  Significant excesses of $e^+e^-$ pair production at very low transverse
momentum ($p_T <$ 0.15 GeV/c) were observed by the STAR collaboration in
hadronic heavy-ion collisions. Such enhancement is assumed to be a sign of
photon-photon production in heavy-ion collisions with hadronic overlap, based
on comparisons with model calculations for spherical Au + Au collisions.
However, there is a lack of calculations for $e^+e^-$ pair production from
coherent photon-photon interactions in hadronic U + U collisions, due to the
deformity of Uranium nuclei. In this article, we present calculations for
$e^+e^-$ pair photoproduction at $\sqrt{s_{NN}}$ = 193 GeV in both spherical
and deformed U + U collisions within STAR detector acceptance using the
equivalent photon approximation (EPA). We conduct event-by-event analysis to
investigate the effects of initial nuclear deformation on pair production. Our
numerical results show good agreement with experimental data for the 40%--60%
and 60%--80% centrality classes in U + U collisions, and the differences
between spherical and deformed configurations are approximately 3\%. We also
calculate the yields of the photoproduced $e^+e^-$ pair in hadronic deformed Ru
+ Ru and Zr + Zr collisions at $\sqrt{s_{NN}}$ = 200 GeV. The results reveal
that the ratios of the yields of Ru to Zr exhibit very small differences ($<$
1%) between spherical and deformed cases.
