Fission stability of huge, locally charge-neutral neutron-rich nuclei ('monsters'): quantitative verification of a qualitative claim

In August 2026, Gupta ('Monsters and neutron stars', arXiv:2608.10904) proposed a second branch of metastable nuclei: droplets of near-saturation nuclear matter with near-maximal neutron excess and baryon number $A \gtrsim 4.3\times10^{7}$ — large enough that the droplet radius exceeds the electron Compton wavelength — rendered locally charge neutral by an internally confined degenerate electron gas, forming a branch continuous with neutron stars. The proposal asserts, in a single qualitative sentence, that such 'monsters' are stable against spontaneous fission because local charge neutrality removes the Coulomb energy gain that drives ordinary heavy nuclei to split. This assertion has never been tested: no calculation exists of the deformation energetics of a charge-neutral neutron-rich droplet, in which residual electron-screening electrostatics must compete against the small and poorly constrained surface tension of nearly pure neutron matter. The open problem is to compute that deformation energy along realistic fission paths across the monster regime and to decide, for which baryon numbers and proton fractions if any, fission stability actually holds.

Background

Spontaneous fission is the decay channel in which a heavy nucleus deforms, necks, and splits into two comparable fragments without external stimulation. In the liquid-drop picture introduced by Bohr and Wheeler, a nucleus of charge $Z$ and mass number $A$ carries a surface energy that grows under deformation and a Coulomb self-energy of the proton charge that is lowered when the charge spreads into separating lobes; their competition is measured by the fissility parameter $x = Z^2/(47A)$ (in the standard parametrization), with $x=1$ the limit at which the liquid-drop fission barrier vanishes. Quantitative fission-barrier theory — macroscopic–microscopic and energy-density-functional (EDF) methods, i.e. self-consistent mean-field calculations of the nuclear energy surface along collective shape coordinates — exists only for nuclei up to roughly $A \lesssim 350$, always with the unscreened Coulomb field of the nuclear charge as the electrodynamics. On the neutron-rich side, nuclear stability ends at the neutron drip line, the boundary beyond which nuclei are unbound to neutron emission.

Very neutron-rich nuclear matter nonetheless exists inside neutron stars. There, matter is in beta-equilibrium ($\beta$-decay and inverse $\beta$-decay in balance, which equalizes the neutron, proton, and electron chemical potentials and fixes a small proton fraction) and is locally electrically neutral because a relativistic degenerate electron gas permeates the nucleons. In the star's crust, at below-saturation densities, nucleons cluster into nuclei immersed in dripped neutrons and this electron background; Ravenhall, Pethick and Wilson showed that minimizing surface energy against the residual (screened but nonzero) Coulomb energy of the proton clusters drives the sequence of 'nuclear pasta' shapes — spheres, rods, slabs — now mapped in detail by modern compressible-liquid-drop, Hartree–Fock, and molecular-dynamics calculations. These clusters are Coulomb-frustrated lattice cells (Wigner–Seitz cells, i.e. charge-neutral cells each containing one cluster plus its share of electrons), not isolated droplets, and their electrodynamics never reduces to zero Coulomb energy. A separate electromagnetic limit is the supercritical-charge problem: solving the Dirac equation in the field of a point charge gives vacuum instability above $Z=137$, and for realistic extended charge distributions above $Z \approx 169$–$173$; neutron-star matter evades this bound only because electrons penetrate the nuclear matter, making it locally charge neutral.

Gupta's proposal connects these threads. He argues that if a droplet of nuclear matter near saturation density ($n \approx 0.16\,\mathrm{fm}^{-3}$, radius $a(A) \approx 1.1\,\mathrm{fm} \times A^{1/3}$) is large enough that $a$ exceeds the electron Compton wavelength $\lambda_e = \hbar/(m_e c) \approx 386\,\mathrm{fm}$ — which requires $A > 4.32\times10^{7}$ — electrons can be localized inside it, the supercritical-charge instability is avoided, and a locally charge-neutral, $\beta$-equilibrated, almost maximally neutron-rich droplet becomes possible ($Z/A \sim 10^{-5}$ in the source's free-Fermi-gas estimate; realistic interactions would raise it toward the few-percent proton fractions of neutron-star matter). He names such objects 'monsters'. Their dominant decay mode would be neutron evaporation, with an estimated lifetime $t \sim \tau A^{1/3}$ ($\tau \approx 2\,\mathrm{fm}/c$) exceeding 100 ps for $A \gtrsim 3.4\times10^{39}$; gravity stabilizes them only for $A \gtrsim 4.6\times10^{56}$. The branch would be continuous with neutron stars, whose minimum masses are about $1.1$–$1.2\,M_\odot$ — leaving a gap of some forty orders of magnitude in baryon number between ordinary nuclei and gravitationally bound neutron-star matter, which monsters would populate. About fission, the source argues in one sentence: since matter is locally charge neutral, 'shape deformations only lead to increase in surface energy without any compensating effect', so 'Monsters are therefore expected to be stable against fission'.

