The facilities designed to study collisions of relativistic nuclei, such as the MPD at NICA (JINR), STAR at RHIC (BNL), ALICE, ATLAS and CMS at the LHC (CERN), are equipped with pairs of hadronic Zero Degree Calorimeters (ZDC) to detect forward nucleons at the both sides of the interaction point and estimate the collision centrality. The energy deposited in a ZDC fluctuates from one event to another, but on average it is proportional to the number of absorbed nucleons. Forward nucleons are also emitted in electromagnetic dissociation (EMD) of nuclei in ultraperipheral collisions, and they are used to monitor the luminosity. As known, ZDC energy spectra are specific to each facility, because they are affected by the ZDC acceptance, and the ZDC energy resolution depends on the beam energy. In this work a simple combinatorial model leading to handy formulas has been proposed to connect the numbers of emitted and detected forward nucleons taking into account a limited ZDC acceptance. The ZDC energy spectra from the EMD with the emission of one, two, three and four forward neutrons and protons have been modeled for collision energies of NICA and the LHC. The case of a rather small ZDC acceptance has been investigated and a possibility to measure the inclusive nucleon emission cross section has been demonstrated.
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