Large-scale fission data generation with BSkG3

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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 as a tiny, super-dense drop of liquid. Sometimes, this drop gets so stretched and unstable that it snaps in two. This snapping process is called fission, and it's the engine behind both nuclear power and the creation of the heaviest elements in the universe.

For a long time, scientists trying to predict how and when this happens have been like cartographers trying to map a mountain range using only a few scattered landmarks. They used "phenomenological models," which are like guessing the shape of a mountain by looking at a few photos and adjusting a dial until it looks right. While this works for known mountains, it fails miserably when you try to predict the shape of a mountain that no one has ever seen (like the exotic, heavy atoms found in deep space).

This paper introduces a new, high-tech way to map these nuclear mountains. Here is the breakdown of what the researchers did, using simple analogies:

1. The New Map-Making Tool (BSkG3 and MOCCa)

The researchers used a powerful new set of rules called BSkG3 (a type of Energy Density Functional) and a super-fast computer code called MOCCa.

The Analogy: Think of previous methods as trying to guess the shape of a clay sculpture by poking it with a stick. This new method is like using a 3D scanner that captures every tiny detail of the clay, no matter how twisted or weird the shape gets.
The Scale: They didn't just look at a few examples; they scanned over 3,300 different types of heavy atoms (from element 80 to 118), including the very rare and unstable ones that don't exist naturally on Earth.

2. Rolling Down the Hill (The Fission Path)

To understand fission, you have to figure out the path an atom takes as it goes from a stable ball to a split shape.

The Old Way: Scientists used to look at a flat, 2D map of the energy landscape. They assumed the atom could only stretch straight out or wobble a little bit.
The New Way: The researchers realized the atom can twist, bend, and become lopsided in complex ways. They allowed the atom to be triaxial (twisted like a rugby ball) and octupole (pear-shaped).
The "Least-Action" Principle: Imagine you are rolling a ball down a hilly landscape to get to the bottom. The ball doesn't just go straight down; it finds the path of least resistance. The researchers used a mathematical trick to find this "path of least resistance" for the nucleus. This path tells them exactly how hard it is for the nucleus to split.

3. Testing the Map (The Results)

Before using this map for the whole universe, they tested it on a known mountain: Plutonium-240.

The Result: Their new map matched the real-world measurements of Plutonium's fission barriers (the "height" of the hill the nucleus must climb to split) with incredible precision—within about the width of a single atom's energy.
The Comparison: They compared their new map against three other existing maps. Their new map (BSkG3) was significantly more accurate, with errors less than half the size of the others. It was the only one that could accurately predict both the stable shape of the atom and the path it takes to split.

4. Why This Matters for the Universe (The R-Process)

The paper focuses on the r-process, which is the cosmic "factory" in exploding stars (like neutron star mergers) that creates heavy elements like gold and uranium.

The Bottleneck: In this cosmic factory, atoms are constantly being smashed together to get heavier. But if they get too heavy, they might split (fission) before they can grow.
The Discovery: The researchers found that for certain very heavy atoms (around element 108), the "hill" they need to climb to split is so low that they split almost instantly (in fractions of a second).
The Implication: This suggests that the creation of super-heavy elements in the universe might stop at a specific point because these atoms are too unstable to survive. This "fission recycling" changes how we understand the abundance of elements in the universe.

5. What's Next?

The researchers have built the "skeleton" of this new understanding. They have mapped the hills and valleys for thousands of atoms.

Current Status: They have the map of the terrain.
Future Work: They are now working on adding the "weather" to the map—specifically, how these atoms behave when hit by neutrons or when they decay. They are also working on predicting exactly what pieces (fragments) the atoms break into, which is crucial for understanding the final chemical makeup of the universe.

In Summary:
This paper is about building the first high-resolution, 3D GPS for the journey of heavy atomic nuclei as they split apart. By using a more realistic mathematical model and a powerful computer, the team created a map that is far more accurate than previous guesses. This map helps scientists understand the limits of how heavy elements can get in the universe and how the cosmic factories that create gold and uranium actually work.

1. Problem Statement

Modeling nuclear fission properties (barriers, rates, and fragment distributions) is a significant challenge in nuclear physics and astrophysics.

Limitations of Current Models: Existing evaluations often rely on phenomenological models with free parameters adjusted to experimental data. While useful for known nuclei, these models lack predictive power for exotic, heavy nuclei near the neutron drip line, which are crucial for understanding the rapid neutron-capture process (r-process) in astrophysics.
Microscopic Gaps: While microscopic approaches based on Hartree-Fock-Bogoliubov (HFB) theory offer a unified description of ground states and fission, previous large-scale studies have been limited. They often rely on semi-empirical microscopic-macroscopic (mic-mac) models that fail to simultaneously reproduce ground state and fission properties, or they neglect complex deformation modes (triaxiality, octupole) due to computational costs.
Need for Data: Reliable predictions for fission barriers, spontaneous fission (SF) half-lives, and fission fragment distributions are required for nuclei heavier than Thorium (Th) to model nucleosynthesis in neutron star mergers.

