The Nuclear Potential in Heavy-Ion Fusion

Abstract

Fits to high precision fusion cross-sections even for Z P Z T < 1000 appear to need a value of the diffuseness parameter a of the Woods-Saxon potential of ≃1 fm, which is much larger than the commonly accepted value of ≃ 0.65 fm. However, use of large values of a necessarily makes the potential pocket very shallow for realistic values of the nuclear potential depth. For larger values of angular momenta the pocket disappears, and a fusion barrier energy or radius can no longer be defined. In the absence of a potential pocket, fusion does not occur in the commonly used realistic coupled channels code CCFULL where fusion is calculated by applying an incoming wave boundary condition at the position of the minimum of the attractive pocket. For this reason, realistic coupled channels calculations with large values of a have needed unrealistically deep nuclear potentials. Once the potential depth is constrained to reasonable values, the data cannot be explained by simply changing the diffuseness of the nuclear potential. This indicates the necessity to go beyond the potential model, and incorporate dynamical effects as the two nuclei move towards fusion, even for light systems with Z P Z T < 1000.