Effect of nuclear deformation and orientation about the symmetry axis of the target nucleus on heavy-ion fusion dynamics

Abstract

Nuclear shape and orientation degrees of freedom are incorporated into the calculation of the double-folding nuclear potential within the relativistic mean-field (RMF) formalism. The quadrupole deformations (${\beta }_2$), nuclear densities, and the effective nucleon-nucleon ($NN$) interaction potential are obtained using the RMF approach for the hybrid, ${\mathrm{NL3}}^{*}$, and NL3 parametrizations. The calculated quadrupole deformations are included in the target densities through the nuclear radius. The deformation and orientation-dependent microscopic nuclear potentials are further employed to obtain fusion barrier characteristics and cross sections for 12 even-even heavy-ion reactions with doubly magic spherical ${}^{16}\mathrm{O}$ and ${}^{48}\mathrm{Ca}$ as projectiles along with deformed targets from different mass regions. The results obtained for the relativistic R3Y $NN$ potential are compared with those of the Reid version of the nonrelativistic M3Y $NN$ potential as well as with the available experimental data. A decrease in the barrier height and increase in the cross-section is observed upon the inclusion of target quadrupole deformations in the nuclear density distributions at the target orientation angles, ${\theta }_2\le {58}^{\circ }$ for the R3Y $NN$ potential and at ${\theta }_2\le {60}^{\circ }$ for the M3Y $NN$ potential. On comparing the ${\theta }_2$-integrated cross section calculated using M3Y and R3Y $NN$ potentials with spherical and deformed densities, one observes that the deformed densities and the relativistic R3Y $NN$ potential obtained for the hybrid parameter set provide better agreement with the available experimental data for all the considered reactions. Moreover, the modifications in the characteristics of the fusion barrier and hence in the cross section with the inclusion of nuclear shape degrees of freedom and orientations are found to become more prominent in reactions forming heavier compound nuclei. This implies that the inclusion of nuclear deformations and orientation in the calculation of the microscopic nuclear potential within the RMF formalism is crucial to provide a reliable description of the sub-barrier nuclear fusion dynamics, especially in the heavy and superheavy mass regions.