2. Methodology

The authors employed a systematic, fully microscopic approach using the BSkG3 Energy Density Functional (EDF) and the MOCCa nuclear structure code.

Theoretical Framework:
- HFB Theory: The study solves constrained HFB equations in a 3D coordinate-space representation, ensuring numerical accuracy regardless of nuclear shape.
- Collective Coordinates: The Potential Energy Surface (PES) is mapped using mass multipole moments ( $Q_{lm}$ $Q_{l m}$ ). The study explicitly includes:
  - Axial quadrupole ( $Q_{20}$ ): Elongation.
  - Triaxial quadrupole ( $Q_{22}$ ): Triaxial shapes (crucial for lowering inner barriers).
  - Axial octupole ( $Q_{30}$ ): Asymmetric fission.
Two-Step Pathfinding Strategy: To manage computational cost while maintaining accuracy, a two-step methodology was used to determine fission paths:
1. Minimum Energy Path (MEP): A PES in $(Q_{20}, Q_{30})$ is computed to find the energy-optimum octupole shape for each quadrupole moment.
2. Least-Action Path (LAP): A PES in $(Q_{20}, Q_{22})$ is computed with $Q_{30}$ constrained by the MEP. The final fission path is determined by minimizing the action integral ( $S$ ) using the PyNEB code.
Calculations:
- Spontaneous Fission (SF) Half-lives: Calculated using the WKB approximation based on the action integral derived from the LAP and microscopic collective inertia.
- Fission Fragments: Preliminary yields were calculated using the time-dependent generator coordinate method (TDGCM) via the FELIX code on $(Q_{20}, Q_{30})$ surfaces.

3. Key Contributions

Scale and Scope: This is the first large-scale campaign to explore fission properties for approximately 3,300 nuclei (covering $Z=80$ to $118$, from proton to neutron drip lines) within a fully microscopic framework.
Explicit Deformation Handling: Unlike previous large-scale studies, this work explicitly accounts for axial, triaxial, and octupole deformations for both even-even and odd-mass (including odd-odd) systems.
Unified Description: The BSkG3 parametrization provides a consistent description of ground state properties, fission barriers, and SF half-lives without relying on phenomenological corrections.
Data Integration: The generated fission barriers and SF half-lives have been integrated into the TALYS nuclear reaction code, with further inputs (neutron-induced/β-delayed fission rates) currently in development.

4. Key Results

Validation against Experiment:
- Fission Barriers: BSkG3 achieved an RMS deviation of 0.32 MeV against 45 empirical primary fission barriers (RIPL-3), outperforming HFB-14 (0.60 MeV) and BCPM (1.42 MeV).
- SF Half-lives: The model reproduces experimental SF half-lives within three orders of magnitude, comparable to highly parameterized mic-mac models. For example, for $^{240}\text{Pu}$ , the calculated half-life ( $2.4 \times 10^{19}$ s) is close to the experimental value ( $3.6 \times 10^{18}$ s).
- Fission Fragments: Pre-neutron emission yields showed good agreement with experimental peak structures and widths for actinides.
Large-Scale Predictions:
- Stability Analysis: The study identified regions susceptible to neutron-induced fission (e.g., around $^{254}\text{Bk}$ where $B_f - S_n \approx 0$ ) and $\beta$ -delayed fission (near the neutron drip line where $B_f - Q_\beta < 0$ ).
- Termination of r-Process: Near $Z=108, N=230$ , SF half-lives drop to $\sim 10^{-2}$ s, competing with $\beta$ -decay timescales. This suggests a potential termination point for heavy element synthesis and a source of fission recycling.
- Discrepancy with Empirical Formulas: When compared to empirical formulas (based on ETFSI/FRLDM), the microscopic BSkG3 predictions for neutron-rich isotopes diverge by more than 40 orders of magnitude, highlighting the unreliability of extrapolating phenomenological models to the drip line.

5. Significance

Astrophysical Impact: The generated dataset provides critical, theoretically consistent inputs for r-process nucleosynthesis simulations, particularly for neutron star mergers. It allows for a more accurate prediction of the abundance of heavy elements and the late-time decay heat of merger ejecta.
Methodological Advancement: The work demonstrates that coordinate-space HFB calculations can be scaled to thousands of nuclei without sacrificing the inclusion of complex degrees of freedom (triaxiality, octupole).
Predictive Power: By avoiding phenomenological adjustments for unknown nuclei, this study offers a robust framework for predicting the properties of super-heavy and exotic nuclei that cannot be reached experimentally, filling a critical gap in nuclear data libraries.

Future Work: The authors plan to finalize the calculation of full fission fragment distributions (including prompt neutron emission) and derive neutron-induced and $\beta$ -delayed fission rates to complete the nuclear input set for astrophysical simulations.