  The STAR collaboration has observed an excess production of $e^+e^-$ pairs in
relativistic heavy ion collisions, over the expectations from hadronic
production models. The excess pairs have transverse momenta $p_T < 150\ {\rm
MeV}/c$ and are most prominent in peripheral gold-gold and uranium-uranium
collisions. The pairs exhibit a peak at the $J/\psi$ mass, but include a wide
continuum, with pair invariant masses from 400 MeV/c$^2$ up to 2.6 GeV/c$^2$.
The ALICE Collaboration observes a similar excess in peripheral lead-lead
collisions, but only at the $J/\psi$ mass, without a corresponding continuum.
  This paper presents a calculation of the cross-section and kinematic for
two-photon production of $e^+e^-$ pairs, and find general agreement with the
STAR data. The calculation is based on the STARlight simulation code, which is
based on the Weizs\"acker-Williams virtual photon approach. The STAR continuum
observations are compatible with two-photon production of $e^+e^-$ pairs. The
ALICE analysis required individual muon $p_T$ be greater than 1 GeV/c; this
eliminated almost all of the pairs from two-photon interactions, while leaving
most of the $J/\psi$ decays.
