Dynamical mechanisms for deuteron production at mid-rapidity in relativistic heavy-ion collisions from energies available at the GSI Schwerionensynchrotron to those at the BNL Relativistic Heavy Ion Collider

The understanding of the mechanisms for the production of weakly bound clusters, such as a deuteron d, in heavy-ion reactions at mid-rapidity is presently one of the challenging problems which is also known as the "ice in a fire" puzzle. In this study we investigate the dynamical formation of deuterons within the parton-hadron quantum molecular dynamics (PHQMD) microscopic transport approach and advance two microscopic production mechanisms to describe deuterons in heavy-ion collisions from energies available at the GSI Schwerionensynchrotron (SIS) to those at the BNL Relativistic Heavy Ion Collider (RHIC): kinetic production by hadronic reactions and potential production by the attractive potential between nucleons. Differently from other studies, for the "kinetic" deuterons we employ the full isospin decomposition of the various & pi;NN & LRARR; & pi;d, NNN & LRARR; Nd channels and take into account the finite-size properties of the deuteron by means of an excluded volume condition in coordinate space and by the projection onto the deuteron wave function in momentum space. We find that considering the quantum nature of the deuteron in coordinate and momentum space reduces substantially the kinetic deuteron production in a dense medium as encountered in heavy-ion collisions. If we add the "potential" deuterons by applying an advanced minimum spanning tree (aMST) procedure, we obtain good agreement with the available experimental data from SIS energies up to the top RHIC energy.