Sub-barrier fusion analysis of ⁴⁰Ca + ^46,48,50Ti systems*

Abstract Considering the simple Wong formula, simple Wong formula with deformed choice of nuclear potential, symmetric-asymmetric Gaussian barrier distribution (SAGBD) model, and coupled channel approach, this work investigates the fusion mechanism of 40 Ca + 46,48,50 Ti systems. For these reactions, the roles of internal structural degrees of freedom of collision partners and diffuseness parameter associated with Woods-Saxon potential in fusion dynamics are investigated. For the chosen systems, simple Wong formula-based calculations are found to be unable to describe actual fusion data at sub-barrier energies. The inclusion of quadrupole deformation with an additional radius parameter in deformed choice of nuclear potential along with the simple Wong formula is capable of retracing experimental data. In the SAGBD model, the simple Wong formula is weighted by a Gaussian function. The SAGBD model with different choices of diffuseness has been explored, and fusion yields have been found to be relatively sensitive to the choice of diffuseness of Woods-Saxon potential. SAGBD outcomes with Winther and Akyüz-Winther diffuseness are unable to retrieve experimental data. To improve theoretical predictions, the diffuseness is optimized relative to Winther and Akyüz-Winther value, and theoretical outcomes with an optimized diffuseness parameter within SAGBD model address the fusion behaviour of 40 Ca + 46,48,50 Ti reactions well. Coupled channel analysis of given reactions, wherein the influences of low-lying vibrational states of participants are directly considered, readily reproduced the fusion data for all studied systems. The low-lying vibrational 2 + and 3 – states are found to be sufficient to reproduce the fusion data for 40 Ca + 46,48 Ti reactions. However, for 40 Ca + 50 Ti reactions, in addition to low-lying 2 + and 3 – vibrational states, the considerations of a pair neutron transfer channel is required to address sub-barrier fusion data.