Measurement of Proton-Induced Reactions on Lanthanum from 55--200 MeV by Stacked-Foil Activation

This study addresses discrepancies in existing data by measuring proton-induced reaction cross sections on lanthanum across a 55–200 MeV energy range using stacked-foil activation, and subsequently improves the predictive accuracy of nuclear reaction models like TALYS through parameter adjustments to better support the production of the therapeutic radionuclide analogue $^{134}$Ce.

The Gist

The Big Picture: Hunting for a "Medical Treasure"

Imagine you are a doctor trying to treat a very aggressive cancer. You have a powerful weapon: a radioactive atom called Actinium-225. It's like a tiny, precision-guided missile that shoots alpha particles (tiny bullets) directly at cancer cells, destroying them while sparing healthy tissue.

However, there's a problem. You can't see where the missile is going once you inject it into the patient. Actinium doesn't glow or emit the signals needed for a PET scan (the kind of camera doctors use to see inside the body).

The Solution: You need a "spy" or a "stand-in" that looks and acts exactly like Actinium but does glow so doctors can track it. The scientists in this paper found that Cerium-134 is the perfect spy. It's a chemical twin to Actinium, but it emits a signal doctors can see.

The Mission: Making the Spy

To get enough Cerium-134 to use as a spy, you have to make it in a giant particle accelerator. Think of the accelerator as a massive cannon that shoots protons (tiny, fast particles) at a target.

• The Target: A stack of thin sheets made of Lanthanum (a rare metal).
• The Cannon: A beam of protons shot at speeds ranging from 55 to 200 million electron volts (a fancy way of saying "very, very fast").

When the protons hit the Lanthanum, they smash into the atoms, breaking them apart and rearranging them into new elements. Sometimes, this creates the Cerium-134 we want. But often, it creates a messy pile of other radioactive junk (impurities) that we don't want.

The Problem: The Map Was Missing

The scientists knew how to make Cerium-134 at lower speeds, but they didn't have a good map for the high-speed zone (above 100 MeV).

• The Old Map: Previous data was like a sketchy, hand-drawn map with huge gaps. It said, "Maybe you get some Cerium here, maybe not."
• The Discrepancy: Different scientists had drawn different maps, and they didn't agree.
• The Risk: If you don't know the map, you might build a factory that produces mostly junk instead of the medicine you need.

The Experiment: The "Stacked-Foil" Sandwich

To fix the map, the team (from Los Alamos, Brookhaven, and Berkeley) built a special experiment.

Imagine you have a stack of 17 thin Lanthanum sandwiches. You shoot a super-fast proton beam through the whole stack at once.

1. The First Sandwich: The protons hit it at full speed (200 MeV). They smash hard, creating a specific mix of new atoms.
2. The Middle Sandwiches: By the time the protons reach the middle, they've lost some energy. They hit these atoms a bit softer, creating a different mix.
3. The Last Sandwich: The protons are now tired and slow (around 55 MeV). They hit gently, creating yet another mix.

By measuring the radioactivity in each individual slice of the sandwich, the scientists could figure out exactly what happens at every single speed. It's like tasting a soup at every stage of the cooking process to see exactly when the flavor changes.

The Result: They measured 30 different types of radioactive products created in the Lanthanum. This is the most detailed map of this process ever created, especially for the high-speed zone (100–200 MeV).

The Surprise: The "Ghost" Signal

When they looked at the data, they found something shocking.

• The Prediction: Computer models (like a video game physics engine) predicted that at high speeds, the production of Cerium-134 would drop off. They thought the "compound peak" (the main production zone) would be lower.
• The Reality: The actual production was much higher than the computers predicted. It was like the computer said, "You'll get 10 cookies," but the oven actually baked 50.

This is huge news for medical manufacturers. It means that if you use high-speed proton beams, you might be able to make way more of the medicine than anyone thought possible.

The Fix: Tuning the Computer Models

The scientists then tried to fix the computer models (TALYS, EMPIRE, ALICE) to match their new data.

