⚛️ nuclear theory

Sensitivity of $^{107,109}$ Ag( $\alpha$ ,xn) cross sections to statistical-model inputs

This study systematically analyzes the sensitivity of $^{107,109}$ Ag( $\alpha$ ,xn) reaction cross sections to statistical-model inputs using TALYS 2.0, revealing that the relative importance of level-density models, pre-equilibrium mechanisms, and $\alpha$ -optical potentials varies significantly across different reaction channels, with no single parameter combination optimally describing all investigated processes.

Original authors: Arunabha Saha

Published 2026-07-28

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Arunabha Saha

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to bake the perfect cake, but instead of flour and sugar, your ingredients are the invisible building blocks of the universe: protons, neutrons, and the mysterious forces that hold them together. This is the world of nuclear physics, a field where scientists act like cosmic chefs, mixing different atomic "flavors" to create new elements. Sometimes, they want to cook up specific radioactive isotopes—tiny, unstable versions of elements—that are incredibly useful for medicine, helping doctors see inside the human body or treat diseases. To do this, they smash particles together at high speeds, hoping to trigger a reaction that creates the exact ingredient they need.

However, predicting exactly how these atomic collisions will turn out is like trying to guess the weather a month in advance, but with even more variables. Scientists use powerful computer programs to simulate these collisions, but these programs rely on a "recipe" made of several different mathematical models. Think of these models as the rules of the game: one set of rules describes how crowded the atomic kitchen is (how many energy states are available), another describes how the incoming particle bumps into the target (like a ball hitting a wall), and a third describes what happens if the collision is messy and chaotic before settling down. The big question is: which combination of rules gives the most accurate prediction? If the recipe is wrong, the "cake" (the medical isotope) might not form, or it might come out with the wrong ingredients mixed in.

In this study, a researcher named Arunabha Saha decided to test every possible combination of these rules for a specific cooking scenario: smashing alpha particles (tiny helium nuclei) into silver atoms to create useful indium isotopes for medical use. The goal was to see which "recipe" worked best for different outcomes. The study didn't just guess; it ran a massive simulation, testing 192 different combinations of these mathematical models against real-world data collected from previous experiments.

The results revealed that there is no single "magic recipe" that works for every situation. Instead, the best combination of rules depends entirely on what exactly is happening during the collision. For reactions where three neutrons are kicked out of the silver atom, the most important rule was the one describing how crowded the atomic kitchen is (the level density model). It was like saying, "To make this specific dish, you just need to know exactly how many people are in the room."

However, for reactions where only one or two neutrons are kicked out, the story changed completely. In these cases, the rules describing the messy, chaotic part of the collision (the pre-equilibrium mechanism) became the most important factor, while the "crowd size" rules mattered very little. It's as if making a different dish required you to ignore the number of people in the room and focus entirely on how fast the ingredients were thrown together. The study found that for some reactions, the way the particles bumped into each other (the optical model) was a close second in importance, while for others, it barely mattered at all.

The researcher also compared their best simulations to a famous, pre-made cookbook called TENDL-2023. They found that while their best simulations were much closer to the real experimental data than the default settings, they still couldn't perfectly match every single measurement. This suggests that while the current rules are good, they aren't perfect yet, and the "kitchen" of silver atoms is a bit more complex than our current models can fully describe. Ultimately, the paper concludes that to get the best results, scientists can't just pick one set of rules and stick with it; they must choose the specific rules that fit the specific reaction they are trying to cook up.

Technical Summary: Sensitivity of $^{107,109}\text{Ag}(\alpha,xn)$ Cross Sections to Statistical-Model Inputs

Problem Statement
The production of medically relevant indium radionuclides ( $^{108m,109g,110m,110g,111g}\text{In}$ ) via $\alpha$ -induced reactions on silver isotopes ( $^{107}\text{Ag}$ and $^{109}\text{Ag}$ ) is critical for nuclear medicine applications, including PET imaging and targeted therapy. While the $\alpha$ -on-Ag pathway offers advantages in radionuclidic purity and target stability, accurate prediction of reaction cross-sections remains challenging. Theoretical models, such as TALYS, rely on statistical inputs including level density models (LDM), $\alpha$ -optical model potentials ( $\alpha$ OMP), and pre-equilibrium (PE) mechanisms. However, the relative importance of these inputs often varies by reaction channel, and it is unclear which combinations of default model parameters best reproduce experimental data for the $A \approx 100$ mass region without local parameter optimization. This study addresses the need to systematically evaluate the sensitivity of calculated cross-sections to these statistical-model ingredients to identify optimal combinations for specific reaction channels.

