Abstract
The formation of deuterons in heavy-ion collisions at relativistic energies is investigated by employing two recently advanced models---the minimum spanning tree (MST) method and the coalescence model---by embedding them in the parton-hadron quantum molecular dynamics (PHQMD) and the ultrarelativistic quantum molecular dynamics (UrQMD) transport approaches. While the coalescence mechanism combines nucleons into deuterons at the kinetic freeze-out hypersurface, the MST identifies the clusters during the different stages of time evolution. We find that both clustering procedures give very similar results for the deuteron observables in the UrQMD as well as in the PHQMD environment. Moreover, the results agree well with the experimental data on deuteron production in Pb$+$Pb collisions at $\sqrt{{s}_{NN}}=8.8$ GeV (selected for the comparison of the methods and models in this study). A detailed investigation shows that the coordinate space distribution of the produced deuterons differs from that of the free nucleons and other hadrons. Thus, deuterons are not destroyed by additional rescattering.
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