• The Analogy: Imagine you are tuning a radio. The default setting (the "factory preset") is full of static and doesn't match the station you want.
• The Adjustment: The team tweaked the "knobs" on the computer code. They adjusted how the code handles the "pre-collision" chaos (when particles are bouncing around before settling down) and how they interact with the nucleus.
• The Outcome: After tuning, the computer models finally matched the real-world data much better. They could now predict how much medicine would be made at different speeds with much higher accuracy.

Why This Matters

1. Better Medicine: We can now produce the "spy" (Cerium-134) more efficiently, which helps doctors treat cancer with Actinium-225 more safely.
2. Better Physics: We learned that our current computer models for high-energy physics aren't perfect. They need to be updated to account for the messy, chaotic nature of high-speed particle collisions.
3. New Discoveries: They found the first-ever measurements for some very rare reactions (like the (p,10n) reaction), filling in blanks on the map of nuclear physics that no one had seen before.

In short: The scientists shot protons at a stack of metal sheets to create a detailed "recipe book" for making a life-saving medical isotope. They found the old recipes were wrong, the real yield is much higher than expected, and they've updated the computer software so we can cook up this medicine more efficiently in the future.

Technical Summary

1. Problem Statement

The production of Cerium-134 ($^{134}\text{Ce}$) is critical for nuclear medicine as a chemical analogue to the therapeutic radionuclide Actinium-225 ($^{225}\text{Ac}$). $^{134}\text{Ce}$ serves as an in vivo generator for the positron-emitter $^{134}\text{La}$, enabling Positron Emission Tomography (PET) imaging to track the biodistribution of $^{225}\text{Ac}$-labeled drugs.

The primary production route for $^{134}\text{Ce}$ is the proton bombardment of natural Lanthanum ($^{139}\text{La}$) via the $(p,6n)$ reaction. However, existing cross-section data for this reaction in the 50–100 MeV energy range suffer from:

• Discrepancies: Conflicting data points between different literature sources.
• Gaps: A lack of data above 70 MeV, where the cross-section peak is expected, and no data above 100 MeV.
• Model Deficiencies: Default nuclear reaction models (TALYS, EMPIRE, ALICE) and libraries (TENDL-2023) have historically exhibited poor predictive capability in this energy range, particularly regarding pre-equilibrium reaction mechanisms and multi-particle emission channels.

2. Methodology

The authors conducted a comprehensive experimental campaign using the stacked-foil activation technique to measure proton-induced reaction cross-sections on $^{139}\text{La}$ across a continuous energy range of 55–200 MeV.

• Experimental Setup:

  • Two Irradiations:
    1. LANL IPF: 100 MeV incident proton beam.
    2. BNL BLIP: 200 MeV incident proton beam.
  • Targets: 17 natural Lanthanum foils (99.919% $^{139}\text{La}$) per stack, paired with monitor foils (natural Cu, Ti for LANL; natural Cu, Al for BNL) to track beam current and energy degradation.
  • Beam Degradation: Aluminum and Copper degraders were placed between foil sets to create a stepped energy profile, allowing the measurement of cross-sections at discrete energy points within the stack.
  • Safety: Targets were sealed in Kapton tape within acrylic frames and irradiated in leak-tight boxes to prevent oxidation and contamination.

• Data Acquisition & Analysis:

  • Gamma Spectrometry: High-Purity Germanium (HPGe) detectors were used to measure induced radioactivity.
  • Software: The open-source CURIE Python library was utilized for isotope identification, peak fitting, and solving Bateman equations for decay chains.
  • Beam Current Determination: Instead of Faraday cups (unavailable due to facility layout), beam currents were calculated using monitor reactions (e.g., $^{27}\text{Al}(p,x)^{22}\text{Na}$, $^{nat}\text{Cu}(p,x)^{58}\text{Co}$) with IAEA-recommended cross-sections.
  • Energy Calibration: A "variance minimization" procedure was applied to refine the proton energy distribution within the stack by adjusting foil areal densities and incident energy to minimize $\chi^2$ against monitor data.

