Heavy-ion collision simulation with high performance computer

This paper reports preliminary work on simulating heavy-ion collisions using the DaeJeon Boltzmann-Uehling-Uhlenbeck (DJBUU) and Sindong Quantum Molecular Dynamics (SQMD) models executed on high-performance computers to address the computational demands of understanding dense nuclear matter.

The Gist

Imagine trying to understand how a car engine works by smashing two cars together at high speed and watching the pieces fly apart. That's essentially what scientists do with heavy-ion collisions. Instead of cars, they smash heavy atomic nuclei (like gold or lead) together to create a tiny, super-hot, super-dense blob of matter. This blob mimics the conditions inside a neutron star—the incredibly dense core of a collapsed star—or the universe just moments after the Big Bang.

This paper is a report from a team of Korean and Canadian scientists who are building a "digital crash test" to predict what happens in these collisions before they actually happen in real life.

Here is the breakdown of their work using simple analogies:

1. The Goal: Why Smash Atoms?

Scientists want to know the "rules of the road" for dense nuclear matter.

• The Real-World Connection: Recently, we detected gravitational waves from two neutron stars crashing into each other. This gave us a new way to look at the universe. But to understand what those waves mean, we need to know how dense matter behaves.
• The Problem: We can't just squeeze a neutron star in a lab. Instead, we use particle accelerators (like the RAON facility being built in Korea) to smash atoms together.
• The Challenge: These collisions are chaotic. To predict the outcome, you can't just use a simple calculator; you need a supercomputer to run millions of simulations.

2. The Tools: Two Different "Crash Simulators"

The team built two different computer programs (models) to simulate these crashes. Think of them as two different video game engines trying to simulate the same car crash.

• Model A: DJBUU (The "Smooth Flow" Engine)

  • How it works: It treats the atomic particles like a flowing fluid or a crowd of people moving through a hallway. It looks at the average behavior of the group.
  • The Math: It uses a complex equation (the BUU equation) to track how the "crowd" moves and bumps into each other.
  • The Upgrade: They recently updated this engine to use a new theory called QMC (Quark-Meson Coupling). Imagine this as upgrading the car's engine from a standard gas motor to a high-tech hybrid. It accounts for the fact that protons and neutrons are made of smaller particles (quarks) that interact in specific ways.

• Model B: SQMD (The "Individual Particle" Engine)

  • How it works: Instead of a smooth crowd, this model treats every single particle as a distinct, fuzzy cloud (a wave packet). It tracks the individual path of every single "cloud" as they bounce off one another.
  • The Difference: It's like watching a game of billiards where you track every single ball's spin and bounce, rather than just looking at the general flow of the balls.

3. The Experiment: The Supercomputer "NURION"

Running these simulations is incredibly expensive in terms of computing power.

• The Scale: To simulate one collision, they might need to track 39,200 particles over 700 tiny time steps.
• The Solution: They used NURION, a massive supercomputer in Korea, to do the heavy lifting. It's like using a fleet of 1,000 laptops working together to solve a puzzle that would take one laptop 100 years to finish.

4. What Did They Find?

The team ran tests to see if their two "engines" agreed with each other.

• The "Good News": When they smashed stable atoms (like Lead and Calcium) together at lower speeds, both models gave very similar results. They agreed on the size of the biggest chunks of debris (fragments) created.

• The "Bad News" (The Twist): When they tried to simulate collisions with unstable, radioactive atoms (like Sodium-20), the two models disagreed significantly.

  • Why? The unstable atoms are like wobbly Jell-O. In the "Smooth Flow" model (DJBUU), the Jell-O held its shape better. In the "Individual Particle" model (SQMD), the Jell-O spread out and got messy.
  • The Lesson: This tells the scientists that their models need to be tweaked to handle "wobbly" atoms better. If they want to study the rare, unstable isotopes that RAON will produce, they need to fix how their models handle these unstable shapes.

• The QMC Discovery: When they used the new "Hybrid Engine" (QMC) in the DJBUU model, they found that the atoms got squeezed denser in the center of the crash than before.

  • Why it matters: If the matter gets squeezed tighter, it might produce more pions (a type of subatomic particle). This is a crucial clue for understanding the "stiffness" of nuclear matter, which helps explain how big neutron stars can get before they collapse.

5. The Big Picture

This paper is essentially a progress report.

• They have built powerful tools (DJBUU and SQMD) running on a supercomputer.
• They have proven the tools work well for standard collisions.
• They have identified where the tools need improvement (handling unstable atoms).
• They have found that new physics (QMC) changes the predicted density of the crash.

In summary: These scientists are building the ultimate "flight simulator" for nuclear physics. By refining their code and using supercomputers, they are preparing to decode the secrets of the universe's densest objects, bridging the gap between smashing atoms in a lab in Korea and listening to the gravitational waves of stars crashing in deep space.

Technical Summary

1. Problem Statement

Understanding the properties of dense nuclear matter is a central challenge in both astrophysics and nuclear physics. Recent multi-messenger astrophysical observations (e.g., gravitational wave event GW170817 and NICER X-ray data) have highlighted the importance of neutron star interiors, where matter exists at densities far exceeding normal nuclear density. To complement these astrophysical observations, terrestrial heavy-ion collision experiments are conducted to probe the Equation of State (EoS) of dense matter.

