Toward a global systematic analysis of sub-barrier fusion enhancement

A global systematic analysis relating the asymptotic enhancement of sub-barrier fusion cross sections with the product of the coupling strength times the value of the Coulomb barrier is presented. It is found that all systems involving static deformations, inelastic excitations, and transfer degrees of freedom, follow the same systematic trend. In the analysis, the Coulomb barrier plays a central role in amplifying the relevance of the couplings associated with a particular degree of freedom. @S0556-2813~98!51106-5# PACS number~s!: 25.70.Jj Fusion cross sections between heavy ions, at bombarding energies near and below the barrier, show large enhancements relative to the predictions of a one-dimensional barrier penetration model. Early attempts to find a global interpretation of the fusion process have focused on extracting fusion barriers and testing several theoretical potentials @1‐3#. Simple parametrizations of measured fusion excitation functions in terms of gross nuclear properties have also been published @4‐6#. More recently considerable progress has been achieved in the understanding of these enhancements by including the internal structure of the participating nuclei in the dynamics of the reaction through coupled-channel calculations @7,8# and the interacting boson model @9# .I n the present work, we propose a global systematic analysis relating the magnitude of the asymptotic enhancement of the subbarrier cross sections with the product of the values of the Coulomb barrier and the values of the coupling strength necessary to account for the fusion cross section. In our analysis, the value of the Coulomb barrier, Vb , acts as an amplifier on the coupling strength of a system ~associated with static deformations, inelastic excitations, or transfer reactions !, i.e., for a nucleus with a quadrupole deformation b 2 , the bigger the product b 2iVb , the larger the sub-barrier fusion enhancement. All the systems studied, which include cases where static deformations, inelastic excitations, and transfer degrees of freedom are involved, fall nicely into the same systematic trend. We have investigated an extensive set of available data on fusion cross section excitation functions and compared them to the same theoretical model. A simplified coupled-channels code, CCMOD @10#, has been used to perform all the calculations. This code is a modified version of the codeCCDEF @11# which can treat static deformations and couplings to inelastic excitations and transfer channels. The nuclear potential used in the code has a Wood-Saxon shape and together with the Coulomb potential determines a parabolic barrier characterized by three parameters: Vb ~height!, Rb ~position!, and \v ~curvature!. This model has been extensively used in describing ~mostly successfully! a large number of fusion excitation functions @12#. In our coupled-channels calculations we have included quadrupole and hexadecapole deformations of the participating nuclei and the main inelastic and transfer reaction channels for each system ~inelastic excitations with large coupling strengths and transfer channels with positive Q values!. The values of the deformation parameters and the electromagnetic transition probabilities for the lowest excited states of the target and/or projectile nuclei for each system