Microscopic Friction Coefficients from Kubo Linear-Response Formulas: A Review of Ab Initio Transport Coefficients for Fusion-Fission Langevin Dynamics

Abstract

The dynamical description of heavy-ion fusion and of nuclear fission as the diffusive motion of a few collective shape coordinates through a viscous medium requires, as its essential input, the transport coefficients of inertia and friction. This article develops a systematic treatment of the microscopic friction coefficient obtained from Kubo linear-response theory, in which the dissipation experienced by the slow collective motion arises from its coupling to the fast intrinsic degrees of freedom of the nucleons in a deforming mean field. The collective response and correlation functions are constructed within the locally harmonic approximation, and the friction, inertia, and stiffness tensors are extracted from their low-frequency behaviour, so that the macroscopic Langevin equation is derived from the microscopic Hamiltonian with no adjustable dissipation parameter. The fluctuation-dissipation theorem fixes the strength of the random force in terms of the friction and the temperature, ensuring thermodynamic consistency. The temperature dependence of the transport coefficients is examined, the friction increasing and the inertia decreasing with rising temperature, together with their variation along the fission path and the influence of shell and pairing effects. The resulting coefficients are confronted with the macroscopic wall formula and applied to the Kramers description of the fission decay rate, where the over-damped character of nuclear collective motion is established. The treatment demonstrates that linear-response theory provides a parameter-free microscopic foundation for the transport coefficients governing fusion-fission Langevin dynamics, replacing the phenomenological friction of macroscopic models