Role of nuclear surface tension coefficients in the isotopic dependence of fusion dynamics for neutron-rich colliding nuclei: New parametrization of fusion barriers

Abstract

A theoretical approach is developed to study systematically the influence of the nuclear surface tension coefficient, γ, of the proximity formalism on the isotopic behavior of the fusion dynamics over a wide range of neutron-rich colliding systems with condition of 1 ≤ N/Z < 1.6 for their compound nuclei. Here six different versions of the surface energy coefficient (γ-PD03, γ-MS67, γ-MS66, γ-MN81-I, γ-MN81-II and γ-MN76) in the calculation of the nuclear potential based on the original proximity potential 1977are employed. It is found that the fusion barrier characteristics and fusion cross sections follow a linear isotopic dependence which is sensitive to the change in the nuclear surface tension between the reacting nuclei. The maximum sensitivity of the data to this technical parameter is obtained for the use of the γ-PD03 version. Further, it is shown that the sensitivity of the isotopic behavior of the fusion cross sections to the coefficient γ increases by decreasing the incident energy. After the calculation of fusion barrier heights and positions using the different versions of proximity potentials, we have searched for their parametrization. Firstly, we present a pocket formula for fusion barriers which is directly dependent on both the coefficient γ and the N/Z ratio of the isotopic systems. Our analysis for the studied isotopic systems reveals that the agreement with the empirical data is improved when we consider the dependence of the analytical parameterized formulas on this coefficient. Further, the fusion cross sections obtained by the present pocket formula are in good agreement with the corresponding experimental data. A comparison with other well known parameterized forms in the context of isotopic studies is also made.

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

“…We can formulate these trends as By substituting the present suggested formulas in equations (4), (5), and (6), the analytical parameterized forms for the percentage difference of the Coulomb barrier positions ΔR B (%), heights ΔV B (%), and curvatures The above equations confirm that the percentage difference of the Coulomb barrier positions, heights, and curvatures depend on not only the N/Z ratio but also the strength of nuclear surface tension coefficient in the whole isotopic region from proton-rich to neutron-rich colliding nuclei. In the previous work [21], we investigated such dependencies only for barrier heights and positions in the N/Z 1 region.…”

“…As a result of the literature, this formalsim enables us to analyze the influence of various physical effects such as surface energy coefficients and nuclear surface diffuseness in the fusion of heavy-ions [18][19][20]. Recently, we systematically developed a theoretical framework to explore the role of nuclear surface tension coefficient γ in the isotopic behavior of the fusion dynamics [21]. In that study, we restricted ourselves to neutron-rich colliding systems with the condition of 1 N/Z < 1.6.…”