That argument is exact only if the proton and electron charge densities are exactly co-located, in which case the electrostatic energy vanishes at every shape. In reality the protons sit in the nuclear liquid while the electrons form a degenerate Fermi gas held by their own bound states, leaving residual electrostatic surface and dipole energies, with a finite screening length, to compete against the surface tension of extremely neutron-rich matter — itself small, suppressed by the neutron skin (the neutron-rich surface layer of neutron-rich nuclei), and known only through extrapolations of the nuclear symmetry energy (the energy cost of proton–neutron imbalance) far beyond measured nuclei. No calculation of this competition exists in any adjacent literature: crust and pasta theory treats lattice-bound clusters with external electrons; fission-barrier theory stops at $A \lesssim 350$ with unscreened Coulomb; decompressed crust ejecta process into ordinary r-process nuclei; and the closest prior concept of stable macroscopic self-bound lumps — strange quark matter — involves different binding physics.

Problem Statement

Determine, by quantitative calculation, whether an isolated droplet of near-saturation-density nuclear matter that is in $\beta$-equilibrium (near-maximal neutron excess, with proton-to-baryon ratio $Z/A$ between roughly $10^{-5}$ and a few percent) and locally charge neutral through a confined degenerate electron gas — the 'monster' configuration of Gupta (arXiv:2608.10904), possible only for $A \gtrsim 4.3\times10^{7}$, where the droplet radius exceeds the electron Compton wavelength — is stable against spontaneous fission.

Specifically: determine whether the deformation energy of such a droplet can be lowered by deformation towards scission into two charge-neutral fragments — that is, whether a fission barrier exists — across the monster regime, from the local-neutrality threshold $A \gtrsim 4.3\times10^{7}$ through the evaporation-metastable range up to the gravitational-stabilization scale $A \gtrsim 4.6\times10^{56}$; and establish, for which $(A, Z/A)$, if any, the fission barrier is positive — the deformation energy rising above its value at the equilibrium shape, whether it increases monotonically all the way to scission or reaches a finite saddle it crosses only by barrier penetration — and where instead the barrier vanishes or the deformation energy falls without a preceding maximum (a deformation instability), with its mechanism identified.

The claim under test is the source's qualitative assertion that local charge neutrality removes the Coulomb driving force of fission altogether; the question is whether that survives the real, screened, two-component electrodynamics and the uncertain surface physics of near-pure neutron matter.

References

1. S. Gupta, 'Monsters and neutron stars', arXiv:2608.10904 (2026), hep-ph preprint of 11 Aug 2026. https://arxiv.org/abs/2608.10904
2. N. Bohr and J. A. Wheeler, 'The Mechanism of Nuclear Fission', Phys. Rev. 56, 426 (1939), doi:10.1103/PhysRev.56.426. https://doi.org/10.1103/PhysRev.56.426
3. D. G. Ravenhall, C. J. Pethick and J. R. Wilson, 'Structure of Matter below Nuclear Saturation Density', Phys. Rev. Lett. 50, 2066 (1983), doi:10.1103/PhysRevLett.50.2066. https://doi.org/10.1103/PhysRevLett.50.2066
4. M. E. Caplan and C. J. Horowitz, 'Colloquium: Astromaterial science and nuclear pasta', Rev. Mod. Phys. 89, 041002 (2017), arXiv:1606.03646. https://arxiv.org/abs/1606.03646
5. B. Schuetrumpf, G. Martínez-Pinedo, Md. Afibuzzaman and H. M. Aktulga, 'Survey of nuclear pasta in the intermediate-density regime: Shapes and energies', Phys. Rev. C 100, 045806 (2019), arXiv:1906.08155. https://arxiv.org/abs/1906.08155
6. F. Minato and K. Hagino, 'Fission barriers in the neutron-proton isospin plane for heavy neutron-rich nuclei', Phys. Rev. C 77, 044308 (2008), arXiv:0802.2614. https://arxiv.org/abs/0802.2614
7. S. Goriely, N. Chamel, H.-T. Janka and J. M. Pearson, 'The decompression of the outer neutron star crust and r-process nucleosynthesis', Astron. Astrophys. 531, A78 (2011), doi:10.1051/0004-6361/201116897, arXiv:1105.2453. https://arxiv.org/abs/1105.2453
8. E. Farhi and R. L. Jaffe, 'Strange matter', Phys. Rev. D 30, 2379 (1984), doi:10.1103/PhysRevD.30.2379. https://doi.org/10.1103/PhysRevD.30.2379
9. A. Czarnecki, 'Negative energy effects in processes involving bound particles: finite nuclear size effects', PoS LL2022 (2022) 055, doi:10.22323/1.416.0055, arXiv:2207.07552 — the finite-size critical-charge bound. https://arxiv.org/abs/2207.07552
10. Y. Suwa, T. Yoshida, M. Shibata, H. Umeda and K. Takahashi, 'On the minimum mass of neutron stars', Mon. Not. R. Astron. Soc. 481, 3305 (2018), doi:10.1093/mnras/sty2460, arXiv:1808.02328. https://arxiv.org/abs/1808.02328
11. B. Müller, A. Heger and J. Powell, 'Minimum Neutron Star Mass in Neutrino-Driven Supernova Explosions', Phys. Rev. Lett. 134, 071403 (2025), doi:10.1103/PhysRevLett.134.071403, arXiv:2407.08407. https://arxiv.org/abs/2407.08407