  A higher order QED calculation of the ultraperipheral heavy ion cross section
for mu+ mu- pair production at RHIC and LHC is carried out. The so-called
"Coulomb corrections" lead to an even greater percentage decrease of mu+ mu-
production from perturbation theory than the corresponding decrease for e+ e-
pair production. Unlike the e+ e- case, the finite charge distribution of the
ions (form factor) and the necessary subtraction of impact parameters with
matter overlap are significant effects in calculation an observable
ultraperipheral mu+ mu- total cross section.
