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

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. (paper)