Microscopic Investigation of Fusion and Quasifission Dynamics

This paper applies Time-Dependent Hartree-Fock theory to investigate fusion and quasifission dynamics in heavy-ion reactions relevant to superheavy element production, demonstrating reasonable agreement with experimental data for $^{48}$Ca+$^{238}$U fusion and revealing the significant impact of tensor forces on shell effects in $^{48}$Ca+$^{249}$Bk quasifission.

The Gist

Imagine you are trying to build a giant, unstable sandcastle (a Superheavy Element) by smashing two smaller sandcastles together. You want them to merge into one big, perfect structure. But there's a catch: the sand is so full of static electricity that the two castles often repel each other, or they crash together and immediately crumble apart into two smaller piles instead of becoming one.

This is the daily struggle of nuclear physicists trying to create the heaviest elements on the periodic table. This paper, written by Liang Li and colleagues, is like a high-tech simulation report on how to make that sandcastle merge successfully. They used a super-computer method called Time-Dependent Hartree-Fock (TDHF) to watch these atomic collisions in slow motion and figure out the best way to build these giant atoms.

Here is the breakdown of their work using simple analogies:

1. The Two Ways a Crash Can Go Wrong

When two heavy atomic nuclei collide, there are two main outcomes:

• Fusion (The Success): The two nuclei smash together, mix their "ingredients" completely, and form a new, larger, stable (for a moment) compound nucleus. This is what we want.
• Quasifission (The Failure): The nuclei crash, touch for a split second, exchange a little bit of sand, but then immediately bounce apart into two separate pieces. They never truly merged. This is the biggest enemy of creating superheavy elements.

The authors studied two specific scenarios to understand how to win the "Fusion" game.

2. Scenario A: The Perfect Merge (48Ca + 238U)

The Setup: They simulated smashing a Calcium-48 atom (the projectile) into a Uranium-238 atom (the target).
The Problem: The Uranium atom isn't a perfect sphere; it's shaped like a rugby ball (football). If you hit it on the side, it's hard to merge. If you hit it on the tip, it's easier.
The Solution:

• The "Tip" Advantage: The simulation showed that hitting the "tip" of the rugby-ball-shaped Uranium is like rolling a ball down a gentle slope—it slides right in. Hitting the "side" is like trying to push a ball up a steep hill; it's much harder.
• The Three-Step Recipe: The authors broke the process down into three steps, like a recipe for a cake:
  1. Capture: Getting the two atoms close enough to touch.
  2. Fusion: Actually merging them into one.
  3. Survival: Making sure the new giant atom doesn't immediately explode (fission).
• The Result: By using their microscopic simulation to calculate the "ingredients" for the first two steps, and a statistical model for the third, they predicted exactly how many new atoms would be made. Their predictions matched real-world experiments perfectly. It's like they built a virtual weather model that predicted the rain exactly right, proving their model works.

3. Scenario B: The "Magic" Force (48Ca + 249Bk)

The Setup: They looked at a different collision: Calcium-48 hitting a Berkelium-249 atom. This is a very difficult reaction where "Quasifission" (the immediate breakup) is the main problem.
The Secret Ingredient (Tensor Force):

• In nuclear physics, there are different "rules" (forces) that tell the particles how to behave. One of these rules is called the Tensor Force. Think of this force as a special kind of "magnetic glue" that only works when particles are arranged in specific, symmetrical patterns.
• The Experiment: The team ran the simulation twice: once with this special glue (Tensor Force) and once without it.
• The Discovery:
  • Without the glue: The fragments (the pieces that break off) were scattered randomly.
  • With the glue: The fragments suddenly started lining up perfectly. They clustered around specific numbers of protons and neutrons (specifically 82 protons and 126 neutrons).
• The Analogy: Imagine you are throwing a bunch of mixed Lego bricks into the air. Without the glue, they land in a messy pile. With the glue, the red bricks magically snap together to form a perfect red tower, and the blue bricks form a blue tower.
• Why it matters: The numbers 82 and 126 are "Magic Numbers" in nuclear physics. They represent a state of perfect stability, like a full shell. The simulation showed that the Tensor Force acts like a guide, steering the collision so that the resulting pieces try to become as close to this "perfect stability" (like the element Lead-208) as possible. This helps scientists understand how to steer these collisions to avoid the "Quasifission" trap.

The Big Picture

This paper is essentially a user manual for building superheavy elements.

1. It proves that if you account for the shape of the atoms (like the rugby ball), you can predict exactly how likely they are to stick together.
2. It reveals that a specific, subtle force (the Tensor Force) acts like a traffic cop, guiding the broken pieces toward stable, "magic" configurations.

By understanding these microscopic details, scientists can better design experiments to finally create elements 119 and 120, which have so far remained out of reach because the atoms keep breaking apart before they can settle down. The authors have provided the map to navigate the chaotic world of atomic collisions.

Technical Summary

Here is a detailed technical summary of the paper "Microscopic Investigation of Fusion and Quasifission Dynamics" by Liang Li, Xiang-Xiang Sun, and Lu Guo.

1. Problem Statement

The synthesis of Superheavy Elements (SHEs), particularly those with atomic numbers $Z \ge 119$, is currently hindered by the dominance of quasifission (QF) over complete fusion.