• Modeling & Optimization:

  • Measured data were compared against default predictions from TALYS-2.0, EMPIRE-3.2.3, ALICE-20, and TENDL-2023.
  • A parameter adjustment procedure was performed on TALYS-2.0. This involved sequentially optimizing:
    1. Base model selection (level density, gamma strength).
    2. Optical model parameters (radius and diffuseness adjustments).
    3. Pre-equilibrium exciton model parameters (specifically $M_2$ constants and limits).

3. Key Contributions

• First High-Energy Data: This work provides the first measurements of proton-induced reactions on Lanthanum above 100 MeV.
• Extensive Dataset: The study measured 30 distinct reaction channels on $^{139}\text{La}$ (covering ~55% of the total non-elastic cross-section) and 24 products in monitor foils.
• Exclusive $(p,10n)$ Measurement: The paper reports the first exclusive excitation function for the $^{139}\text{La}(p,10n)^{130}\text{Ce}$ reaction in this energy range.
• Model Optimization: The authors developed a refined parameter set for TALYS-2.0 that significantly improves the prediction of high-energy proton-induced reactions on Lanthanum, addressing deficiencies in pre-equilibrium modeling.

4. Key Results

• $^{134}\text{Ce}$ Production:
  • The measured cross-section for $^{139}\text{La}(p,6n)^{134}\text{Ce}$ was found to be significantly higher than theoretical predictions in the 100–200 MeV range.
  • This implies that medical isotope production facilities operating at higher energies (e.g., >100 MeV) may achieve higher yields than previously estimated.
• Model Performance:
  • Default Models: All default codes (TALYS, EMPIRE, ALICE) struggled to predict the centroid energy of the "compound peak" and the magnitude of the pre-equilibrium tail, often under-predicting cross-sections by factors of 2–5 at high energies.
  • ALICE Limitations: ALICE consistently failed to predict isomeric ratios (e.g., for $^{133}\text{Ce}$ and $^{137}\text{Ce}$), likely due to poor angular momentum modeling.
  • TALYS Optimization: The adjusted TALYS-2.0 model showed a dramatic improvement in the "training" dataset (weighted $\chi^2_\nu$ reduced from 1980 to 48.1). While the fit to the "validation" dataset (cumulative channels) was less perfect, it still outperformed default predictions and the previous Fox et al. parameter set.
• Specific Channels:
  • $^{139}\text{La}(p,n)^{139}\text{Ce}$: Measured cross-sections were higher than predicted at high energies. This is critical as $^{139}\text{Ce}$ is a long-lived contaminant that limits the radiopurity of $^{134}\text{Ce}$.
  • $^{130}\text{Ce}$: The $(p,10n)$ channel showed almost no compound peak, suggesting the compound mechanism is significantly damped in high-multiplicity neutron emission channels.

5. Significance

• Medical Isotope Production: The finding that $^{134}\text{Ce}$ yields are higher than predicted at energies >100 MeV has direct implications for the design and operation of cyclotrons and linacs intended for therapeutic radionuclide production. It suggests that higher-energy beams may be more efficient for this specific application.
• Nuclear Data Evaluation: The study highlights the inadequacy of current default nuclear reaction models for high-energy charged particle interactions. The provided parameter adjustments for TALYS-2.0 offer a more reliable tool for predicting reaction outcomes in the 55–200 MeV range, reducing reliance on uncertain extrapolations.
• Methodological Benchmark: The work establishes a robust framework for stacked-foil activation experiments and parameter optimization, serving as a reference for future evaluations of proton-induced reactions on heavy nuclei.

In conclusion, this paper resolves long-standing discrepancies in Lanthanum cross-section data, provides the first high-energy measurements for this system, and delivers a physically consistent, optimized nuclear reaction model that improves the reliability of predictions for medical isotope production.