Incomplete fusion in $^{193}$Ir($^{12}$C, x)$^{205}$Bi reaction at $E_{lab}$ $\approx$ 5-7 AMeV

This study investigates incomplete fusion in the $^{12}$C+$^{193}$Ir reaction at 5–7 AMeV using the stacked-foil activation technique, finding that the incomplete fusion fraction increases with energy and entrance-channel parameters like mass asymmetry and Coulomb factor, while also demonstrating that projectile breakup suppresses complete fusion relative to standard theoretical models.

The Gist

The Tale of the "Messy" Cosmic Collision

Imagine you are playing a game of high-speed bumper cars at a carnival. Usually, when two cars collide, they stick together for a moment, spin around, and then move on as one single, combined unit. In the world of nuclear physics, scientists call this Complete Fusion (CF). It’s a clean, predictable "hug" between two atomic nuclei.

But sometimes, things get messy. Instead of a clean hug, one of the cars hits the other so hard or at such a weird angle that it breaks into pieces. One piece might stick to the target, while the other piece flies off into the distance like a splinter. This "messy" collision is what scientists call Incomplete Fusion (ICF).

This paper is a detailed report from a team of researchers studying exactly how and why these "messy" collisions happen when they fire a tiny projectile (Carbon-12) at a larger target (Iridium-193).

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1. The "Splinter" Effect (What they found)

The researchers used a high-tech particle accelerator to smash these nuclei together at speeds of about 5 to 7% of the speed of light.

They discovered that as they increased the energy of the collision, the "messiness" increased. At lower energies, the nuclei mostly performed a clean "hug" (Complete Fusion). But as they sped up, the Carbon nucleus started acting like a piece of brittle wood—hitting the Iridium target and splintering into smaller bits (specifically, alpha particles).

The Analogy: Think of throwing a water balloon at a wall. At low speeds, the balloon hits and stays in one clump. At high speeds, the balloon bursts, and water droplets spray everywhere. The researchers measured those "droplets" to figure out how much of the "balloon" actually stuck to the wall.

2. The "Rules of the Road" (What causes the mess?)

The scientists wanted to know: What determines if a collision will be clean or messy? They looked at three main "rules":

• The Weight Difference (Mass Asymmetry): They found that the more different the weights of the two colliding objects are, the more likely they are to have a messy collision.
• The Electric Repulsion (Coulomb Factor): Nuclei are like magnets with the same poles facing each other—they hate being close. The stronger this "magnetic" push, the more likely the projectile is to break apart before it can successfully "hug" the target.
• The "Skin" of the Target (Neutron Skin): Heavy nuclei have a fuzzy outer layer of neutrons, like a soft cushion. The researchers found that a thicker "cushion" actually makes the messy collisions more likely.

3. The "Spin" Problem (Angular Momentum)

In physics, everything that moves has "spin" or angular momentum. The researchers found something surprising: even when the collision seemed like it should be "clean" based on old math models, the messiness was still happening.

They realized that the "boundary" between a clean hug and a messy breakup isn't a sharp line; it’s more like a blurry, fuzzy zone. Even collisions that aren't spinning fast enough to technically "break" the nucleus are still causing it to splinter.

4. Why does this matter?

You might ask, "Who cares about tiny nuclei smashing into each other?"

Well, understanding these messy collisions is like understanding how a car crash works so you can build better airbags. By mastering the math of these "splinters," scientists can:

1. Create New Elements: This helps us learn how to manufacture rare and heavy elements that don't exist naturally on Earth.
2. Understand the Stars: These same types of collisions happen inside exploding stars (supernovas). If we want to understand how the universe was built, we have to understand the "messy" physics of the tiny world.

Summary in a Nutshell

The researchers proved that at certain speeds, Carbon nuclei don't just merge with Iridium; they shatter. By measuring the "shards" left behind, they've created a better map for how matter behaves when it's pushed to its limits.

