  We calculate the Coulomb dissociation of 9Li on Pb and U targets at 28.5
MeV/A beam energy within a finite range distorted wave Born approximation
formalism of the breakup reactions. Invoking the principle of detailed balance,
these cross sections are used to determine the excitation function and
subsequently the rate of the radiative capture reaction 8Li(n,g)9Li at
astrophysical energies. Our method is free from the uncertainties associated
with the multipole strength distributions of the 9Li nucleus. The rate of this
reaction at a temperature of 10^9K is found to be about 2900 cm^3 mole^{-1}
s^{-1}.
