Impact of pear-shape nuclei on fusion barrier and synthesis of new elements

Abstract

In heavy-ion induced reactions, the deformations and orientation degrees of freedom are considered as important tools to understand nuclear fusion dynamics. For the synthesis of new isotope, the projectile nucleus has to penetrate through the Coulomb barrier, posed due to long-range repulsive Coulomb and short-range attractive nuclear potentials, which get altered at different orientations of the deformed colliding partners. In the present work, the importance of octupole deformation (up to β₃) and related optimum orientations [1] has been explored in terms of fusion barrier characteristics (barrier height V_B, barrier position R_B and barrier curvature hw_B) and fusion cross-sections. For the above analysis, different pairs of target-projectile combinations (spherical-octupole, quadrupole-octupole and octupole-octupole) have been taken into account. Here, the doubly magic (spherical) nuclei, i.e. ¹⁶O and ⁴⁸Ca, the quadrupole deformed nuclei ⁴⁸Ar (β₂ = -0.205), and ⁶²Fe (β₂ = 0.152) are used respectively as projectile of first two combinations. The soft-pear shape ¹⁴⁴Ba (β₂ = 0.163, β₃ = -0.124) with small value of β₃ and rigid-pear shape ²⁸⁰Ra (β₂ = 0.069, β₃ = -0.163) are taken as target in all considered reactions. The results obtained are discussed in reference to the spherical and quadrupole configurations of considered choices of octupole deformed nuclei. Many authors have given various models to obtain the barrier characteristics. In this respect, some of the Skyrme forces of different parameter sets [2 – 4], i.e. SIII, SLy4, SkT1, eMSL07, GSkI, GSkII and SSk, employed in deriving the interaction potential has been found to address the nucleus-nucleus interaction problems [5]. In the present work, the barrier modifications observed with the inclusion of deformations up to β₃ and related orientation degrees of freedom, in reference to that of spherical and β₂ deformation, illustrate the impact of pear-shape octupole deformed nuclei in the formation of an excited Compound Nucleus (CN). Furthermore, the fusion cross-sections have been calculated using the Wong formula [6] over a wide range of centre of mass energies, E_c.m. (MeV), which spread across the Coulomb barrier. The incorporation of octupole deformation and related orientations within the Skyrme Energy Density Formalism may help to explore the possible combinations for the synthesis of new isotopes.