Study of fusion-fission in inverse kinematics with a fragment separator

This paper demonstrates the effectiveness of inverse kinematics fusion-fission reactions, utilizing a 238U beam on 9Be and 12C targets at GANIL with the LISE3 spectrometer, to systematically measure and identify unique isotopic yields of fission fragments, thereby providing critical experimental benchmarks for fission models.

The Gist

Imagine you have a giant, heavy bowling ball (a Uranium atom) and you want to smash it into tiny, interesting pieces to study them. In the world of nuclear physics, this is called fission. Usually, scientists try to do this by shooting the bowling ball at a wall and hoping it breaks apart. But there's a problem: the pieces fly off in all directions, and the heavy ones move so slowly that they get stuck in the wall or are hard to catch.

This paper describes a clever new way to play this game, called "Inverse Kinematics." Instead of throwing the bowling ball at a wall, imagine you are standing on a skateboard (the Uranium beam) and you roll into a stationary, light object (a Beryllium or Carbon target).

Here is the story of what happened, explained simply:

1. The Setup: The Skateboard and the Wall

The scientists at a big lab in France (GANIL) took a beam of Uranium-238 atoms and accelerated them to incredible speeds (24 million electron volts per atom). They aimed this "Uranium skateboard" at two different targets:

• Target A: A thin sheet of Beryllium (very light).
• Target B: A thin sheet of Carbon (slightly heavier).

Because the Uranium was moving so fast, when it hit the target, it didn't just bounce off. Sometimes it stuck to the target atom, forming a super-hot, super-heavy "compound" nucleus. This new giant nucleus was so excited that it immediately snapped in half (fission).

The Magic Trick: Because the original Uranium was moving so fast, the two new pieces (the fission fragments) kept that forward momentum. They flew out like bullets from a gun, making them very easy to catch and identify, unlike the slow-moving pieces in traditional experiments.

2. The Catcher's Mitt: The LISE3 Spectrometer

To catch these flying fragments, the scientists used a giant machine called a fragment separator (LISE3). Think of this machine as a high-tech, magnetic sorting hat.

• It uses powerful magnets to bend the path of the flying particles.
• It measures how long they take to fly (Time-of-Flight).
• It measures how much energy they lose when hitting a detector (like a car crash test).

By combining all these measurements, the machine could tell exactly what each piece was (its mass, its atomic number, and its electric charge) with incredible precision. It was like being able to look at a broken piece of a puzzle and instantly know exactly which picture it came from and what color it was.

3. The Surprise: Two Different Ways to Break

The scientists expected the Uranium to break apart in a similar way for both targets. But they found something fascinating: The target material changed the rules of the game.

• The Beryllium Target (The Gentle Break): When the Uranium hit the light Beryllium, it mostly formed a stable, heavy compound nucleus that then split in a "standard" way. This is called Complete Fusion-Fission. It produced a lot of heavy, neutron-rich fragments (like heavy isotopes of elements with atomic numbers around 48).

  • Analogy: Imagine dropping a water balloon onto a soft pillow. It squishes, forms a big blob, and then gently splits into two large, heavy halves.

• The Carbon Target (The Wild Break): When the Uranium hit the slightly heavier Carbon, the collision was more violent. The spinning motion (angular momentum) was so high that the nucleus didn't have time to settle into a stable blob. Instead, it spun so fast that it tore itself apart immediately. This is called Fast-Fission.

  • Analogy: Imagine spinning a water balloon on a string so fast that the centrifugal force rips it apart before it even touches the ground. The pieces fly off in a wider, more chaotic pattern, creating lighter fragments (around atomic number 44).

4. Why Does This Matter?

The goal of this experiment wasn't just to smash things; it was to find rare, neutron-rich isotopes. These are weird, unstable versions of elements that don't exist naturally on Earth but are crucial for understanding how stars create heavy elements.

The study showed that:

1. Inverse Kinematics works: It's a fantastic way to catch these fast-moving fragments.
2. Target matters: By choosing the right target (Beryllium vs. Carbon), scientists can control how the nucleus breaks and what kind of fragments they get.
3. New Beams: This method can be used to create new "beams" of rare isotopes for future experiments, helping us map out the "island of stability" where super-heavy elements might live.

The Bottom Line

Think of this paper as a recipe for breaking a giant cookie. The scientists discovered that if you use a light spoon (Beryllium), the cookie breaks into big, heavy chunks. If you use a slightly heavier spoon (Carbon) and spin it faster, it shatters into smaller, different pieces. By understanding this, they can now "bake" specific types of rare atomic ingredients that were previously impossible to get, helping us solve the mystery of how the universe builds heavy elements.

Technical Summary

1. Problem Statement

The production of rare, neutron-rich isotopes is essential for understanding nuclear structure and astrophysical processes. Traditional methods for producing these isotopes, such as spallation with thick Uranium targets in "normal kinematics," face significant challenges:

• Extraction Difficulties: Slow-moving fragments are difficult to extract from thick targets.
• Identification Issues: Identifying slow fragments is experimentally cumbersome.
• Limited Reach: Existing techniques struggle to efficiently produce and identify isotopes in the $55 < Z < 75$ region.

While "in-flight fission" (abrasion-fission) and Coulomb fission are established methods, there is a need to explore inverse kinematics fusion-fission as a production mechanism. In this approach, a heavy projectile (e.g., $^{238}\text{U}$) strikes a light target, creating fast-moving fission fragments that are easier to separate and identify. However, the specific reaction mechanisms (complete fusion-fission vs. fast-fission vs. incomplete fusion) and their yields under different target conditions (specifically $^9\text{Be}$ vs. $^{12}\text{C}$) at intermediate energies ($\sim 20\text{--}24$ MeV/u) require systematic experimental validation and theoretical modeling.