Technical Summary

Technical Summary: Incomplete Fusion in $^{193}\text{Ir}(^{12}\text{C}, x)^{205}\text{Bi}$ Reaction at $E_{\text{lab}} \approx 5\text{--}7$ AMeV

1. Problem Statement

In low-energy heavy-ion induced reactions, the competition between Complete Fusion (CF)—where the projectile and target coalesce into a fully equilibrated compound nucleus (CN)—and Incomplete Fusion (ICF)—where the projectile breaks up and only a fragment fuses with the target—is a critical area of study. While ICF is well-documented at higher energies ($>10$ AMeV), its dynamics and dependence on entrance-channel parameters at very low energies ($3\text{--}7$ AMeV) remain poorly understood. Specifically, the role of projectile structure (such as $\alpha$-clustering) and the exact onset of ICF relative to critical angular momentum ($\ell_{\text{crit}}$) in this energy regime require investigation.

2. Methodology

• Reaction System: The study focuses on the $^{12}\text{C} + ^{193}\text{Ir} \rightarrow ^{205}\text{Bi}^*$ system at incident energies of $64\text{--}84$ MeV ($\approx 5\text{--}7$ AMeV).
• Experimental Technique: The researchers employed the stacked-foil activation technique at the Inter-University Accelerator Centre (IUAC), New Delhi. This was followed by offline $\gamma$-spectroscopy using high-resolution clover HPGe detectors to identify evaporation residues (ERs).
• Data Analysis:
  • Statistical Model: Experimental excitation functions (EFs) were compared against predictions from the PACE4 code.
  • Parameter Optimization: The level-density parameter ($a = A/K$) was adjusted (specifically finding $K=13$ to be optimal) to distinguish between CF and ICF contributions.
  • Mathematical Modeling: The study used the Universal Fusion Function (UFF) and the Improved Fusion Function (IFF) to analyze fusion suppression and the impact of $\ell$-dependent barrier parameters.

3. Key Contributions

• Channel-by-Channel Analysis: The paper provides a granular look at how different evaporation channels ($xn$, $pxn$, $\alpha xn$, and $2\alpha n$) are populated.
• Identification of ICF Signatures: By demonstrating that neutron-emitting channels follow CF predictions while $\alpha$-emitting channels show massive enhancement, the study provides a clear experimental signature for ICF in this system.
• Parameter Correlation: The work establishes how the Incomplete Fusion Fraction (FICF) correlates with mass asymmetry ($\mu_m$), Coulomb factor ($Z_P Z_T$), and target neutron skin thickness ($t_N$).
• Refinement of Empirical Models: The authors modified Wang’s empirical formula to better correlate fusion suppression with the projectile's breakup threshold energy ($E_{B.U.}$).

4. Results

• ICF Evidence: The $xn$ and $pxn$ channels were well-explained by CF using $a = A/13$ MeV$^{-1}$. However, $\alpha$-emitting channels showed enhancements of one to two orders of magnitude over PACE4 predictions, confirming they are dominated by ICF.
• FICF Trends: The Incomplete Fusion Fraction (FICF) increases linearly with energy, rising from 12% at 64 MeV to 18% at 84 MeV.
• Entrance-Channel Dependencies:
  • Mass Asymmetry: FICF increases with $\mu_m$, but shows strong projectile dependence (e.g., $^{16}\text{O}$ shows higher ICF than $^{12}\text{C}$ at similar asymmetries).
  • Coulomb Factor: FICF increases linearly with $Z_P Z_T$.
  • Neutron Skin: FICF increases with the target's neutron skin thickness ($t_N$), suggesting neutron-rich targets facilitate breakup.
  • Projectile Structure: The study identifies that the $Q_\alpha$ value is a decisive factor; projectiles with less negative $Q_\alpha$ values (weaker $\alpha$-separation energies) exhibit higher ICF.
• Angular Momentum: The study finds that ICF occurs even at angular momenta below the theoretical critical limit ($\ell < \ell_{\text{crit}}$), suggesting a "diffuse" boundary for the fusion window rather than a sharp cutoff.
• Fusion Suppression: Projectile breakup suppresses CF by approximately 12% when analyzed via UFF, though this is refined to 6% when using the IFF (which accounts for $\ell$-dependent barrier parameters).

5. Significance

This research provides critical quantitative constraints on the dynamics of breakup fusion at near-barrier energies. By highlighting the importance of projectile structure (specifically $\alpha$-clustering and $Q_\alpha$ values) over simple geometric parameters, the study improves the accuracy of reaction modeling. These findings have broader implications for high-spin spectroscopy, the production of heavy/superheavy nuclei, and the calculation of astrophysical reaction rates where low-energy heavy-ion interactions are fundamental.