Fusion and transfer + breakup channels have been studied in the collision induced by the two-neutron-halo 6He on a 64Zn target at energies from below to above the Coulomb barrier. For comparison, the reaction induced by the stable isotope 4He on the same target has been studied. The fusion cross section has been measured by using an activation technique, detecting off-line the delayed x-ray activity following the electron capture decay of the evaporation residues. New measurements of the 4He + 64Zn fusion cross section at sub-barrier energies have been performed in order to cover the same energy range of the 6He + 64Zn fusion cross section and to compare the excitation functions for the two systems down to the lowest energy data point measured for 6He. From the new comparison a sub-barrier fusion enhancement has been observed in the 6He case with respect to the 4He one whereas no effect on the 6He fusion cross section has been seen at energies above the barrier. It has been concluded that such enhancement seems to be due to the diffuse halo structure properties of the 6He nucleus. Moreover, the reactions induced by 6He have shown a strong yield of α particles coming from direct processes
