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

TL;DR

This paper extends the time-dependent generator coordinate method to include dissipation effects in nuclear fission, providing a more accurate quantum description of energy loss during induced fission processes.

Contribution

It introduces a generalized GCM framework that incorporates dissipation through excited states and derives a Schrödinger-like equation with a dissipation term, applied to thorium-228 fission.

Findings

The model reproduces experimental fission yields for $^{228}$Th.

Dissipation significantly affects fission dynamics.

The approach enhances quantum modeling of energy transfer in nuclear fission.

Abstract

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.