  When a Brownian particle, initially being in the potential well, overcomes
the barrier and moves to the absorptive border, it still has a chance to be
scattered back to the well by thermal fluctuations. We study this phenomenon
carefully modeling numerically the motion of the particle with the Langevin
equations. Four potentials which coincide near the well and the barrier but
differ in the tail (i.e. beyond the barrier) are considered. It is shown that
the potential for which the well and the barrier are described by two smoothly
joined parabolas ("the parabolic potential") plays a role of a dividing range
for the mutual layout of the quasistationary dynamical rate and the widely used
in the literature Kramers rate. Namely, for the potentials with a steeper
tails, the Kramers rate R_K0 underestimates the true quasistationary dynamical
rate R_D, whereas for the less steep tails opposite holds (inversion of
R_D/R_K0). It is proved that the mutual layout of the values of the R_D for
different potentials is explained by the re-scattering of the particles from
the potential tail.
