  Gluon density and its distributions inside nuclei and the parton modification
of bounded nucleons inside a nucleus, are some of the main standing problems in
nuclear and particle physics. In recent years, ultra-peripheral collisions
(UPC) of heavy ions have provided a new way of probing the gluon density, which
is based on coherent diffractive vector-meson productions, e.g., $J/\psi$
meson. For heavy ions, e.g., Pb, the gluon density is found to be significantly
suppressed through the UPC $J/\psi$ measurement, suggesting a strong gluon
shadowing effect in heavy nuclei. In this analysis, we aim to look at a unique
set of data taken by the STAR experiment, where $J/\psi$ mesons are
photoproduced off the deuteron target with no other particle produced, except
for the deuteron or its breakup products. The Zero Degree Calorimeter response
with respect to the deuteron dissociation by detecting a beam-rapidity neutron
is also investigated and provides additional information about the underlying
physics process. The cross section of $J/\psi$ photoproduction in the
photon-deuteron system is measured at the photon-nucleon center-of-mass energy
$W\sim25~\rm{GeV}$, as well as the momentum transfer $t$ dependence cross
section, $d\sigma/dt$. Data suggests a wider gluon density distribution than
the Hulthen charge density distribution in deuteron.
