  We study in detail the influence of the nuclear form factor both on the Born
cross section and on the Coulomb corrections to the photo-production of muon
pairs off heavy nuclei (gamma Z -> mu+ mu- Z$) and in heavy-ion collisions (ZZ
-> ZZ mu+ mu-). Our findings indicate a number of issues which have not been
sufficiently described as yet in the literature: (i) the use of a realistic
form factor, based on the Fermi charge distribution for the nucleus, is
absolutely indispensable for reliable theoretical predictions; (ii) we checked
quantitatively that the equivalent photon approximation has a very good
accuracy for the discussed processes; and (iii) we present a leading
logarithmic calculation of the Coulomb corrections which correspond to
multi-photon exchange of the produced mu+/- with the nuclei. These corrections
are found to be small (on the percent level). Our result justifies using the
Born approximation for numerical simulations of the discussed process at the
RHIC and LHC colliders. Finally, we calculate the total cross section for muon
pair production at RHIC and LHC.
