  The dynamical theory of thermally activated resonant magnetization tunneling
in uniaxially anisotropic magnetic molecules such as Mn_12Ac (S=10) is
developed.The observed slow dynamics of the system is described by master
equations for the populations of spin levels.The latter are obtained by the
adiabatic elimination of fast degrees of freedom from the density matrix
equation with the help of the perturbation theory developed earlier for the
tunneling level splitting [D. A. Garanin, J. Phys. A, 24, L61 (1991)]. There
exists a temperature range (thermally activated tunneling) where the escape
rate follows the Arrhenius law, but has a nonmonotonic dependence on the bias
field due to tunneling at the top of the barrier. At lower temperatures this
regime crosses over to the non-Arrhenius law (thermally assisted tunneling).
The transition between the two regimes can be first or second order, depending
on the transverse field, which can be tested in experiments. In both regimes
the resonant maxima of the rate occur when spin levels in the two potential
wells match at certain field values. In the thermally activated regime at low
dissipation each resonance has a multitower self-similar structure with
progressively narrowing peaks mounting on top of each other.
