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Starting from a quantum theory of dissipation for nuclear collective motion,the time-dependent generator coordinate method (TDGCM) is extended to allow fordissipation effects in the description of induced fission dynamics. Theextension is based on a generalization of the GCM generating functions thatincludes excited states, and the resulting equation of motion in the collectivecoordinates and excitation energy. With the assumption of a narrow hamiltoniankernel, an expansion in a power series in collective momenta leads to aSchr\"odinger-like equation that explicitly includes a dissipation term,proportional to the momentum of the statistical wave function. An illustrativecalculation is performed for induced fission of $^{228}$Th. Thethree-dimensional model space includes the axially-symmetric quadrupole andoctupole shape variables, and the nuclear temperature. When compared to datafor photo-induced fission of $^{228}$Th, the calculated fission yieldsdemonstrate the important role of the additional term in the hamiltonian thatexplicitly takes into account the dissipation of energy of collective motioninto intrinsic degrees of freedom.

Time-dependent generator coordinate method study of fission: dissipation effects