  The time-dependent flux over the fission barrier of an excited nucleus under
the influence of dissipation is investigated. Characteristic features of the
evolution of the amplitude of the probability distribution and the velocity
profile at the fission barrier are derived. Analytical results are compared to
numerical Langevin calculations and used to develop a new analytical
approximation to the solution of the Fokker-Planck equation for the
time-dependent fission-decay width. This approximation is shown to be more
realistic than previously proposed descriptions, which were widely used in the
past.
