  We report on the first measurements of J/$\psi$ production at very low
transverse momentum ($p_{T} <$ 0.2 GeV/c) in hadronic Au+Au collisions at
$\sqrt{s_{\rm{NN}}} =$ 200 GeV and U+U collisions at $\sqrt{s_{\rm{NN}}} =$ 193
GeV. Remarkably, the inferred nuclear modification factor of J/$\psi$ at
mid-rapidity in Au+Au (U+U) collisions reaches about 24 (52) for $p_{T} <$ 0.05
GeV/c in the 60-80$\%$ collision centrality class. This noteworthy enhancement
cannot be explained by hadronic production accompanied by cold and hot medium
effects. In addition, the $dN/dt$ distribution of J/$\psi$ for the very low
$p_{T}$ range is presented for the first time. The distribution is consistent
with that expected from the Au nucleus and shows a hint of interference.
Comparison of the measurements to theoretical calculations of coherent
production shows that the excess yield can be described reasonably well and
reveals a partial disruption of coherent production in semi-central collisions,
perhaps due to the violent hadronic interactions. Incorporating theoretical
calculations, the results strongly suggest that the dramatic enhancement of
J/$\psi$ yield observed at extremely low $p_{T}$ originates from coherent
photon-nucleus interactions. In particular, coherently produced J/$\psi$'s in
violent hadronic collisions may provide a novel probe of the
quark-gluon-plasma.
