  The effect of an external force on the kinetics of diffusion-assisted
escaping of Brownian particles from a potential well is analyzed in detail. The
analysis is made within the two-state model of the process which is known to be
valid in the deep well limit in the absence of external force. The generalized
variant of this model, taking into account the effect of the force, is shown to
be quite accurate as well for some shapes of the well. Within the generalized
two-state model simple expressions for the well depopulation kinetics and, in
particular, the for the escape rate are obtained. These expressions show that
the effect of the force ($F$) manifests itself in the escape rate dependence on
the only parameter $\varphi = Fa/(2k_b T)$, where $a$ is the Onzager radius of
the attractive part of the well $U(r)$, defined by the relation $|U(a)| = k_b
T$. The limiting behavior of this dependence in the cases of weak and strong
force is analyzed in detail. Possible applications as well as the relation of
the results of the analysis to those obtained earlier are briefly discussed.
