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Microscopic Spin-Parity Distributions of Fission Fragments

This study presents the first microscopic characterization of fission fragment spin-parity distributions using time-dependent Hartree-Fock-Bogoliubov calculations, revealing that dynamical pair breaking significantly populates unnatural-parity states and creates parity patterns dependent on fragment mass parity, thereby challenging the equiprobable assumptions of current statistical de-excitation models.

Original authors: Guillaume Scamps, Petar Marević, Antonio Bjelčić, Nicolas Schunck

Published 2026-07-28

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CC BY 4.0

Original authors: Guillaume Scamps, Petar Marević, Antonio Bjelčić, Nicolas Schunck

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the atomic nucleus not as a solid marble, but as a bustling, chaotic dance floor filled with tiny particles called protons and neutrons. These particles are constantly spinning and pairing up, holding hands in a quantum waltz. Sometimes, this dance floor gets so excited—perhaps because a stray neutron bumps into it—that the whole thing splits in two. This is nuclear fission, the process that powers stars and nuclear reactors. When the nucleus breaks apart, it doesn't just split into two random chunks; it creates two new "fragments" that are still spinning wildly and vibrating with energy.

For a long time, scientists trying to predict what happens next have made a big, simple guess: they assumed that when these fragments settle down, they are equally likely to be "right-handed" or "left-handed" in a quantum sense called parity. Think of parity like a mirror image. If you look at a state in a mirror, does it look the same (positive parity) or flipped (negative parity)? The old models assumed it was a 50/50 coin toss. But nature is rarely that simple, and this new study suggests that the dance partners have a very specific, unbalanced way of choosing their final moves.

The Great Nuclear Split: A Quantum Dance of Mirrors and Spins

In a new study, a team of physicists decided to stop guessing and start watching the dance floor in ultra-high definition. They used a powerful computer simulation called the "time-dependent Hartree–Fock–Bogoliubov" framework. Don't let the fancy name scare you; think of it as a super-advanced movie camera that can freeze-frame the exact moment a heavy nucleus, specifically Plutonium-239, splits apart after being hit by a thermal neutron.

Usually, scientists could only see the total spin (how fast the fragments are spinning) of the pieces. But this team did something never done before: they simultaneously tracked the spin, the number of particles, and the parity (the mirror symmetry) of the fragments as they formed. They ran these simulations using two different sets of rules for how nuclear particles interact (known as Gogny and Skyrme energy density functionals), just to make sure their results weren't a fluke of one specific math trick.

The Surprise: The Dance Floor is Biased

The results shattered the old "50/50 coin toss" idea. The simulations showed that the fragments don't choose their parity randomly. Instead, the way the nucleus breaks apart creates a strong bias.

Here is the key discovery: The fragments are not equally likely to be positive or negative parity.

When the nucleus splits, it's a violent event. The "Cooper pairs" (the hand-holding dance partners) get ripped apart by the sheer force of the separation. This "dynamical pair breaking" is the culprit. It turns out that when these pairs break, they don't just create random chaos; they populate a significant number of "unnatural" states. In the quantum world, "natural" states are the ones that fit the rules of the dance floor perfectly, while "unnatural" states are the wild, unexpected moves. The study found that these unnatural moves happen much more often than the old models predicted.

The Shape of the Spin

The researchers looked at the two main pieces of the split: the "light" fragment and the "heavy" fragment.

The Light Fragment: This piece is squashed and stretched (deformed), like a rugby ball. It spins fast, with an average spin of 11–12 ℏ (a unit of angular momentum). It mostly sticks to the "natural" rules, but because it's spinning so fast, it still has a decent mix of the wild, unnatural states.
The Heavy Fragment: This piece is more like a round, compact ball. It spins much slower, with an average spin of 5–6 ℏ. Because it's so round and stable, it loves the "natural" states even more, especially the 0+ state (no spin, positive parity). However, even here, the simulations showed that the "unnatural" states are popping up more than anyone expected.

The "Odd" and "Even" Rules

The study also found that the parity depends heavily on whether the fragment has an odd or even number of protons and neutrons.

Even-Even Fragments: These are the most orderly. They have an even number of protons and neutrons. They strongly prefer positive, natural parity.
Odd-Mass Fragments: If a fragment has an odd number of particles, the "odd one out" (the unpaired nucleon) dictates the rules.
- If the unpaired particle is a neutron, the fragment tends to favor positive parity.
- If the unpaired particle is a proton, the fragment tends to favor negative parity.
Odd-Odd Fragments: These have both an odd proton and an odd neutron. Because these two unpaired particles often have opposite "mirror" properties, they team up to create a strong preference for negative parity.

Why This Matters

The authors suggest that these findings are a big deal for how we model nuclear decay. For decades, scientists have used statistical models that assume a simple, equal split between positive and negative parity. This new research suggests that assumption is wrong. The "dance" of fission is more complex and biased than we thought.

By understanding that the fragments have a specific "personality" based on their shape and their odd or even particle counts, scientists can build better models for how these fragments release energy later on. This could improve everything from our understanding of nuclear reactors to how we detect nuclear materials.

The study is a simulation, not a direct measurement of a single event, but the fact that two completely different computer codes (Gogny and Skyrme) arrived at the same conclusion gives the scientists high confidence. They aren't just guessing anymore; they have a microscopic map of the quantum dance floor, and it shows that the universe has a distinct preference for how it breaks apart.

