  The $^8$Li($n,\gamma$)$^9$Li reaction plays an important role in both the
r-process nucleosynthesis and the inhomogeneous big bang models, its direct
capture rates can be extracted from the $^8$Li($d, p$)$^9$Li reaction,
indirectly. We have measured the angular distribution of the $^8$Li($d,
p$)$^9$Li$_{\textrm{g.s.}}$ reaction at $E_{\textrm{c.m.}}$ = 7.8 MeV in
inverse kinematics using coincidence detection of $^{9}\textrm{Li}$ and recoil
proton, for the first time. Based on Distorted Wave Born Approximation (DWBA)
analysis, the $^{8}\textrm{Li}(d, p)^{9}\textrm{Li}_{\textrm{g.s.}}$ cross
section was determined to be 7.9 $\pm$ 2.0 mb. The single particle
spectroscopic factor, $S_{1,3/2}$, for the ground state of $^{9}\textrm{Li}$ =
$^{8}\textrm{Li} \otimes n$ was derived to be $0.68\pm 0.14$, and then used to
calculate the direct capture cross sections for the $^{8}\textrm{Li}(n,
\gamma)^{9}\textrm{Li}_{\textrm{g.s.}}$ reaction at energies of astrophysical
interest. The astrophysical $^{8}\textrm{Li}(n,
\gamma)^{9}\textrm{Li}_{\textrm{g.s.}}$ reaction rate for the direct capture
was found to be 3970 $\pm$ 950 $\textrm{cm}^{3}\textrm{mole}^{-1}s^{-1}$ at
$T_9$ = 1. This presents the first experimental constraint for the
$^{8}\textrm{Li}(n, \gamma)^{9}\textrm{Li}$ reaction rates of astrophysical
relevance.
