Excitation function for natMo(p,x) reactions with covariance analysis

This study presents high-precision excitation functions for proton-induced reactions on natural molybdenum targets in the 13–22 MeV energy range, resolving previous data discrepancies for specific technetium isotopes and providing a comprehensive covariance analysis for medical isotope production.

The Gist

Imagine you are a master chef trying to perfect a recipe for a very special dish: medical isotopes. These are tiny, radioactive ingredients used by doctors to take pictures of our insides (like finding a tumor or checking a heart) or to treat diseases.

The main ingredient in this recipe is Molybdenum (a metal), and the "cooking method" involves shooting tiny, fast-moving particles called protons at it. When the protons hit the molybdenum, they smash into the atoms and break them apart or rearrange them, creating new, useful radioactive elements.

This paper is essentially a new, ultra-precise cookbook written by a team of scientists from India. Here is the story of what they did, explained simply:

1. The Problem: Old Recipes Were Messy

For a long time, scientists had "recipes" (data) for how to make these medical isotopes. But the old recipes were a bit sloppy.

• The "Thick Target" Issue: Imagine trying to measure how fast a car is going, but you are looking at it through a thick, foggy window. The old experiments used thick chunks of metal, which made it hard to know exactly how much energy the protons had when they hit the target.
• The "Double-Counting" Issue: Sometimes, when you make one type of isotope, it accidentally turns into another type while you are measuring it. The old recipes often didn't account for this, leading to confusing numbers.
• The "Guesswork" on Errors: If you bake a cake and it's slightly too sweet, you need to know why and how much so you can fix it next time. Old data didn't always tell you how the errors in one measurement were connected to errors in another.

2. The Solution: A Precision Kitchen

The scientists in this paper decided to rewrite the recipe with much better tools.

• Thin Slices, Clear Vision: Instead of thick chunks, they used ultra-thin foils of Molybdenum (like slicing a piece of paper). This let the protons pass through cleanly, so the scientists knew exactly how much energy they had. It's like looking through a clean window instead of foggy glass.
• The "Time-Travel" Math: They realized that some isotopes are like "parents" that turn into "children" (other isotopes) over time. They used complex math to separate the "parent" from the "child" so they could measure exactly how much of each was made directly.
• The "Covariance" Map: This is the paper's biggest innovation. Imagine you are baking a cake. If you measure the flour wrong, your sugar measurement might also be off because you used the same scale. This paper draws a map of connections (called a covariance analysis) showing exactly how a mistake in one part of the experiment affects the rest. This helps other scientists know exactly how much they can trust the numbers.

3. The Results: What Did They Cook Up?

They tested their method across a range of energies (from 12 to 22 MeV) and found the exact "sweet spots" for making several important medical ingredients:

• The Star Player (Technetium-99m): This is the most famous medical isotope, used in about 80% of all nuclear medicine scans. The team confirmed the best way to make it and fixed some confusion in the old data.
• The New Stars (Zirconium-89 & Technetium-94): They found better ways to make these, which are becoming popular for advanced PET scans (a high-tech version of an X-ray).
• The "Parent" (Molybdenum-99): This is the "mother" of Technetium-99m. Hospitals use it to generate the isotope they need on demand. The paper provides a cleaner recipe for making this parent, which is crucial because the old way of making it relied on nuclear reactors (which are becoming harder to use due to safety rules).

4. Why Does This Matter?

Think of this paper as upgrading the GPS system for nuclear scientists.

• For Doctors: It means they can produce medical isotopes more efficiently and safely, ensuring hospitals have the "fuel" they need to diagnose cancer and heart disease.
• For Scientists: It provides a "gold standard" to test their computer models against. If a computer simulation doesn't match this new, high-precision data, the scientists know they need to fix their code.
• For the Future: By understanding exactly how these reactions work, we can move away from dangerous nuclear reactors and use safer, cleaner particle accelerators to make the medicines that save lives.

In a nutshell: This paper took a messy, foggy recipe for making life-saving medical isotopes and turned it into a crystal-clear, step-by-step guide with a detailed error-checking system, ensuring that doctors can rely on these tools to heal patients with greater confidence.

Technical Summary

Here is a detailed technical summary of the paper "Excitation function for natMo(p,x) reactions with covariance analysis":

1. Problem Statement

The production of medical radioisotopes via proton-induced reactions on natural Molybdenum ($nat$Mo) is critical for nuclear medicine, particularly for generating Technetium-99m ($^{99m}$Tc), which accounts for ~80% of nuclear medicine procedures. However, existing nuclear data for $nat$Mo(p,x) reactions suffer from several limitations:

• Discrepancies: Significant inconsistencies exist between datasets in the EXFOR library.
• Low Precision: Much of the existing data relies on thick-target irradiations, leading to large spreads in incident beam energy and high uncertainties.
• Isomeric Confusion: Many studies report cumulative yields (ground state + isomer) without properly deconvoluting the contributions of short-lived isomers (e.g., $^{93m}$Tc feeding $^{93g}$Tc) or parent decay chains (e.g., $^{99}$Mo feeding $^{99m}$Tc).
• Lack of Covariance Data: Previous measurements rarely include covariance matrices or correlation coefficients, making it difficult to perform accurate uncertainty propagation for model benchmarking or interpolation.