• The Challenge: In heavy-ion collisions involving actinide targets, the enormous Coulomb repulsion often causes the colliding nuclei to separate into two fragments before forming a fully equilibrated compound nucleus (CN). This QF process competes with fusion, drastically reducing the probability of CN formation ($P_{CN}$).
• The Gap: While macroscopic models can reproduce known cross-sections via parameter fitting, they lack predictive power for unmeasured systems due to their limited treatment of dynamics and reliance on adjustable parameters. There is a critical need for a microscopic, quantitative understanding of the fusion-QF competition to reliably predict SHE synthesis cross-sections.

2. Methodology

The authors employ a hybrid theoretical framework combining microscopic Time-Dependent Hartree-Fock (TDHF) theory with macroscopic/statistical models to simulate the three-step fusion-evaporation process:

1. Capture: Projectile capture by the target.
2. Fusion: Formation of a compound nucleus.
3. Survival: De-excitation of the CN via neutron emission against fission.

Key Technical Components:

• TDHF Theory: Used to simulate the dynamical evolution of the one-body density. It captures collective motion and shell effects but omits quantum tunneling.
• Density Constrained Frozen HF (DC-FHF): Used to derive internuclear potentials ($V(R)$) as a function of the target's orientation ($\theta$). This is crucial for deformed actinide targets (e.g., $^{238}\text{U}$, $^{249}\text{Bk}$).
• Coupled-Channels (CC) Calculations: The TDHF-derived potentials serve as inputs for the CCFULL code to calculate capture cross-sections ($\sigma_{cap}$) and penetration probabilities ($T_J$).
• Fusion-by-Diffusion (FbD) Model: Used to calculate the fusion probability ($P_{CN}$). The "injection point" (distance where the system enters the diffusion region) is extracted directly from TDHF simulations, avoiding empirical assumptions.
• Statistical Model: Used to calculate the survival probability ($W_{sur}$) of the CN, accounting for the competition between neutron evaporation and fission.
• Skyrme Interactions: For QF studies, the authors compare two Skyrme energy density functionals: SLy5 (standard) and SLy5t (includes the tensor force).

3. Key Contributions

• Unified Framework: The paper demonstrates a robust workflow integrating microscopic TDHF inputs with CC, FbD, and statistical models to describe the entire hot-fusion reaction chain for $^{48}\text{Ca} + ^{238}\text{U}$.
• Microscopic Input for Fusion Probability: Instead of using phenomenological parameters for the fusion barrier or injection point, the authors extract these directly from TDHF simulations, enhancing the predictive reliability of the FbD model.
• Quantification of Tensor Force: The study systematically isolates the impact of the tensor force in the nuclear interaction on QF dynamics, specifically regarding fragment mass-angle distributions.

4. Results

A. Fusion Dynamics: $^{48}\text{Ca} + ^{238}\text{U}$

• Capture Cross-Sections: The orientation-averaged capture cross-sections calculated using DC-FHF potentials and CC theory show excellent agreement with experimental data. The model significantly outperforms empirical coupled-channels (ECC) predictions, especially at sub-barrier energies ($E_{c.m.} < 190$ MeV).
• Orientation Dependence: The results confirm a strong dependence on the orientation of the prolate-deformed $^{238}\text{U}$ target. "Tip" collisions ($\theta \approx 9.3^\circ$) have significantly lower capture barriers and higher cross-sections than "side" collisions ($\theta \approx 83.8^\circ$).
• Fusion Probabilities: The calculated effective fusion probability ($P_{fus} = \sigma_{fus}/\sigma_{cap}$) ranges from $(2-6) \times 10^{-4}$.
• Evaporation Residues: By combining the calculated fusion cross-sections with statistical survival probabilities, the predicted evaporation-residue cross-sections for the $3n$and$4n$ channels align well with available experimental data.

B. Quasifission Dynamics: $^{48}\text{Ca} + ^{249}\text{Bk}$

• Fragment Distributions: The study analyzes Mass-Angle Distributions (MADs) and fragment yields.
• Impact of Tensor Force:
  • Neutron Shell Effects: Simulations using SLy5t (with tensor force) show a pronounced clustering of QF fragments around the $N=126$ magic neutron shell. In contrast, SLy5 (without tensor force) peaks at a lower neutron number ($N \approx 122$), indicating a weaker shell effect.
  • Proton Shell Effects: Similarly, the tensor force drives fragments closer to the $Z=82$ magic proton shell. SLy5t yields peak near $Z=82$, while SLy5 peaks near $Z=79$.
• Conclusion on QF: The inclusion of the tensor force significantly amplifies spherical shell effects, driving the QF dynamics toward the production of fragments near the doubly-magic $^{208}\text{Pb}$ ($Z=82, N=126$).

5. Significance

• Predictive Power for SHE Synthesis: The validated hybrid framework provides a reliable tool for predicting cross-sections for yet-to-be-synthesized elements (e.g., $Z=119, 120$), where experimental data is currently unavailable.
• Role of Tensor Force: The work provides compelling microscopic evidence that the tensor force is a critical component in nuclear interactions, specifically enhancing the role of shell closures in heavy-ion collisions. This suggests that accurate theoretical models for SHE synthesis must include tensor interactions to correctly predict QF barriers and fragment yields.
• Mechanistic Insight: The study clarifies how entrance channel properties (orientation, deformation) and microscopic forces (tensor) dictate the competition between fusion and quasifission, offering guidance for optimizing reaction pathways in future experiments.