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

TL;DR

This study investigates how nuclear deformation and orientation influence heavy-ion fusion by incorporating these factors into nuclear potential calculations using relativistic mean-field theory, comparing different potentials and with experimental data.

Contribution

It introduces a detailed method to include nuclear shape and orientation effects in fusion calculations using RMF-derived densities and compares relativistic and non-relativistic potentials against experimental results.

Findings

Deformation reduces fusion barrier height and increases cross-section.

Relativistic R3Y potential with deformed densities aligns better with experimental data.

Effects are more significant in reactions forming heavier nuclei.

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, NL3$^*$ and NL3 parameterizations. 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 $^{16}$O and $^{48}$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 non-relativistic 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, $\theta_2\le58^\circ$ for the R3Y NN potential and at $\theta_2\le60^\circ$ 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.