Isotopic fission yields of ${}^{240}$Pu as a function of the excitation energy

This paper presents complete isotopic fission yield distributions of $^{240}$Pu measured as a function of excitation energy (8.2–11.9 MeV), revealing that increasing excitation energy dampens shell effects in the symmetry valley and reduces neutron content specifically in heavy fragments while leaving light fragments unaffected.

The Gist

Imagine a heavy, unstable atom like a giant, wobbly water balloon filled with energy. If you poke it just right, it splits into two smaller balloons. This is nuclear fission. For a long time, scientists have known that when these atoms split, they don't always break into equal halves; they usually break into one big piece and one small piece. But why they break that way, and how the "temperature" (excitation energy) of the atom changes the split, has been a bit of a mystery.

This paper is like a high-speed, microscopic photography session of that split, specifically looking at an atom called Plutonium-240.

Here is the story of what they did and what they found, explained simply:

The Experiment: A Cosmic Billiard Game

The scientists didn't just wait for these atoms to split naturally. They had to force it to happen in a very controlled way.

• The Setup: They fired a beam of heavy Uranium atoms at a thin sheet of Carbon.
• The Trick: Instead of smashing them head-on, they used a "two-proton transfer." Imagine two billiard balls glancing off each other, where one ball gently hands over two tiny marbles (protons) to the other. This turned the Uranium into Plutonium-240.
• The "Temperature" Control: By changing how hard they hit the target, they could control how "excited" (hot) the new Plutonium atom was. They tested it at three different "temperatures": a cool 8.2 MeV, a medium 10.0 MeV, and a hot 11.9 MeV.
• The Camera: They used a giant, super-sensitive magnetic spectrometer (called VAMOS++) to catch the two pieces flying apart. This camera was so good it could identify exactly what kind of atom each piece was, counting every single proton and neutron.

The Big Discoveries

1. The "Shell Effect" Fades with Heat
At low temperatures, atoms have a "preference" for breaking in specific ways because of their internal structure (like how a crystal has a specific shape). This is called a "shell effect." It usually forces the atom to split into very uneven pieces (one heavy, one light).

• What they found: As they heated up the Plutonium (increased the excitation energy), this rigid preference started to melt away. The atom became more willing to split into more equal halves.
• The Analogy: Think of a rigid ice sculpture. When it's cold, it holds a specific, jagged shape. As you warm it up, it starts to slump and become more fluid, allowing it to take on a more balanced shape. The "heat" damped the rigid rules of the atom's structure.

2. The Heavy Piece Loses Weight (Neutrons)
When the atom splits, it usually spits out extra neutrons (tiny neutral particles) like steam escaping a boiling pot.

• What they found: As the Plutonium got hotter, the heavy piece of the split started losing more neutrons. It became lighter and less "neutron-rich."
• The Surprise: The light piece of the split didn't change at all. It kept the same number of neutrons, regardless of how hot the system got.
• The Analogy: Imagine two people sharing a heavy blanket. If the room gets hotter, the person on the heavy side of the blanket starts sweating and shedding layers (neutrons) to cool down. But the person on the light side stays perfectly comfortable and keeps their layers on. The heat energy seems to flow only to the heavy side, which then dumps the excess.

3. The "Snack" at the Center
The scientists looked closely at the middle of the split (where the pieces are roughly equal size).

• What they found: At the very center, the atom seemed to have a "compact" shape that was very sensitive to heat. When the temperature rose, this compact shape started shedding neutrons much faster than the uneven shapes did.
• The Analogy: It's like a tightly packed suitcase. When you shake it gently (low heat), nothing falls out. But if you start shaking it violently (high heat), the tightly packed items in the middle spill out much faster than the loose items on the edges.

The Verdict: Models vs. Reality

The scientists compared their real-world photos with computer models (specifically a model called GEF) that try to predict how fission works.

• The Good News: The computer model was pretty good at predicting how the "uneven" splits would change as the atom got hotter.
• The Bad News: The model got the "light" piece wrong. It predicted the light piece would lose neutrons, but in reality, it didn't lose any. The model also guessed the light pieces were slightly "lighter" (had fewer neutrons) than they actually were.

Why This Matters (According to the Paper)

This paper doesn't talk about building better bombs or reactors. Instead, it says this data is a crucial test for scientists trying to build better computer models of the nucleus.

• Because they measured both the heavy and light pieces at the same time, they found a "correlated" truth: the light piece stays stable while the heavy piece changes.
• Current computer models miss this specific detail. By feeding this new, precise data into the models, scientists can fix their equations to better understand the fundamental laws of how matter behaves when it breaks apart.

In short, they heated up a Plutonium atom, watched it split, and discovered that while the "heavy" side of the split reacts to the heat, the "light" side remains stubbornly unchanged—a detail that current computer simulations are still struggling to get right.

