UrQMD Model Reveals Neutron Origin of Stopped Protons

A new microscopic study using the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model has quantified the origin of protons stopped in low-energy heavy-ion collisions. The research, focused on minimum-bias gold-on-gold (Au+Au) collisions across a wide energy range, reveals that many protons appearing at mid-rapidity come from initial neutrons through a process called isospin conversion.

Baryon stopping is a key process in these collisions, where protons from the colliding nuclei are halted in the central region. Quantifying this stopping provides important information about the properties of the nuclear medium, such as net-baryon density. While experiments measure the final net-proton rapidity spectra, they cannot directly access the microscopic origins of these particles. Transport models like UrQMD fill this gap by allowing researchers to track the interaction history of every proton in the simulation.

Classifying Proton Origins

The study classified final-state protons based on their origin within the UrQMD simulation. The analysis covered collisions at beam energies from √s_NN = 2.4 to 17.3 GeV, corresponding to laboratory energies of 1.23A to 158A GeV. By tracing particle histories, the researchers could distinguish between protons that started as protons and those that originated from neutrons.

The results were striking. A significant fraction of the transported protons found at mid-rapidity did not come from the initial protons in the colliding nuclei. Instead, they originated from initial neutrons. These are termed isospin-converted protons. The research quantified the contribution of these converted protons as a function of both collision energy and centrality.

Flow and Isospin Comparisons

The anisotropic flow coefficients for the different categories of protons were estimated and compared with available experimental measurements. Also, the team performed a comparison between the ratio of negative to positive pions (π-/π+) and the rate of isospin conversion observed in the model.

This isospin conversion rate was then compared with the α parameters from the Kitazawa-Asakawa formalism, a theoretical framework. The comparison revealed a significant deviation from the assumption of chemical equilibrium, where α_N equals α_π, at collision energies below approximately √s_NN = 10 GeV. This finding suggests that simple equilibrium assumptions do not hold in this energy regime.

Coupling Stopping and Transparency

A key finding links the saturation of the isospin conversion rate with the onset of nuclear transparency. The study demonstrates that isospin randomization-the process behind the conversion-and baryon stopping are coupled phenomena within the hadronic transport description. This coupling persists across the energy range relevant for major facilities like the Nuclotron-based Ion Collider fAcility (NICA) and the Facility for Antiproton and Ion Research (FAIR).

The work, authored by Sudhir Pandurang Rode and submitted to the arXiv preprint server, provides a detailed microscopic picture that complements experimental efforts. It shows the complex interplay of particle identity and transport in creating the dense nuclear matter observed in heavy-ion collisions.