A three-body cluster He-4+t+n model is developed for Li-8 using the me
thod of hyperspherical harmonics with realistic cluster-cluster intera
ctions fitted to experimental data. The model is used to calculate wav
e functions, spatial and matter densities of the ground state and the
low lying excited state of 8Li, The model reproduces experimentally kn
own properties of Li-8. Contrary to two-body models, our prediction fo
r the radiative neutron capture on Li-7 at low energies supports a low
er cross section value.