The sub-barrier fusion of halo nuclei such as Be-11 and Li-11 with hea
vy target nuclei is discussed. The couplings to the soft dipole mode a
s well as to the break-up channels are taken into account. At barrier
energies, the fusion cross section was found to be more than one order
of magnitude smaller than that corresponding to the uncoupled problem
. At sub-barrier energies, it was shown to be larger.