Systematic Failure of the Woods-Saxon Nuclear Potential to Describe Both Fusion and Elastic Scattering: Possible Need for a New Dynamical Approach to Fusion

Abstract

A large number of precision fusion excitation functions, at energies above the average fusion barriers, have been fitted using the Woods-Saxon form for the nuclear potential in a barrier passing model of fusion. They give values for the empirical diffuseness parameter a ranging between 0.75 and 1.5 fm, compared with values of about 0.65 fm which generally reproduce elastic scattering data. There is a clear tendency for the deduced a to increase strongly with the reaction charge product Z1Z2, and some evidence for the effect of nuclear structure on the value of a, particularly with regard to the degree of neutron richness of the fusing nuclei, and possibly with regard to deformation. The measured fusion-barrier energies are always lower than those of the bare potentials used, which is expected as a result of adiabatic coupling to high energy collective states. This difference increases with increasing Z1Z2 and calculations show that about 1/3 of it may be attributed to coupling to the isoscalar giant-quadrupole resonances in the target and projectile. Coupling to all giant resonances may account for a significant part. Fluctuations about the trend line may be due to systematic errors in the data and/or structure effects such as coupling to collective octupole states. Previously suggested reasons for the large values of a have been related to departures from the Woods-Saxon potential and to dissipative effects. This work suggests that the apparently large values of a may be an artifact of trying to describe the dynamical fusion process by use of a static potential. Another partial explaination might reside in fusion inhibition, due for example to deep-inelastic scattering, again a process requiring dynamical calculations.