  Quantal diffusion mechanism of nucleon exchange is studied in the central
collisions of $^{238}$U + $^{238}$U in the framework of the stochastic
mean-field (SMF) approach. For bombarding energies considered in this work, the
di-nuclear structure is maintained during the collision. Hence, it is possible
to describe nucleon exchange as a diffusion process for mass and charge
asymmetry. Quantal neutron and proton diffusion coefficients, including memory
effects, are extracted from the SMF approach and the primary fragment
distributions are calculated.