Technical Summary: Microscopic Spin–Parity Distributions of Fission Fragments

Problem Statement
While recent microscopic studies have characterized the total angular momentum ( $J$ ) and its projection on the fission axis ( $K$ ) of fission fragments, the parity ( $\pi$ ) distributions of these fragments remain largely unexplored within a microscopic framework. Current state-of-the-art statistical models for fragment decay typically assume an equiprobable partition between positive and negative parities, lacking a theoretical basis for this assumption. Furthermore, the distinction between "natural" parity states (where $\pi = (-1)^J$ for integer $J$ or $\pi = (-1)^{J-1/2}$ for half-integer $J$ ) and "unnatural" parity states has not been systematically investigated in the context of fission dynamics. Understanding the combined spin–parity content is essential for modeling the subsequent de-excitation of fragments and accessing their internal structure.

Methodology
The authors employ the time-dependent Hartree–Fock–Bogoliubov (TDHFB) framework to simulate the thermal neutron-induced fission of $^{239}\text{Pu}$ . The study utilizes two independent, state-of-the-art energy density functionals (EDFs): the Gogny D1S and the Skyrme SkM* interactions.

Simulation Setup: The time evolution is initiated from a static configuration beyond the saddle point in $^{240}\text{Pu}$ . The fragments are evolved until full separation (defined by center-of-mass separation or skin distance).
Projection Technique: To extract observables from the global, parity-breaking TDHFB wave function $|\Psi\rangle$ , the authors introduce a localized parity projection operator $\hat{P}^\pi_F$ acting exclusively on the spatial coordinates of a specific fragment ( $F \in \{H, L\}$ ).
Joint Distribution: By performing simultaneous projections on particle number ( $N, Z$ ), total angular momentum ( $J$ ), its intrinsic projection ( $K$ ), and parity ( $\pi$ ), the authors calculate the joint probability distribution:
$P_F(J, K, \pi, N, Z) = \langle\Psi| \hat{P}^N_F \hat{P}^Z_F \hat{P}^J_{K,F} \hat{P}^\pi_F |\Psi\rangle$
These overlaps are evaluated using the Pfaffian method. The calculations utilize large bases ( $N_{\text{basis}} > 5700$ states) to ensure convergence.

Key Contributions
This work provides the first complete microscopic characterization of the spin–parity content of fission fragments, specifically addressing:

The simultaneous projection of angular momentum, particle number, and parity.
The quantification of unnatural-parity state populations generated by dynamical pair breaking.
The dependence of parity distributions on the number parity of the fragments (even-even, odd-mass, and odd-odd).
A rigorous test of model robustness by comparing predictions from two distinct EDFs (Gogny and Skyrme).

Results

General Spin–Parity Distributions: Both Gogny and Skyrme calculations yield consistent qualitative results. The light fragment (well-deformed, $\beta_2 \approx 0.50$ ) exhibits a spin distribution well-described by a spin-cutoff behavior with an average of $11-12\hbar$ . Even- $J$ , positive-parity states dominate, though unnatural-parity states are significantly populated in the odd-mass channel. The heavy fragment (nearly spherical, $\beta_2 \approx 0.05$ ) shows a lower average spin ( $5-6\hbar$ ) and a more complex landscape where the $0^+$ state is enhanced beyond statistical expectations.
Role of Dynamical Pair Breaking: The population of unnatural-parity states and non-zero $K$ components is attributed to the dynamical breaking of pairing correlations during scission. While the $K=0$ mode is dominated by natural parity (associated with the paired vacuum), higher $|K|$ values ( $|K| \ge 1$ ) result from multi-quasiparticle excitations that break time-reversal pairs, leading to an essentially equiprobable mixture of natural and unnatural parity.
Dependence on Number Parity:
- Even-Even Fragments: Strongly dominated by natural, positive-parity states, consistent with preserved pairing correlations.
- Odd-Mass Fragments: Exhibit pronounced parity staggering. Odd-neutron fragments favor positive parity (linked to the $sdg$ shell), while odd-proton fragments favor negative parity (due to the proximity of $g_{9/2}$ and $pf$ orbitals near the Fermi surface at large deformations).
- Odd-Odd Fragments: Show a dominance of negative-parity states, resulting from the coupling of an odd proton and odd neutron with opposite intrinsic parities.
Shell Structure Influence: The heavy fragment distributions are strongly influenced by shell structure, effectively behaving as a doubly-magic $^{132}\text{Sn}$ core coupled to a valence nucleon. The specific single-particle orbitals occupied (e.g., $1h_{11/2}$ in Skyrme vs. Gogny for $^{133}\text{Sb}$ ) dictate the specific spin–parity populations.

Significance and Claims
The authors claim that their results demonstrate that the parity distribution of fission fragments can depart significantly from the equiprobable partition commonly assumed in statistical de-excitation models. Specifically:

Dynamical pair breaking is a crucial mechanism generating unnatural-parity states and non-zero $K$ components.
The parity content is not random but is tightly coupled to the fragment's number parity and underlying shell structure.
These microscopic findings suggest that current statistical models may require revision to accurately account for the specific parity populations, which could impact predictions of fragment decay observables such as photon multiplicities and spectra.

The study is limited to a single TDHFB trajectory representing the most probable fission path; the authors note that a quantitative description of the full fragment yield range would require an ensemble of trajectories (e.g., via the time-dependent generator coordinate method).

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