Dependence of fusion on isospin dynamics

We introduce a new microscopic approach to calculate the dependence of fusion barriers and cross-sections on isospin dynamics. The method is based on the time-dependent Hartree-Fock theory and the isoscalar and isovector properties of the energy density functional (EDF). The contribution to the fusion barriers originating from the isoscalar and isovector parts of the EDF is calculated. It is shown that for non-symmetric systems the isovector dynamics influence the sub-barrier fusion cross-sections. For most systems this results in an enhancement of the sub-barrier cross-sections, while for others we observe differing degrees of hindrance. We use this approach to provide an explanation of recently measured fusion cross sections which show a surprising enhancement at low $E_\mathrm{c.m.}$ energies for the system $^{40}$Ca+$^{132}$Sn as compared to the more neutron-rich system $^{48}$Ca+$^{132}$Sn, and discuss the dependence of sub-barrier fusion cross-sections on transfer.