  We investigate microscopically the tunneling dynamics in spontaneous fission
of atomic nuclei. To this end, we employ a schematic solvable model with a
pairing-plus-quadrupole interaction. The spontaneous decay of a system is
simulated by introducing a small imaginary part to the energy of a fission
doorway state. We show that the many-body Hamiltonian can be reduced to an
effective 2$\times$2 Hamiltonian, from which one can derive a simple
approximate formula for the decay width. We particularly investigate the
applicability of the adiabatic approximation, which has often been used in the
literature. With typical value of the parameters, we find that the adiabatic
approximation works within a factor of around 5 for the decay width.
