We report rigorous quantum dynamics studies of the Li+HF reaction usin
g the time-dependent wavepacket approach. The dynamics study is carrie
d out on a recent ab initio potential energy surface, and state-select
ed reaction probabilities and cross sections are calculated up to 0.4
eV of collision energy. Many long-lived resonances (as long as 10 ps)
at low collision energies (below 0.1 eV) are uncovered from the dynami
cs calculation. These long-lived resonances play a dominant role in th
e title reaction at low collision energies (below 0.1 eV). At higher e
nergies, the direct reaction process becomes very important. The react
ion probabilities from even rotational states exhibit a different ener
gy dependence than those from odd rotational states. Our calculated in
tegral cross section exhibits a broad maximum near the collision energ
y of 0.26 eV with small oscillations superimposed on the broad envelop
e which is reminiscent of the underlying resonance structures in react
ion probabilities. The energy dependence of the present CS cross secti
on is qualitatively different from the simple J-shifting approximation
, in which a monotonic increase of cross section with collision energy
was obtained.