Fusion of $^(48)Ca$ + $^(90,96)Zr$ above and below the Coulomb barrier
Abstract
Fusion-evaporation cross sections were measured in the two systems $^(48)Ca$ + $^(90,96)Zr$ in an energy range from well below to well above the Coulomb barrier. The sub-barrier fusion of $^(48)Ca$ + $^(90)Zr$ is reproduced by coupled-channels calculations including the lowest quadrupole and octupole vibrations of $^(90)Zr$, and using a Woods-Saxon potential with a standard diffuseness parameter a = 0.68 fm. However, the fusion cross sections are overestimated above the barrier. The low-energy slope of the excitation function for $^(48)Ca$ + $^(96)Zr$ is steeper. This implies a larger diffuseness parameter a = 0.85 fm. Fusion cross sections are well fit in the whole energy range, and the effect of the strong octupole vibration in $^(96)Zr$ is predominant. The extracted fusion barrier distributions are reasonably well reproduced by calculations for both systems. A comparison with previous data for $^(40)Ca$ + $^(90,96)Zr$ is made in an attempt to clarify the role of transfer couplings in sub-barrier fusion.