Impact of octupole correlation on the inverse quasifission in ${}^{160}\text{Gd}+{}^{186}\text{W}$ collisions

Using time-dependent Hartree-Fock theory, this study demonstrates that octupole deformed shell effects, particularly the $N=88$ shell, rather than spherical shells, dominate the inverse quasifission mechanism in ${}^{160}\text{Gd}+{}^{186}\text{W}$ collisions, thereby explaining the enhanced yields of neutron-rich transtarget nuclei in the Au region.

The Gist

The Big Picture: A Cosmic Dance of Heavy Nuclei

Imagine two heavy, deformed dancers (atomic nuclei) approaching each other on a dance floor. One is Gadolinium-160 (the projectile) and the other is Tungsten-186 (the target). They are spinning and wobbling because they aren't perfect spheres; they are shaped like slightly squashed or stretched rugby balls.

The scientists wanted to know: What happens when these two heavy nuclei collide?

Usually, when heavy nuclei crash, they either fuse into a super-heavy blob or they bounce apart immediately. But in a special type of collision called Inverse Quasifission, they do something unique: they stick together for a moment, swap some "clothes" (neutrons and protons), and then split apart into two new, different heavy nuclei.

The goal of this dance is to create neutron-rich heavy nuclei—the "superheroes" of the atomic world that are hard to make any other way.

The Mystery: Why did the experiment surprise everyone?

For a long time, physicists thought the reason these collisions created specific heavy elements was due to the "magic" stability of a famous nucleus called Lead-208. Think of Lead-208 as a perfectly round, super-stable fortress. The theory was: "The dance partners swap parts until they accidentally build a piece that looks like this fortress, and that's why the reaction stops there."

However, experiments showed something weird. Instead of stopping near the Lead-208 fortress, the reaction seemed to stop near Gold (Au). It was as if the dancers were trying to build a fortress, but they kept stopping at a different, unexpected landmark.

The Investigation: Watching the Dance in Slow Motion

The authors of this paper used a super-powerful computer simulation called Time-Dependent Hartree-Fock (TDHF). You can think of this as a high-speed, frame-by-frame movie camera that can see inside the nucleus, watching every single proton and neutron move.

They simulated the collision of Gadolinium and Tungsten at different angles and speeds to see what was really happening.

1. The Angle Matters (The "Tip-Top" vs. "Side-Side" Dance)

Because the nuclei are shaped like rugby balls, how they hit each other matters immensely.

• Tip-Top: Hitting the pointy end of one ball against the pointy end of the other.
• Side-Side: Hitting the flat sides together.

The Discovery: The simulation showed that the "Tip-Top" and "Tip-Side" collisions were the most effective at swapping particles. It's like trying to pass a baton: if you hold it end-to-end, it's easier to pass than if you try to pass it while holding it sideways. These specific angles allowed the nuclei to stick together long enough to swap a lot of neutrons and protons, creating the heavy elements the scientists wanted.

2. The Real "Magic" Number (It's not Lead-208!)

This is the paper's biggest breakthrough. When the scientists looked at the results, they found that the reaction wasn't stopping because of the Lead-208 fortress.

Instead, it was stopping because of a hidden, octopus-shaped shell.

• The Analogy: Imagine the nucleus isn't a smooth ball, but a shape that wobbles like an octopus (this is called "octupole deformation").
• The simulation revealed that the light fragments (the smaller pieces after the split) were stopping at a specific number of neutrons: 88.
• At N=88, the nucleus has a special "octupole shell" that acts like a magnetic trap. It's energetically very comfortable for the nucleus to be shaped like an octopus at this specific number.

The Result: The reaction produced a peak in Gold (Au) because the "Octopus Shell" at N=88 was pulling the reaction there, not the "Spherical Fortress" of Lead-208. This explains why the experiments saw Gold instead of Lead.

3. Speed Changes the Rules (Energy Dependence)

The scientists also tested what happens if they make the dancers run faster (higher energy).

• At moderate speeds: The "Octopus Shell" (N=88) is the boss. The reaction stops there.
• At very high speeds: The dancers have so much energy that they can smash through the Octopus Shell. Now, the "Spherical Fortress" (Lead-208) starts to matter again, competing with the octopus shape.

Why Does This Matter?

This paper solves a long-standing mystery. It tells us that to create new, heavy elements (like those needed for future super-heavy element research), we can't just rely on the old rules about spherical shapes.

The Takeaway:
To build the heaviest atoms, we need to aim our collisions carefully (using the right angles) and understand that wobbly, octopus-shaped nuclei are just as important as perfect spheres in guiding the reaction. It's like realizing that to build a stable tower, you don't just need round bricks; sometimes, you need bricks with a specific, wobbly shape to lock everything together perfectly.

This discovery helps scientists design better experiments to synthesize new elements that could exist in the "Island of Stability," potentially leading to new materials or a deeper understanding of the universe.

Technical Summary

1. Problem Statement

Multinucleon transfer (MNT) reactions are a promising pathway for synthesizing neutron-rich heavy and superheavy nuclei. A key mechanism in these reactions is inverse quasifission, where the products have a larger mass asymmetry than the reactants (i.e., nucleons transfer from the light projectile to the heavy target).

Despite its potential, the microscopic mechanism driving inverse quasifission remains poorly understood.

