binding energies, deformations, and separation energies.

pith-pipeline@v0.9.0 · 5513 in / 1255 out tokens · 49639 ms · 2026-05-12T03:38:29.596358+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The relativistic density functional PC-PK1 is adopted... pairing strength V0 = -300 MeV fm³... angular momentum cutoff Jmax = 31/2 ħ
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

ground-state properties... binding energies, Fermi energies, nucleon separation energies... possible magic numbers N=184, 258, and 350

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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For the particle-particle channel, the pairing strength V0 = − 300 MeV ·fm3 in Eq

is λ max = 12, which is suﬃcient for our study. For the particle-particle channel, the pairing strength V0 = − 300 MeV ·fm3 in Eq. ( 4), and the pairing window is chosen as 100 MeV. The examinations for the above numerical cutoﬀs and the pairing parameters have been carried out for Z = 134 and 135 isotopes [ 89]. For com- parison, the RCHB calculations ar...

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Results obtained from the DRHBc calcula- tions are also plotted as blue open circles for compar- ison

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