Methodology
The study employed the TALYS-2.0 code to simulate excitation functions for five specific reaction channels:

$^{107}\text{Ag}(\alpha,3n)^{108m}\text{In}$
$^{107}\text{Ag}(\alpha,2n)^{109g}\text{In}$
$^{107}\text{Ag}(\alpha,n)^{110m}\text{In}$
$^{109}\text{Ag}(\alpha,3n)^{110g}\text{In}$
$^{109}\text{Ag}(\alpha,2n)^{111g}\text{In}$

A total of 192 distinct model combinations were generated by systematically varying three key components:

Level Density Models (LDM): Six models were tested, including three phenomenological (Constant Temperature Fermi Gas, Back-shifted Fermi Gas, Generalized Superfluid) and three microscopic (Skyrme-HFB, Gogny-HFB, Temperature-dependent Gogny-HFB) approaches.
$\alpha$ -Optical Model Potentials ( $\alpha$ OMP): Eight different potentials were utilized, ranging from folding approaches (Watanabe) to phenomenological and dispersive models (McFadden-Satchler, Demetriou, Avrigeanu, Nolte).
Pre-equilibrium (PE) Models: Four formalisms were evaluated, including various exciton models (analytical and numerical transition rates) and multi-step direct/compound models.

The theoretical cross-sections were compared against experimental data compiled from the EXFOR library. The goodness-of-fit was quantified using the reduced chi-square ( $\chi^2_\nu$ ) metric. To handle datasets with zero reported uncertainties (specifically from Fukushima et al.), a minimum relative uncertainty floor of 5% was assigned, with a robustness check performed using a 10% floor. The analysis was conducted in a predictive mode without adjusting model parameters to fit the data, distinguishing this work from evaluated libraries like TENDL-2023, which utilize optimized parameters.

Key Contributions and Results
The systematic evaluation of the 192 combinations revealed pronounced channel-dependent sensitivities, demonstrating that no single parameter set optimally describes all investigated reactions.

Dominance of Level Density Models (LDM): The multi-neutron emission channels, $^{107}\text{Ag}(\alpha,3n)^{108m}\text{In}$ and $^{109}\text{Ag}(\alpha,3n)^{110g}\text{In}$ , were found to be primarily governed by the LDM. Sensitivity analysis indicated that LDM contributions accounted for approximately 85–88% of the variance in $\chi^2$ . These reactions are dominated by compound-nucleus formation and statistical decay, showing reduced sensitivity to the fine details of the optical potential or pre-equilibrium mechanisms.
Balanced Sensitivity: The $^{107}\text{Ag}(\alpha,2n)^{109g}\text{In}$ reaction exhibited nearly equal sensitivities to the LDM (~~43%) and the pre-equilibrium mechanism (~~46%), suggesting that both compound-nucleus decay and pre-equilibrium emission play significant roles.
Dominance of Pre-equilibrium (PE) Mechanisms: In contrast, the $^{107}\text{Ag}(\alpha,n)^{110m}\text{In}$ and $^{109}\text{Ag}(\alpha,2n)^{111g}\text{In}$ reactions were dominated by the PE mechanism (~63% sensitivity). For these channels, the $\alpha$ OMP provided a secondary contribution, while the LDM contributed minimally. This indicates enhanced importance of direct reaction dynamics in channels with fewer emitted neutrons.
Model Performance: While specific combinations (e.g., LDM6 + $\alpha$ OMP1 + PE3 for $^{107}\text{Ag}(\alpha,3n)$ ) yielded the lowest $\chi^2$ values, none of the 192 combinations quantitatively reproduced the experimental excitation functions across the entire energy range. The study noted that discrepancies between the default TALYS-2.0 results and the TENDL-2023 evaluated library arise because TENDL employs locally optimized parameters, whereas this study used fixed, predefined model combinations.
Robustness: The sensitivity conclusions remained robust even when the uncertainty floor for data points lacking reported errors was increased from 5% to 10%.

Significance and Claims
The paper claims that the relative importance of statistical-model ingredients is strongly reaction-channel dependent. The findings provide useful guidance for selecting TALYS model ingredients for specific $\alpha$ -induced reactions on silver isotopes, emphasizing that reaction-specific parameter combinations are necessary rather than a universal set.

The authors modestly conclude that the inability of any single combination to perfectly reproduce experimental data suggests that further refinement of nuclear reaction models or parameterizations is required for the $A \approx 100$ mass region. The study highlights that the observed channel-dependent sensitivities serve as comparative indicators within the TALYS-2.0 framework rather than definitive, globally optimized solutions. Future work is suggested to incorporate additional experimental datasets and model-uncertainty quantification to further assess the robustness of the preferred parameter combinations. The paper does not claim to have solved the discrepancies with experimental data but rather maps the sensitivity landscape to inform future model development and data evaluation efforts.

More like this