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Influence of clustering and hadron potentials on the rapidity distribution of protons from the UrQMD model

The Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model supplemented by potentials for both pre-formed hadrons and confined baryons (called UrQMD/M) are used to describe rapidity distributions of both the E895 proton data at AGS energies and the NA49 net proton data at SPS energies. With the help of a coalescence afterburner using only one parameter set of ($R_0$, $P_0$)=(3.8 fm, 0.3 GeV$/$c), both sets of experimental data can be described fairly well except for a small discrepancy seen for the net protons at mid-rapidity from heavy ion collisions (HICs) at high SPS energies. Furthermore, in contrast to the logarithmic dependence with beam energy at SIS energies there are still about 10$\%$ of protons in clusters from central HICs at the beam energy of $80$ GeV$/$nucleon.