  In this paper we investigate the photoproduction of QED bound states in
proton -- proton, proton -- nucleus and nucleus -- nucleus collisions at RHIC,
LHC and FCC energies considering an accurate treatment of the absorptive
corrections and for the nuclear form factor. The total cross sections for the
production of singlet and triplet $(l^+ l^-)$ states, with $l = e,\, \mu, \,
\tau$, are estimated and a detailed analysis of the photoproduction of singlet
QED bound states is performed considering the rapidity ranges covered by
central and forward detectors. The impact of the Coulomb corrections on the
parapositronium production in heavy ion collisions is estimated. We predict a
large number of events associated to the production of ($e^+ e^-$) and ($\mu^+
\mu^-$) states in hadronic collisions.
