  Starting from a quantum theory of dissipation for nuclear collective motion,
the time-dependent generator coordinate method (TDGCM) is extended to allow for
dissipation effects in the description of induced fission dynamics. The
extension is based on a generalization of the GCM generating functions that
includes excited states, and the resulting equation of motion in the collective
coordinates and excitation energy. With the assumption of a narrow hamiltonian
kernel, an expansion in a power series in collective momenta leads to a
Schr\"odinger-like equation that explicitly includes a dissipation term,
proportional to the momentum of the statistical wave function. An illustrative
calculation is performed for induced fission of $^{228}$Th. The
three-dimensional model space includes the axially-symmetric quadrupole and
octupole shape variables, and the nuclear temperature. When compared to data
for photo-induced fission of $^{228}$Th, the calculated fission yields
demonstrate the important role of the additional term in the hamiltonian that
explicitly takes into account the dissipation of energy of collective motion
into intrinsic degrees of freedom.

Nuclear Theory;Nuclear Experiment