Coulomb Corrections and Ion Finite Size Effects in $\mu$ Pair Production at RHIC and LHC

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 calculating an observable ultraperipheral $\mu^+ \mu^-$ total cross section.