However, simulating these collisions is computationally intensive due to:

• The complexity of the many-body quantum system.
• The need for microscopic degrees of freedom to track time evolution.
• The requirement for high statistical significance (accumulating many collision events).
• The specific challenge of simulating collisions involving unstable rare isotopes (e.g., $^{20}\text{Na}$), which are difficult to model due to their low stability and sensitivity to initial conditions.

The authors aim to address these challenges by utilizing High-Performance Computing (HPC) resources to run advanced transport models for upcoming experiments at the RAON (Rare isotope Accelerator complex for ON-line experiment) facility in Korea.

2. Methodology

The study employs two distinct transport models, both implemented on the NURION HPC system provided by the Korea Institute of Science and Technology Information (KISTI).

A. Transport Models

1. DaeJeon Boltzmann-Uehling-Uhlenbeck (DJBUU):

   • Framework: Based on the relativistic BUU equation, treating nucleons as an ensemble of test particles propagating in mean fields.
   • Key Features:
     • Uses a polynomial profile for test particles (unlike the Gaussian or triangular profiles in other models), offering finite endpoints and smoother integration.
     • Solves the equations of motion derived from a Relativistic Mean Field (RMF) Lagrangian.
     • Model Variants: The authors compare the original QHD (Quantum Hadrodynamics) implementation against a new implementation using the QMC (Quark-Meson Coupling) model. The QMC model incorporates Bag constant effects and quark-level calculations to determine the effective nucleon mass, allowing for a realistic incompressibility ($K_0$) without needing a specific self-interaction potential $U(\sigma)$.
   • Collisions: Treated semi-classically using Bertsch's prescription with Pauli blocking.

2. Sindong Quantum Molecular Dynamics (SQMD):

   • Framework: A QMD approach dealing with $N$-body dynamics where nucleons are represented as Gaussian wave packets with fixed width.
   • Key Features:
     • Uses a density-dependent Skyrme potential for nuclear interactions.
     • Utilizes a Minimal Spanning Tree (MST) algorithm for fragmentation and clustering analysis.
     • Currently focuses on elastic collisions (inelastic channels like pion production are planned for future versions).

B. Computational Strategy

• Scale: Simulations involve massive grids (e.g., $100 \text{ fm}^3$ boxes), thousands of particles, and thousands of time steps (e.g., 700 steps for 140 fm/c).
• HPC Usage: The NURION system is used to handle the massive parallelization required for accumulating statistically meaningful events, particularly for SQMD which requires more events than DJBUU.

3. Key Contributions

• Implementation of QMC in DJBUU: The paper presents the first integration of the Quark-Meson Coupling (QMC) model into the DJBUU transport code, benchmarking it against the standard QHD model.
• Comparative Analysis of Transport Models: A systematic comparison between the semi-classical BUU approach (DJBUU) and the quantum N-body approach (SQMD) regarding fragment production.
• Investigation of Rare Isotope Stability: A specific study on the stability of the unstable projectile $^{20}\text{Na}$, analyzing how different model initializations affect density evolution and collision outcomes.
• HPC Integration: Demonstrating the feasibility of running complex heavy-ion simulations for the RAON facility using Korean HPC infrastructure.

4. Key Results

A. Model Comparison ($^{208}\text{Pb} + ^{40,48}\text{Ca}$)

• Low Energy (50 AMeV): Both DJBUU and SQMD produce consistent results regarding the size of the Biggest Fragments (BFs).
• High Energy (100 AMeV): Significant model dependence emerges, particularly at small impact parameters. The discrepancies are attributed to differences in the Equation of State (EoS) and the intrinsic differences between 1-body (BUU) and N-body (QMD) dynamics.

B. Rare Isotope Study ($^{20}\text{Na} + ^{208}\text{Pb}$)

• Discrepancy: DJBUU simulations predict BFs approximately 30% larger than those predicted by SQMD.
• Root Cause: Analysis of the "free propagation" (non-collision) of the unstable $^{20}\text{Na}$ projectile revealed divergent stability behaviors:
  • DJBUU: The central density became more compact over time.
  • SQMD: The central density decreased and spread out.
• Implication: The low stability of $^{20}\text{Na}$ makes the simulation results highly sensitive to how the initial density profile is defined and evolved in each model.

C. QMC vs. QHD in DJBUU

• Validation: The QMC implementation in DJBUU produces results similar to the QHD version for standard systems ($^{40}\text{Ca} + ^{40}\text{Ca}$), confirming correct implementation.
• Density Difference: The DJBUU+QMC model yields a higher maximum nucleon density at the collision center compared to DJBUU+QHD.
• Future Impact: This density difference is expected to significantly affect observables sensitive to the EoS, such as pion multiplicity and direct flow, which are currently under analysis.

5. Significance and Future Outlook

• RAON Readiness: The work establishes a robust computational framework for predicting and interpreting data from the upcoming RAON facility, particularly for experiments involving rare isotope beams.
• Astrophysical Connection: By refining the Equation of State through these simulations, the research contributes to a better understanding of dense nuclear matter, directly linking terrestrial experiments with neutron star physics (e.g., tidal deformability).
• Model Refinement: The identified discrepancies highlight the need for further development, such as implementing surface terms in the meson field solver and time-dependent wave packet widths, to improve the stability of unstable nuclei in simulations.
• Observables: The higher densities predicted by the QMC model suggest that future analyses of pion yields and flow observables could provide new constraints on the nuclear EoS.

In conclusion, this paper demonstrates the critical role of HPC in advancing nuclear transport theory, providing a comparative baseline for different theoretical approaches, and paving the way for precise predictions of rare isotope collision experiments.