Do Electron Shells Really Mark Where the Decay Chains of Elements 119 and 120 Break?

Two calculations published three days apart in September 2026 put the weak points of the element 119 and 120 decay chains in the same two places. Spontaneous fission takes over around copernicium (Z = 112 → 110) and again around rutherfordium and nobelium (Z = 104 → 102). One calculation is nuclear physics in the ordinary sense: Skyrme-Hartree-Fock plus WKB tunnelling. The other never touches a nuclear potential. It reads the walls off the relativistic electron-shell structure of the periodic table and the binary digits of Z.

A question on Physics Stack Exchange asks whether something physical links them. The proposed candidate is a shared symmetry, such as Dirac spin-orbit splitting acting the same way on proton levels and on Dirac-Fock electron orbitals. The question is pressing because the Dubna Superheavy Element Factory is running ⁵⁴Cr + ²⁴⁸Cm and ⁵⁰Ti + ²⁴⁹Bk on its DGFRS-2 separator, and China's HIAF is also aiming at period 8. Whether a single atom of 119 or 120 can be identified depends on its α-decay chain reaching known daughters before fission cuts it off.

No known mechanism ties electron subshells to nuclear fission barriers at these charges. The coincidence comes apart once you look at what each method is actually counting, and the reasons it comes apart are worth knowing.

What the two calculations claim

Xiao, Wu and Dong, in Physics Letters B, used Skyrme-Hartree-Fock with WKB barrier penetration to set α emission against spontaneous fission along both chains. α decay dominates from 120 and 119 down through the 118–114 region. The chains then hit sharp fission bottlenecks. On the even chain these come at ²⁸²Cn → ²⁷⁸Ds and ²⁶⁶Rf → ²⁶²No. On the odd chain they come at ²⁸⁵Nh → ²⁸¹Rg and ²⁶⁹Db → ²⁶⁵Lr, each marked as a step where α decay and SF compete.

Logvinovich and Perez deposited their work on Zenodo on 21 September 2026 (DOI 10.5281/zenodo.22655608). They build a relativistic Dirac-Fock extended periodic table up to Zmax = 172, the point at which the 1s level dives into the negative-energy continuum. They branch continuous SO(3) orbitals onto the octahedral group Oh to get subshell capacities of 2, 6, 10 and 14 across twelve floors. α decay becomes a step operator on that matrix, scored with two numbers. The first is TFI, the Hamming weight of Z ⊕ (Z − 2). The second is ATFI = √((Δns)² + 2(Δnp)² + 3(Δnd)²), a weighted count of how many electrons change block.

The papers differ in standing. One is a journal article built on a nuclear model. The other is a repository deposit, and it presents its lack of nuclear input as a strength. That same lack of input is exactly why the agreement needs explaining: a model that knows nothing about nucleons is reproducing nucleon physics.

Two rails that are only even and odd

The Zenodo paper argues that every floor capacity (2, 8, 18, 32) and every cumulative noble-gas closure (2, 10, 18, 36, 54, 86, 118) is even. On that basis, α decay conserves Z mod 2 and splits the cascades into two non-intersecting ‘parity rails’. The even rail runs from ²⁹⁸120 to ²⁰⁶Pb. The odd rail runs from ²⁹⁷119 towards ²⁰⁹Bi and ²⁰⁵Tl.

The conclusion is correct, but none of the premises is needed to reach it. Subtract 2 from an even number and you get an even number, so any decay that removes protons two at a time stays on its rail whatever the periodic table looks like. A table with odd capacities would produce the same two rails. The agreement between the rails and the SHF/WKB pathways therefore carries no information about electron shells.

The rails do matter in nuclear physics, for a separate reason. An odd-Z nucleus carries an unpaired proton, and unpaired nucleons are known to hinder fission compared with fully paired neighbours. That is why the 119 and 120 chains need to be calculated separately. It is a statement about nucleon pairing, not about electron counting.

