We investigate the production of secondary nuclei in the hadronic fragmentation and electromagnetic dissociation (EMD) of Ne beams at the LHC and Xe beams at NICA. For light nuclei at LHC energies, our calculations show that hadronic interactions are the dominant channel for nuclear transmutation. This contrasts with the previously established dominance of EMD in Pb-Pb collisions. For Ne-Ne collisions at TeV, we provide calculated cross sections and momentum distributions of produced nuclei such as He, C, N, and O. These results are essential for assessing potential contamination of the Ne-Ne event sample by collisions involving other nuclear species. Secondary nuclei will be also produced in the EMD of Xe beams at NICA, but they will not contaminate Xe-Xe data.

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