Investigation of the role of neutron transfer and fusion hindrance in Si28+Gd158 at deep sub-barrier energies

The challenging task in heavy-ion collisions is unambiguously identifying the true fusion events in the deep sub-barrier region. Considering the primary challenge, we have measured fusion excitation functions for $^{28}\mathrm{Si}+^{158}\mathrm{Gd}$ reaction at energies above to deep sub-barrier region to decipher the role of multineutron transfer with positive $Q$ value and fusion hindrance in an asymmetric system. A comparison has been made with our previous measurement for $^{30}\mathrm{Si}+^{156}\mathrm{Gd}$ system where only one transfer channel with $Q>$ 0 exists and populates the same compound nucleus $^{186}\mathrm{Pt}^{*}$. The enhancement in fusion cross sections is observed on a reduced scale in the $^{28}\mathrm{Si}+^{158}\mathrm{Gd}$ reaction over $^{30}\mathrm{Si}+^{156}\mathrm{Gd}$ system at sub-barrier energies. The measured fusion data and extracted barrier distribution have been analyzed within the framework of coupled-channels (CC) programs, CCFULL and empirical channel coupling. Coupling to rotational excitations in projectile and target along with up to $2n$ transfer channel with positive $Q$ value is found to be promising to explain the fusion excitation functions except for the lowest energy point. However, the influence of more than two neutrons transfer is insignificant in $^{28}\mathrm{Si}+^{158}\mathrm{Gd}$ system. At the lowest energy ($\ensuremath{\approx}14%$ down the Coulomb barrier), a deviation from standard CC has been found, which may indicate the threshold for fusion hindrance, but additional lower-energy data are needed to prove this. The experimental threshold energy (${E}_{S}$) for fusion hindrance is in good agreement with the empirical formula, and it is consistent with the observed pattern of ${E}_{S}$ as a function of the entrance channel parameter ($\ensuremath{\zeta}$) for other nearly symmetric and asymmetric systems.