Where the electron shells close and where the chains break

The correspondence table gives one electronic event per step. On the even rail, 120 → 118 crosses from the period-8 8s² rim into oganesson's closed 7p⁶ shell, and α decay is fast. From 118 down to 112 the chain slides inside the open 7p block, and α decay strongly dominates. 112 → 110 crosses the closed relativistic 6d¹⁰ shell at copernicium, which is the primary fission wall. 104 → 102 exhausts the 6d block into nobelium's closed 5f¹⁴, which is the secondary wall. From radium down to lead the chain runs smoothly to its end.

Read the table for its largest electronic events and the pattern turns around. The biggest closures in this range are the full noble-gas shells: oganesson at 118 and radon at 86. Neither comes with a wall. At 118 the chain is at its fastest. The walls sit at the 6d¹⁰ and 5f¹⁴ subshell boundaries instead, which are lesser features of the electronic structure. The rule cannot be ‘closed shell, then wall’. In practice it becomes ‘whichever boundary sits nearest a wall’, and with s, p, d and f boundaries spaced a few units of Z apart, there is always one nearby.

The end of the chain shows the same thing. The even rail terminates at ²⁰⁶Pb, Z = 82. Lead's 82 protons fill a closed nuclear shell, while its electrons are four short of radon's closure. This is the one place where the nuclear and electronic magic numbers clearly disagree, and the decay chain follows the nucleus.

What a binary borrow measures

TFI is the Hamming weight of Z ⊕ (Z − 2). Subtracting 2 in binary flips bit 1 and then borrows through any run of zeros above it, so the weight comes out as one plus the number of trailing zeros of ⌊Z/2⌋. Copernicium, 112, is 1110000 in binary, and the borrow runs through three zeros, giving a weight of 4. Nihonium, 113, has the same upper bits and also scores 4, which is why the odd-rail ‘wall’ at Nh → Rg lines up so neatly with Cn → Ds. Rutherfordium (104) and dubnium (105) both score 3. So does element 120.

Working the formula through every step exposes some slips. 116 → 114 and 117 → 115 each score 2, not the 1 listed in the table's ‘smooth slide’ rows. The more serious problem is 120 → 118, which scores 3, the same as Rf → No, even though it is the fastest α step on the chain. Further from the superheavies, Cm → Pu (96 → 94) scores 5, deeper than the copernicium ‘primary bottleneck’. 128 → 126 scores 7. Taken at face value, the metric predicts its largest walls at round binary numbers, including in the actinides, where α decay to plutonium has been studied for decades.

ATFI handles the 120 → 118 step better. It reads 2.00 there and 3.46 at the walls. But 3.46 is √12, which corresponds to two 6d electrons changing. Under straightforward filling, every step from 112 down to 104 removes two 6d electrons, so ATFI would read the same across the whole d block, including the Ds → Hs → Sg steps that the nuclear calculation treats as α-dominated. A metric that is the same on both sides of a wall cannot be what picks the wall out.

One alpha step moves three numbers

An α particle carries away two protons and two neutrons, so along a chain Z, N and A all fall in lockstep. Subtracting Z from A in each isotope gives the neutron numbers. ²⁸²Cn has 170 neutrons and its daughter ²⁷⁸Ds has 168. The odd-rail wall at ²⁸⁵Nh → ²⁸¹Rg runs from N = 172 to 170. ²⁶⁶Rf → ²⁶²No runs from 162 to 160, and ²⁶⁹Db → ²⁶⁵Lr from 164 to 162.

On any single chain, every value of Z corresponds to exactly one value of N. A wall that lines up with an electronic boundary in Z therefore lines up equally well with a particular neutron number, and the chain on its own cannot tell the two readings apart. Spontaneous fission depends heavily on neutron number. The fission barrier comes from shell corrections in both the proton and neutron spectra, balanced against the contest between Coulomb repulsion and surface tension. Skyrme-Hartree-Fock calculates exactly those quantities.

