  An one dimensional adiabatic model has been proposed for fusion of loosely
bound and halo light nuclei with various heavy targets. It is shown that fusion
cross sections at near and sub-barrier energies can be explained using a simple
WKB tunneling through an adiabatic barrier without invoking breakup coupling
explicitly. The model has been applied successfully to explain fusion cross
sections for several systems including recently measured $^{6}Li+^{198}Pt$
system (Phy. Rev. Lett. 103, 232702, 2009) where data exists well above and
below the barrier and $^{8}He+^{197}Au$ system (Phy. Rev. Lett. 103, 232701,
2009) where $^{8}He$ is highly neutron rich. Interestingly, the fusion of
stable $^{4}He+^{197}Au$ system can not be explained on the basis of this
adiabatic model as it requires normal tunneling through the sudden barrier. The
requirement of adiabatic potential for the loosely bound and halo nuclei is
linked to the fact that for such systems neutron flow leading to neck formation
is initiated at a larger distance which modifies the sudden potential.
