Sensitivity of $\beta _4$ values extracted from quasi elastic barrier distribution to the 2n transfer channel

Abstract

In recent times, the Fusion Barrier Distributions (FBD) determined from quasi-elastic scattering measurements have been employed to determine the hexadecapole deformation parameter $\beta _4$ value precisely. In reactions where transfer channels are favourable, coupling due to transfer may affect the determination of $\beta _4$. In order to study the role of transfer channels while determining $\beta _4$ from barrier distribution, the quasi-elastic scattering measurements have been carried out in $^{16}$O + $^{176}$Yb. Quasi-elastic scattering excitation function has been measured at backward angles with respect to the beam direction and barrier distribution $D^{\text {qel}}(E)$ has been derived. Experimentally obtained barrier distribution has been compared with coupled channel calculations using CCFULL code. The effect of two neutron transfer and hexadecapole deformation has been studied using coupled channel calculation. $\chi ^2$ was calculated in a two dimensional space of $\beta _4$ and neutron transfer strength $P_{tr}$. Without considering neutron transfer, $\chi ^2$ minimization of $D^{\text {qel}}(E)$ was not possible and the best-fit was found over a small range of $\beta _4$ and $P_{tr}$. At $P_{tr}=0.37$, corresponding to minimum $\chi ^2$, the $\beta _4$ of $^{176}$Yb is determined to be $0.00 \pm 0.015$. This value of $\beta _4$ is in agreement with that obtained from Coulomb excitation measurement.