A quantal transport theory for nuclear collective motion: The merits of a locally harmonic approximation

Abstract

A transport theory is developed for collective motion of systems such as an atomic nucleus, which may be considered as a typical representative of a self-bound micro-system. Albeit for pragmatic reasons, collective variables are introduced as shape parameters, self-consistency with respect to the nucleonic degrees of freedom has been implemented at various important stages. This feature leads to subsidiary conditions which are obeyed locally for both the average motion as well as for the quantized Hamiltonian constructed through a Bohm-Pines procedure. Furthermore, self-consistency governs the definition of the transport coefficients appearing in the equations for collective motion. The latter is associated to the time evolution of the density in collective phase space, for which the concept of the Wigner function is employed. Global motion is described by propagating the system in successive time laps which are macroscopically small, but microscopically large. This enables one to exploit linearization procedures and to take advantage of the benefits of linear response theory. A microscopic damping mechanism is introduced by dressing the energies of the independent particle model by complex self-energies, the parameters of which are determined from optical model considerations. Numerical evaluations of transport coefficients are described and tested for the case of fission in the light of recent experimental findings. The theory allows one to extend both Kramers' picture of this process as well as his equation for the density distribution into the quantum regime. These quantum effects are seen to show up at smaller excitations, say below T ≈ 1−1.5 MeV in case that the concept of temperature may be used. This extension is possible down to a critical temperature T c below which for unstable modes as encountered for motion in barrier regions, diffusion coefficients can no longer be defined. For large damping the T c is only slightly greater than the so-called “cross over temperature” known from conventional treatments of dissipative tunneling, but the T c is small on the nuclear scale. Last but not least, relations are established to other approaches, such as “dissipative diabatic dynamics”, or ones based on random matrix models as well as those employing wall friction and two body viscosity.