We study the influence of the nuclear equation of state (EOS) on collective observables—the directed ($v_1$) and elliptic flow ($v_2$) of nucleons and light clusters—in heavy-ion collisions at gigaelectronvolt energies energies using the parton-hadron-quantum-molecular dynamics (PHQMD) approach. A novel development in this work is the inclusion of a momentum-dependent nucleon potential in the PHQMD in addition to the static, density-dependent Skyrme interaction. This enables three distinct EOS scenarios: two static (“soft” and “hard,” differing in compressibility) and a soft, momentum-dependent EOS calibrated to $pA$ elastic scattering data. In PHQMD, clusters form during the entire heavy-ion collision via nucleon interactions and are identified using the minimum spanning tree (MST) algorithm, including additional deuteron production from hadronic kinetic reactions. We find a strong EOS sensitivity in proton and cluster rapidity and $p_T$ distributions: soft and soft momentum-dependent EOS yield similar results, markedly different from the hard EOS. Softening the EOS reduces proton yields at midrapidity while enhancing light-cluster production. The EOS also affects flow observables differently for nucleons and clusters. For protons, a soft momentum-dependent potential increases slightly the magnitude of $v_1$ and $v_2$ relative to the hard EOS, whereas cluster flows are nearly similar. The soft momentum-dependent EOS provides an overall good agreement with experimental data from HADES and FOPI Collaborations while the soft EOS is not in line with the data. A scaling of $v_2$ with cluster mass number $A$ is observed at midrapidity for low $p_T$, which breaks at higher $p_T$. Finally, we examine the sensitivity of flow observables to deuteron production mechanisms. Deuterons formed via MST clustering exhibit different flow patterns from those produced by coalescence at freeze-out, indicating that flow harmonics may help discriminate between cluster formation scenarios.

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• Cluster models
• Equations of state of nuclear matter
• Nuclear forces
• Nuclear reactions
• Particle & resonance production
• Relativistic heavy-ion collisions
• Monte Carlo methods