VALIDITY OF THE LINEAR COUPLING APPROXIMATION IN HEAVY-ION FUSION REACTIONS AT SUBBARRIER ENERGIES

The role of higher order coupling of surface vibrations to the relativ e motion in heavy-ion fusion reactions at near-barrier energies is inv estigated. The coupled channels equations are solved to all orders and also in the linear and the quadratic coupling approximations. Taking Ni-64 + Zr-92,Zr-96 reactions as examples, it is shown that all order couplings lead to considerably improved agreement with the experimenta lly measured fusion cross sections and average angular momenta of the compound nucleus for such heavy, nearly symmetric systems. The importa nce of higher order coupling is also examined for asymmetric systems l ike O-16 + Cd-112, Sm-144, for which previous calculations of the fusi on cross section seemed to indicate that the linear coupling approxima tion was adequate. It is shown that the shape of the barrier distribut ions and the energy dependence of the average angular momentum can cha nge significantly when the higher order couplings are included, even f or systems where measured fusion cross sections may seem to be well re produced by the linear coupling approximation.