The role of higher order coupling of surface vibrations to the relative
motion in heavy-ion fusion reactions at near-barrier energies is investigated.
The coupled channels equations are solved to all orders, and also in the linear
and the quadratic coupling approximations. Taking 64Ni + 92,96Zr
reactions as examples, it is shown that all order couplings lead to
considerably improved agreement with the experimentally measured fusion cross
sections and average angular momenta of the compound nucleus for such heavy
nearly symmetric systems. The importance of higher order coupling is also
examined for asymmetric systems like 16O + 112Cd, 144Sm, for
which previous calculations of the fusion cross section seemed to indicate that
the linear coupling approximation was adequate. It is shown that the shape of
the barrier distributions and the energy dependence of the average angular
momentum can change significantly when the higher order couplings are included,
even for systems where measured fusion cross sections may seem to be well
reproduced by the linear coupling approximation.Comment: Latex file, 15 pages, 6 figure