  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.