2. Methodology

The study was conducted at the BARC-TIFR Pelletron Linac Facility in Mumbai using the activation technique followed by off-line $\gamma$-ray spectroscopy.

• Experimental Setup:
  • Target: High-purity ($\approx$99.9%) natural molybdenum foils with thin thicknesses (7.79 – 10.34 mg/cm$^2$) to minimize energy straggling.
  • Beam: Proton beams with energies ranging from 12 to 22 MeV.
  • Stacking: Targets were stacked with Zr and Cu foils for beam monitoring and energy degradation calculations.
  • Detection: Three HPGe detectors (38% and 30% relative efficiency) were used for $\gamma$-ray spectroscopy. Absolute efficiency was calibrated using a $^{152}$Eu source and fitted with an exponential function.
• Data Analysis & Corrections:
  • Cross-Section Calculation: Calculated using standard activation equations, accounting for beam current fluctuations by integrating charge over short time intervals.
  • Isomeric Separation: A rigorous step-by-step decay chain analysis was performed to separate direct ground-state production from isomeric feeding.
    • Example: For $^{93}$Tc, the contribution of $^{93m}$Tc decay to the $^{93g}$Tc yield was subtracted to isolate the direct $^{93g}$Tc cross-section.
    • Example: For $^{99m}$Tc, the contribution from the $\beta^-$ decay of parent $^{99}$Mo was subtracted from the total 140.5 keV peak yield.
  • Covariance Analysis: A comprehensive uncertainty analysis was performed. The authors calculated correlation coefficients between cross-sections at different energies, accounting for shared systematic uncertainties (e.g., detector efficiency, branching ratios, target thickness).

3. Key Contributions

• High-Precision Excitation Functions: Measured cross-sections for various isotopes ($^{89g+m}$Zr, $^{93g+m}$Tc, $^{93m}$Tc, $^{93g}$Tc, $^{94g}$Tc, $^{95g+m}$Tc, $^{96g+m}$Tc, $^{99m}$Tc, and $^{99}$Mo) with significantly reduced uncertainties compared to previous literature.
• First Covariance Data for Mo(p,x): This is the first study to provide full covariance matrices and correlation coefficients for Molybdenum proton-induced reactions, enabling rigorous error propagation in nuclear data evaluations.
• Deconvolution of Isomers: Successfully extracted pure ground-state cross-sections (e.g., $^{93g}$Tc) by mathematically removing isomeric contributions, resolving ambiguities in previous "cumulative" yield reports.
• Resolution of Discrepancies: The new data clarifies conflicting trends in the EXFOR database, particularly for $^{89g+m}$Zr and $^{93g}$Tc.

4. Key Results

• $^{89g+m}$Zr: The excitation function shows an increasing trend with energy. The new data resolves large discrepancies found in previous thick-target studies (e.g., Khandaker et al.), showing better agreement with Tarkanyi et al.
• $^{93}$Tc System:
  • $^{93g+m}$Tc: Cross-sections rise from 12 to 18 MeV and plateau.
  • $^{93m}$Tc: Measured independently; values agree with literature but with higher precision.
  • $^{93g}$Tc (Direct): Extracted by subtracting isomer feed. The data shows a rapid rise up to 18 MeV. The study highlights that previous data often failed to correct for isomer decay, leading to overestimation of direct production.
• $^{94g}$Tc, $^{95g+m}$Tc, $^{96g+m}$Tc: The measured cross-sections generally agree with existing trends but with much smaller error bars.
  • $^{95g+m}$Tc is nearly constant up to 20 MeV.
  • $^{96g+m}$Tc decreases from 12 to 16 MeV and then stabilizes.
• $^{99}$Mo and $^{99m}$Tc:
  • $^{99}$Mo production is consistent with prior studies.
  • $^{99m}$Tc production (derived from both direct reaction and $^{99}$Mo decay) shows a constant trend up to 18 MeV followed by a rapid decrease. The study notes that absolute values are higher than some previous reports at energies $<14$ MeV.
• Uncertainty Reduction: The use of thin targets and precise beam monitoring reduced total uncertainties to the range of 2–5% for most major isotopes, compared to often >10% in older datasets.

5. Significance

• Medical Isotope Production: The high-precision data is vital for optimizing the accelerator-based production of $^{99m}$Tc (via $^{99}$Mo) and exploring alternatives like $^{96}$Tc and $^{95}$Tc for theranostics. It supports the transition away from reactor-based HEU fission methods.
• Nuclear Data Evaluation: The inclusion of covariance matrices allows theoretical models (TALYS, EMPIRE, ALICE) to be benchmarked more accurately. It prevents incorrect uncertainty propagation when data is interpolated or extrapolated for energy ranges not directly measured.
• Database Improvement: The results provide a robust benchmark to update the EXFOR database, replacing scattered and inconsistent older data with a coherent, high-precision dataset.
• Broader Impact: Beyond medicine, the data supports nuclear technology applications involving Molybdenum, such as advanced fuel element structures in liquid-metal cooled reactors, where precise reaction cross-sections are needed for safety margins and reactivity feedback.