In this paper we investigate the production of a true muonium state, which is an atom consisting of a $mu^+ mu^-$ bound state, by $gamma gamma$ interactions in ultraperipheral $PbPb$ collisions considering an accurate treatment of the absorptive corrections and for the nuclear form factor. The rapidity distributions and cross sections are estimated considering the RHIC, LHC and FCC energies. Our results indicate that the experimental analysis can be useful to observe, for the first time, the true muonium state.
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