2. Methodology

The study employed an experimental setup at the GANIL facility (France) coupled with theoretical modeling using the LISE++ code.

Experimental Setup:

• Beam: A $^{238}\text{U}^{58+}$ beam accelerated to 24 MeV/u (approx. 20 MeV/u in the target center) with an intensity of $\sim 10^9$ particles per second.
• Targets: Two light targets were used: $^9\text{Be}$ (15 mg/cm$^2$) and natural $^{12}\text{C}$ (15 mg/cm$^2$).
• Separator: The LISE3 fragment separator was used to select and transport fission products. The beam entered at a $3^\circ$ angle to prevent unreacted beam from entering the spectrometer.
• Detection System: A comprehensive identification system was used to determine Mass ($A$), Atomic Number ($Z$), and Charge State ($q$):
  • Magnetic Rigidity ($B\rho$): Measured via position-sensitive micro-channel plate detectors (MCP) at intermediate and final focal planes.
  • Time-of-Flight (ToF): Measured between the intermediate MCP and the final detector.
  • Energy Loss ($\Delta E$) & Total Kinetic Energy (TKE): Measured using a stack of four silicon detectors.
  • Gamma-Ray Tagging: Two Germanium detectors placed near the silicon stack identified isomeric states (e.g., $^{128m}\text{Te}$) to independently verify particle identification.
• Data Reconstruction: Yields were measured at four magnetic rigidity settings. Transmission corrections were applied using LISE++ simulations, dividing the thick targets into 5 sections to account for energy loss variations.

Theoretical Modeling:

• The LISE++ code was utilized with a new fusion-fission model to calculate cross-sections, kinematics, and charge-state distributions.
• The model incorporated partial-wave descriptions and the Sierk model for fission barrier dependence on angular momentum.
• Reaction channels considered included Complete Fusion-Fission (FF), Fast-Fission (FA), and Incomplete Fusion (IF/Deep-Inelastic).

3. Key Contributions

• Demonstration of Inverse Kinematics: The paper validates inverse kinematics coupled with a high-resolution fragment separator as a powerful tool for producing and identifying neutron-rich isotopes in the $Z=30\text{--}64$ range.
• Reaction Mechanism Differentiation: It provides a systematic comparison of how target mass ($^9\text{Be}$ vs. $^{12}\text{C}$) alters the dominant reaction mechanism at intermediate energies.
• Model Validation: The study compares experimental data against LISE++ simulations, refining the understanding of fusion-fission cross-sections and charge-state distributions in this energy regime.
• Charge-State Calibration: New measurements of uranium beam charge-state distributions after passing through various foils were compared against parameterizations (Leon, Schiwietz, Winger), highlighting the limitations of equilibrium assumptions for thin targets.

4. Key Results

A. Cross Sections and Yields:

• Total Fission Cross Sections: Measured as 3.6 $\pm$ 1.0 barn for Be and 2.4 $\pm$ 0.7 barn for C. These values are significantly higher than high-energy ($1$ GeV/u) interactions, indicating a substantial contribution from the complete fusion channel at lower energies.
• Fragment Distributions:
  • Be Target: Produced heavier fission fragments (average $Z \approx 48$) with a trapezoidal distribution shape (plateau from $Z=46\text{--}53$).
  • C Target: Produced lighter fragments (average $Z \approx 46$) with a more Gaussian shape.
  • Neutron Richness: The Be target produced isotopes approximately 9–13 mass units heavier than those produced in high-energy proton/deuteron reactions.

B. Reaction Mechanism Breakdown (Experimental vs. Calculated):
The study decomposed the total yield into three channels:

1. Complete Fusion-Fission (FF): Dominant for the Be target (73.5% of yield).
2. Fast-Fission (FA): Dominant for the C target (66.8% of yield).
3. Incomplete Fusion (IF): Minor contribution for both.

• Experimental Ratio (FF / (FF+FA)):
  • Be Target: 85.4%
  • C Target: 28.6%
• LISE++ Prediction Ratio:
  • Be Target: 75.5%
  • C Target: 41.1%
• Interpretation: The shift from FF dominance (Be) to FA dominance (C) is driven by the angular momentum. The heavier C target allows for higher angular momentum collisions where the fission barrier vanishes, leading to fast-fission. The Be target, being lighter, favors lower angular momentum and complete fusion.

C. High-Z Production:
The study confirmed that the Complete Fusion-Fission mechanism is primarily responsible for producing fragments with $Z > 60$. This is crucial for accessing the most neutron-rich isotopes in the heavy element region.

5. Significance

• New Production Method: The results establish in-flight fusion-fission in inverse kinematics as a viable and efficient method for generating radioactive beams of neutron-rich isotopes, particularly for elements where traditional spallation or ISOL methods are less effective.
• Mechanism Control: The study demonstrates that by selecting the target material ($^9\text{Be}$ vs. $^{12}\text{C}$), researchers can tune the reaction mechanism to favor either complete fusion (for heavy, neutron-rich fragments) or fast-fission.
• Benchmark for Models: The data serves as a critical benchmark for fission models, highlighting the need to account for angular momentum effects and the transition between fusion-fission and fast-fission regimes.
• Future Applications: The findings support the use of this technique for future facilities (like FRIB) to explore the limits of nuclear stability and study the properties of exotic nuclei.