Every high energy nuclear collision leaves behind a trail of clues about the structure of atomic nuclei. Deciphering those clues, however, depends on the accuracy of the underlying theory.

Physicists at Osaka Metropolitan University have now performed a full calculation within Glauber theory, a cornerstone framework for describing high-energy nuclear collisions. By overcoming a computational challenge that has long forced researchers to rely on approximations to reduce computational demands, the team has shown that its full calculation can accurately reproduce experimental data and provide a reliable framework for predicting the outcomes of future experiments involving ordinary and exotic nuclei.

Atomic nuclei are too small, and many too short-lived, to observe directly, even with the most powerful microscopes. So, to probe nucleus structure, physicists accelerate one nucleus toward another at high speed and analyze how the particles scatter after the collision. By comparing the observed scattering pattern with theoretical models, scientists can infer otherwise invisible properties, such as the nucleus’ size and density.

Accurately modeling these collisions, however, is far from simple.

“The concept known as Glauber theory has long been used to study what happens when atomic nuclei collide at high speeds,” Wataru Horiuchi, Associate Professor at Osaka Metropolitan University’s Graduate School of Science, and lead author of the study said.

“However, because the calculations are highly complex, the theory has often been studied using approximations.”

Glauber theory describes a nuclear collision as a series of interactions between the individual protons and neutrons in the colliding nuclei. In principle, all possible multiple-scattering processes must be included in the calculation; however, the sheer number of possible interactions makes the full calculation challenging.

To overcome this obstacle, the team combined realistic quantum-mechanical models of nuclear structure with large-scale Monte Carlo calculations. For collisions involving protons, helium nuclei, and carbon nuclei, their approach accounted for all orders of the multiple-scattering processes predicted by Glauber theory, rather than relying on the simplifying approximations traditionally used to make the calculations manageable.

The results closely matched available experimental data, including recent high-precision measurements of carbon-12 collisions. This agreement demonstrates that the full Glauber calculation can accurately describe the observed behavior of high-energy nuclear collisions.

However, this raised another question: is it always necessary to include every possible scattering interaction in the calculation?

Their precise calculation provided a benchmark for finding out an answer to this conundrum. Using a mathematical technique called cumulant expansion, the researchers showed the first two terms of a mathematical expansion, known as cumulants, are sufficient to closely approximate the full calculation. This suggests that future analyses could ensure computational efficiency without sacrificing reliability.

By demonstrating that all-order Glauber-theory calculations are both feasible and highly accurate, the study offers a more reliable theoretical benchmark for interpreting high-energy nuclear collisions.

“We successfully performed an exact calculation based on Glauber theory,” Horiuchi said. “This approach not only provides a good explanation for existing experimental results but also enables us to predict the outcomes of future experiments.”

The study was published in Physical Review Letters on May 18 and Physical Review C on June 1. Physical Review Letters provides a brief overview of the main findings, while Physical Review C contains the complete paper with additional details, results and analysis.

###

About OMU
Established in Osaka as one of the largest public universities in Japan, Osaka Metropolitan University is committed to shaping the future of society through the “Convergence of Knowledge” and the promotion of world-class research. For more research news, visit https://www.omu.ac.jp/en/ and follow us on social media: X, Instagram, LinkedIn.