Theoretical study of dynamic effects on fusion cross sections for reactions S32,34,36+Pb204,206,208

Abstract

The universal fusion function prescription and the empirical coupled-channel (ECC) model are used to analyze the dynamic effects on fusion cross sections for reactions $^{32,34,36}\mathrm{S}+^{204,206,208}\mathrm{Pb}$. An examination of the reduced fusion functions shows that the total dynamic effects on fusion cross sections in $^{36}\mathrm{S}+^{204,206,208}\mathrm{Pb}$ are almost the same as those in $^{34}\mathrm{S}+^{204,206,208}\mathrm{Pb}$. Furthermore, at sub-barrier energies of the reactions $^{32,34,36}\mathrm{S}+^{208}\mathrm{Pb}$, the largest enhancement of reduced fusion function is observed in the reaction $^{32}\mathrm{S}+^{208}\mathrm{Pb}$. Then the enhancement of fusion cross sections due to couplings to inelastic excitation channels and neutron transfer channels with positive $Q$ values is investigated by using the ECC model. The results show that the experimental data of the reactions $^{34,36}\mathrm{S}+^{204,206,208}\mathrm{Pb}$ and $^{32}\mathrm{S}+^{208}\mathrm{Pb}$ are reproduced well by the ECC model. In addition, it can be found that the effect of coupling to positive $Q$-value neutron transfer channels is necessary to reproduce the sub-barrier fusion data of the reaction $^{32}\mathrm{S}+^{208}\mathrm{Pb}$. Furthermore, for the two reactions $^{32}\mathrm{S}+^{204}\mathrm{Pb}$ and $^{32}\mathrm{S}+^{206}\mathrm{Pb}$, the effects of coupling to positive $Q$-value neutron transfer channels are predicted to be significant. The fusion cross sections for these two reactions are also predicted.