Theoretical study of fusion reactions $^{32}$S + $^{94,96}$Zr and $^{40}$Ca + $^{94,96}$Zr and quadrupole deformation of $^{94}$Zr

TL;DR

This study investigates how nuclear deformation and coupling effects influence fusion cross sections in specific sulfur and calcium reactions with zirconium isotopes, revealing similar coupling effects despite differing deformation predictions.

Contribution

It applies the ECC model to analyze coupling effects on fusion, highlighting the similarity in effects for different zirconium isotopes and questioning deformation parameter predictions.

Findings

Couplings to inelastic channels are similar for reactions with $^{94}$Zr and $^{96}$Zr.

Fusion enhancement at sub-barrier energies is quantified for different channels.

Discrepancies in deformation parameters suggest need for further experiments.

Abstract

The dynamic coupling effects on fusion cross sections for reactions $^{32}$S + $^{94,96}$Zr and $^{40}$Ca + $^{94,96}$Zr are studied with the universal fusion function formalism and an empirical coupled channel (ECC) model. An examination of the reduced fusion functions shows that the total effect of couplings to inelastic excitations and neutron transfer channels on fusion in $^{32}$S + $^{94}$Zr ($^{40}$Ca + $^{94}$Zr) is almost the same as that in $^{32}$S + $^{96}$Zr ($^{40}$Ca + $^{96}$Zr). The enhancements of the fusion cross section at sub-barrier energies due to inelastic channel coupling and neutron transfer channel coupling are evaluated separately by using the ECC model. The results show that effect of couplings to inelastic excitations channels in the reactions with $^{94}$Zr as target should be similar as that in the reactions with $^{96}$Zr as target. This implies that the quadrupole deformation parameters $\beta_2$ of $^{94}$Zr and $^{96}$Zr should be similar to each other. However, $\beta_2$'s predicted from the finite-range droplet model, which are used in the ECC model, are quite different. Experiments on $^{48}$Ca + $^{94}$Zr or $^{36}$S + $^{94}$Zr are suggested to solve the puzzling issue concerning $\beta_2$ for $^{94}$Zr.