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 $1.5\mathrm{fm}$, compared with values of about $0.65\mathrm{fm}$ which generally reproduce elastic scattering data. There is a clear tendency for the deduced $a$ to increase strongly with the reaction charge product $Z_1{Z}_2$, 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 $Z_1{Z}_2$ 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.