• The Discrepancy: The prevailing theoretical view suggests that inverse quasifission in actinide systems is driven by spherical shell closures at $Z=82$ and $N=126$ (associated with the doubly magic nucleus $^{208}\text{Pb}$). These shells create potential energy valleys that guide reaction trajectories.
• The Anomaly: Experimental data for the $^{160}\text{Gd} + ^{186}\text{W}$ reaction show a yield enhancement for trans-target products in the Gold (Au, $Z=79$) region, not near Lead ($Z=82$) as predicted by spherical shell models.
• The Gap: Previous theoretical attempts (e.g., Stochastic Mean-Field theory) reproduced mass distributions but failed to explain why the $^{208}\text{Pb}$ shell effects were inactive and what specific shell structure was driving the reaction. The role of deformed shells (specifically octupole deformations) in inverse quasifission had not been rigorously investigated.

2. Methodology

The authors employed the Time-Dependent Hartree-Fock (TDHF) theory, a microscopic mean-field approach that provides a parameter-free description of nuclear dynamics based on energy density functionals.

• System: The collision of $^{160}\text{Gd}$ (projectile) and $^{186}\text{W}$ (target).
• Interaction: The SLy5 Skyrme effective interaction was used, incorporating both time-even and time-odd components.
• Initial Conditions:
  • Both nuclei are well-deformed. $^{160}\text{Gd}$ has quadrupole ($\beta_2 \approx 0.32$), triaxial, and slight octupole ($\beta_3 \approx 0.03$) deformations. $^{186}\text{W}$ is prolate ($\beta_2 \approx 0.24$).
  • Orientation Effects: The study systematically simulated 18 distinct initial orientations (combinations of projectile angle $\theta_P$ and target angle $\theta_T$) to account for the strong influence of deformation on reaction dynamics.
  • Energy Range: Simulations were performed at a center-of-mass energy of $E_{c.m.} = 502.6$ MeV (matching experimental conditions) and extended from 440 to 820 MeV to study energy dependence.
• Analysis Techniques:
  • Particle Number Projection (PNP): Used to extract transfer probabilities for specific proton ($Z$) and neutron ($N$) numbers from the mean-field wave function.
  • Single-Particle Spectra: Analyzed the energy levels of fragments at the scission point to identify shell gaps.

3. Key Contributions

1. Identification of the Driving Shell: The study definitively identifies that the $N=88$ octupole-deformed shell in the light fragments, rather than the spherical $Z=82/N=126$ shells of $^{208}\text{Pb}$, is the primary driver of inverse quasifission in this system at $E_{c.m.} = 502.6$ MeV.
2. Resolution of the Yield Anomaly: The findings explain the experimental observation of enhanced yields in the Au region ($Z \approx 79$). The reaction favors the formation of fragments with $N=88$, which corresponds to the observed peak, while the system lacks sufficient energy to reach the $^{208}\text{Pb}$ region where spherical shells would dominate.
3. Energy Dependence of Shell Effects: The paper demonstrates that the dominant shell structure in inverse quasifission is energy-dependent.
   • At lower energies (560–640 MeV), the octupole deformed shell ($N=88$) dominates.
   • At higher energies (700–780 MeV), the system transfers more nucleons, allowing heavy fragments to approach the spherical $Z=82$ shell, creating a competition between spherical and deformed shell effects.
4. Orientation Sensitivity: The study confirms that inverse quasifission is highly sensitive to the collision geometry, occurring most favorably in tip-tip and tip-side orientations, which maximize nucleon transfer and neck formation.

4. Key Results

• Reaction Dynamics: Inverse quasifission occurs when deformed nuclei collide in near tip-tip or tip-side orientations. The process involves the formation of a dinuclear system with a neck, followed by nucleon transfer and eventual scission into two fragments (e.g., $^{147}\text{Pr}$ and $^{199}\text{Au}$).
• Fragment Distribution: At $E_{c.m.} = 502.6$ MeV, the primary heavy fragments peak around $^{199}\text{Au}$ ($Z=79, N=120$), and light fragments peak at $N=88$.
• Single-Particle Evidence: Analysis of single-particle energy levels for fragments near the enhancement peak (e.g., $^{144-148}\text{Ce}$, $^{146-150}\text{Nd}$) reveals pronounced octupole neutron shell gaps at $N=88$. These gaps are absent or less significant for the spherical $^{208}\text{Pb}$ configuration at this energy.
• Mechanism Explanation: The stretched neck formed during the collision induces octupole deformation in the fragments. This deformation energetically favors the formation of nuclei with octupole shell correlations (minimizing deformation energy), thereby driving the system toward the $N=88$ region. The system does not gain enough energy at 502.6 MeV to overcome the barrier to reach the $^{208}\text{Pb}$ region.

5. Significance

• Theoretical Advancement: This work shifts the paradigm for understanding inverse quasifission from a purely spherical-shell-driven model to one that incorporates deformed shell correlations. It highlights that in MNT reactions involving deformed nuclei, octupole deformations can be the dominant factor in determining reaction outcomes.
• Experimental Guidance: The results provide a microscopic explanation for existing experimental data and offer predictions for future experiments. They suggest that to synthesize specific neutron-rich nuclei, one must consider not just the ground-state shell closures of the products, but the dynamic shell structures (deformed shells) formed during the scission process.
• Synthesis of Superheavy Elements: By clarifying the mechanisms that enhance the production of trans-target nuclei, this research aids in optimizing reaction pathways for synthesizing new neutron-rich heavy and superheavy elements that are inaccessible via fusion-evaporation reactions.