Technical Summary

Technical Summary: Isotopic Fission Yields of $^{240}$Pu as a Function of the Excitation Energy

Problem and Motivation
The fission process serves as a critical laboratory for investigating the dynamical effects of nuclear matter and nuclear structure. While nuclear structure favors specific potential energy configurations leading to asymmetric fission at low excitation energies, and non-equilibrium collective motion between saddle and scission points is influenced by dissipation and inertia, a fully microscopic description of the interplay between these aspects remains elusive. Specifically, open questions persist regarding the timing of pre-fragment structure definition, the dissipative character of the process, angular momentum generation, and competition with other decay channels. Historically, experimental limitations restricted access to only long-lived fissioning systems and fragment masses. Recent advancements, including surrogate techniques and inverse kinematics, have expanded access to exotic systems and full fragment distributions, yet precise measurements of fission-fragment observables are required to guide and challenge theoretical models.

Methodology
This study reports on the complete isotopic fission yields distributions of $^{240}$Pu as a function of initial excitation energy ($E_x$). The experiment was conducted at GANIL using a $^{238}$U beam accelerated to 6.14 AMeV impinging on a 12C target. The $^{240}$Pu fissioning system was produced via a two-proton transfer reaction, $^{12}$C($^{238}$U, $^{240}$Pu$^*$)$^{10}$Be, in inverse kinematics.

Key experimental components included:

• Reaction Identification: The fissioning system was identified by detecting the target-like recoil $^{10}$Be using a segmented silicon telescope (SPIDER). The excitation energy was determined on an event-by-event basis by reconstructing the binary reaction using energy and momentum conservation laws.
• Excitation Energy Correction: The measured excitation energy distribution was corrected for the population of the first excited state ($2^+$) of $^{10}$Be (3.37 MeV), which effectively reduces the energy available to the $^{240}$Pu system.
• Fragment Detection: Fission fragments were detected at the focal plane of the VAMOS++ magnetic spectrometer. The spectrometer allowed for the simultaneous measurement of proton ($Z$) and mass ($A$) numbers of the full distribution of fragments, enabling isotopic identification.
• Data Selection: Three weighted-average excitation energy ranges were analyzed: 8.2 MeV, 10.0 MeV, and 11.9 MeV. Isotopic yields were normalized to 200% and corrected for spectrometer acceptance and efficiency.

Key Contributions and Results
The manuscript presents the evolution of isotopic, elemental, and mass fission yields for $^{240}$Pu across the selected excitation energy range.

1. Damping of Shell Effects: As excitation energy increases from 8.2 to 11.9 MeV, the yields in the symmetry valley (elements Rh, Pd, Ag, Cd, In) increase. This observation indicates a clear damping of nuclear shell effects that typically drive asymmetric fission at lower energies.
2. Neutron Content Evolution: A distinct asymmetry in neutron evaporation was observed. As $E_x$ increases, the heavy fragments shift toward less neutron-rich isotopes, indicating increased neutron evaporation. Conversely, the neutron content of the light fragments remains largely unaffected by the increase in excitation energy.
3. Neutron Excess and Scission Configurations: The neutron excess ($\langle N \rangle/Z$) of the fragments shows pronounced charge polarization. The maximum neutron excess occurs around $Z \approx 50$ (near the doubly magic $^{132}$Sn), while the maximum fission yield occurs at $Z \approx 54$. The total prompt-neutron multiplicity exhibits a minimum at $Z=50$ and a maximum at symmetry. The data suggests that the compact scission configuration around Sn is highly sensitive to initial excitation energy, with neutron evaporation increasing more rapidly at $Z=50$ than at larger asymmetries.
4. Comparison with Models: The experimental data were compared with GEF (General Fission) semi-empirical calculations.
   • Agreement: GEF successfully reproduces the damping of shell effects in the symmetry valley and the general trend of increasing neutron evaporation in heavy fragments with rising $E_x$.
   • Discrepancies: The model systematically predicts light fragments that are approximately half a neutron less neutron-rich than the measured data. Additionally, GEF predicts a strong even-odd staggering in neutron multiplicity that is not observed in the experimental data. The model also overestimates yields in very asymmetric splits.

Significance and Claims
The authors claim that this work provides a high-quality dataset extending experimental information on fission yields to higher excitation energies (fast neutron range). The primary significance lies in the use of correlated observables—specifically the simultaneous measurement of mass and proton numbers—which allows for the disentanglement of structural effects from dynamical dissipation.

The observation that light fragments retain their neutron content while heavy fragments dissipate excess energy suggests a constant flow of energy from light to heavy fragments in a superfluid regime prior to scission. This finding challenges and refines current fission models, highlighting the necessity of correlated observables for accurate modeling. The authors note that while the current data improves constraints on fission models and evaluations, the resolution is limited by the experimental setup. They indicate that future measurements using the PISTA setup, which offers a four-fold improvement in excitation energy resolution, will address these limitations and allow for finer sampling of the evolution of fission yields near the fission barrier.