Systematic study of the isotopic dependence of heavy-ion fusion cross sections at below- and above-barrier energies

Abstract

The present work provides a systematic study on the role of nuclear surface tension in the isotopic dependence of the fusion cross sections at below- and above-barrier energies over wide range of neutron content (0.5 < N/Z < 1.7). To realize our goal, we select three different versions of proximity-based potential, involving proximity potential 1977, 1988, and 2010, in order to calculate the nucleus-nucleus potential and ultimately the fusion barrier parameters. It is shown that the barrier positions, heights, and curvatures follow a (second-order) non-linear isotopic behavior with addition of neutrons which are dependent on the effect of variation in the nuclear surface tension. Our findings reveal that the sensitivity of isotopic dependence of the fusion barrier characteristics to the effect of surface energy coefficients γ increases by increasing the asymmetry of the colliding pair. In addition, we demonstrate the sensitivity toward the coefficient γ is seen more clearly from the more neutron-rich nuclei compared to the neutron-deficient ones. We discuss the isotopic dependence of the fusion cross sections at below- and above-barrier energies within the framework of the Wong model for a single potential barrier. For above-barrier energies, it is shown that the fusion cross sections follow an increasing (second-order) non-linear trend due to the addition of neutrons. While a decreasing (second-order) non-linear trend exists for the variation in the fusion cross sections at below-barrier energies. Simultaneous comparison the results obtained by the 3 versions of proximity potential for the isotopic dependence of fusion cross sections in the mentioned energy regions reveal the importance of the quantum tunneling and also nuclear structure effects.