J/$\psi$ suppression in heavy-ion collisions due to color screening of quark and antiquark potential in the deconfined medium has been proposed as a signature of the QGP formation. Other mechanisms, such as the cold nuclear matter effect and charm quark recombination, are likely to contribute to the observed modification of J/$\psi$ production in heavy-ion collisions. Recently, a significant excess of J/$\psi$ yield at very low transverse momentum ($p_{T}$) ($<$ 0.3 GeV/c) in peripheral hadronic Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}$= 2.76 TeV at forward-rapidity has been observed by the ALICE collaboration, which can not be explained within the scenarios mentioned above. The excess observed may originate from the coherent photoproduction of J/$\psi$, which would be very challenging for the existing coherent photoproduction models. Measurements of J/$\psi$ production at very low $p_{T}$ in different collision energies, collision systems, and centralities can shed new lights on the origin of the excess.
In this article, we report the STAR measurements of J/$\psi$ production at very low $p_{T}$ in hadronic Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}$ = 200 GeV and U+U collisions at $\sqrt{s_{\mathrm{NN}}}$ = 193 GeV at mid-rapidity. Centrality dependence of J/$\psi$ yields and nuclear modification factors at very low $p_{T}$ are presented.