System Size and Energy Dependence of Dilepton Production in Heavy-Ion Collisions at SIS Energies

We study the dilepton production in heavy-ion collisions at energies of 1-2 AGeV as well as in proton induced pp, pn, pd and p+A reactions from 1 GeV up to 3.5 GeV. For the analysis we employ three different transport models - the microscopic off-shell Hadron-String-Dynamics (HSD) transport approach, the Isospin Quantum Molecular Dynamics (IQMD) approach as well as the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) approach. We confirm the experimentally observed enhancement of the dilepton yield (normalized to the multiplicity of neutral pions $N_{\pi^0}$) in heavy-ion collisions with respect to that measured in $NN = (pp+pn)/2$ collisions. We identify two contributions to this enhancement: a) the $pN$ bremsstrahlung which scales with the number of collisions and not with the number of participants, i.e. pions; b) the dilepton emission from intermediate $\Delta$'s which are part of the reaction cycles $\Delta \to \pi N ; \pi N \to \Delta$ and $NN\to N\Delta; N\Delta \to NN$. With increasing system size more generations of intermediate $\Delta$'s are created. If such $\Delta$ decays into a pion, the pion can be reabsorbed, however, if it decays into a dilepton, the dilepton escapes from the system. Thus, experimentally one observes only one pion (from the last produced $\Delta$) whereas the dilepton yield accumulates the contributions from all $\Delta$'s of the cycle. We show as well that the Fermi motion enhances the production of pions and dileptons in the same way. Furthermore, employing the off-shell HSD approach, we explore the influence of in-medium effects like the modification of self-energies and spectral functions of the vector mesons due to their interactions with the hadronic environment.