The nuclear walls therefore have a nuclear explanation. The electronic map appears to match them because it shares the Z axis, and on a single chain the Z axis cannot be separated from the N axis.

Is there any physical coupling at all?

The two problems share mathematical language, and that is where the impression of a connection comes from. Electrons in a heavy atom and nucleons in a heavy nucleus are both described by shell models with near-spherical symmetry. Both have spin-orbit splitting into j = l ± ½ levels, and the degeneracies 2j + 1 and 2(2l + 1) appear in both. Any spherically symmetric problem produces the counts 2, 6, 10 and 14. Recovering them by branching SO(3) onto Oh confirms the group theory. It says nothing new about nuclei.

The Hamiltonians are different. Electronic spin-orbit coupling is a relativistic effect of the nuclear Coulomb field, and it grows strongly with Z. That growth is why Dirac-Fock rather than plain Hartree-Fock is needed for copernicium and lawrencium, whose predicted ground state is 5f¹⁴7s²7p1/2¹. Nuclear spin-orbit coupling comes from the strong interaction and is powerful enough to reorder shells. That reordering is why the nuclear closed shells, such as lead's 82 protons, fall at different numbers from the noble gases. The group theory is the same, but the forces and the closures are not.

Some real couplings do exist, but they are small and smooth. Atomic electrons screen part of the Coulomb barrier an α particle must tunnel through. The Q-value is also shifted by the difference in total electronic binding energy between parent and daughter. Both effects are tiny next to the energy an α decay releases. They are dominated by the inner shells, so they vary smoothly with Z and do not jump at valence subshell boundaries. Fission has no electronic ingredient worth mentioning. The only quantity the two models truly share is Z itself. The Coulomb repulsion that drives fission and the relativistic contraction of inner orbitals both grow with nuclear charge, which gives them a common cause but no mechanism for pinning walls to particular subshells.

Electrons and nucleus genuinely interact near the supercritical limit the Zenodo paper uses for its edge, Z = 172. There, where the 1s level sits depends on the size and charge distribution of the nucleus. That regime lies sixty units of charge above copernicium and has no bearing on fission barriers along these chains.

What the Dubna and HIAF runs can settle

The two reactions at Dubna match their targets: chromium (24) plus curium (96) makes 120, and titanium (22) plus berkelium (97) makes 119. If a chain from 120 is seen to fission at copernicium, or to pass through it, that tests the SHF/WKB prediction directly. A sharper test distinguishes the two explanations. A nuclear model predicts that walls move when the neutron number changes. An electron-shell rule has no access to neutron number, so it must place the same walls at 112 and 104 for every isotope of 120.

1. Sep 18, 2026

   SHF/WKB chains published

   Xiao, Wu and Dong place fission bottlenecks at Cn and Rf/No in Physics Letters B.

2. Sep 21, 2026

   Periodic-matrix deposit

   Logvinovich and Perez post their Dirac-Fock matrix and TFI/ATFI metrics to Zenodo.

3. Oct 2026

   Dubna runs under way

   ⁵⁴Cr + ²⁴⁸Cm and ⁵⁰Ti + ²⁴⁹Bk on DGFRS-2 at the Superheavy Element Factory.

Before relying on the periodic-matrix metrics, check whether they have been tested out of sample. That means checking them against chains whose fission branches are already measured, and against steps such as Cm → Pu where the binary borrow is deep. It also means checking whether ATFI's scores depend on which electron configurations were assumed for the 6d elements. Until that is done, the agreement between the two September papers is best read as two models that both index on Z. Only one of them contains the physics that governs fission.

Questions readers ask

This article draws on Why do $Z=$119 and 120 decay bottlenecks coincide with the relativistic $6d^{10}$ (${\rm Cn}, Z=112$) and $6d/5f^{14}$ (Rf/No) subshell boun, on the Stack Exchange network, licensed under CC BY-SA 4.0.