Master equations in the microscopic theory of nuclear collective dynamics

Abstract

In an isolated finite many-body quantal system as the nucleus in which the self-consistent mean field is realized, collective modes of motion (associated with time evolution of the mean field) are highly involved with non-collective modes of motion in a strongly self-consistent way. By paying attention to this strong self-consistency, a general microscopic framework is given to derive master equations which enable us to investigate various dynamical mechanism of the nuclear large-amplitude collective motion. The theory consists of two ingredients: (i) Introduction of a dynamical canonical coordinate (DCC) system, where the whole nuclear dynamics is optimally described in terms of the collective (relevant) and the non-collective (irrelevant) variables in a self-consistent way on the basis of the self-consistent collective coordinate (SCC) method. (ii) Application of the time-dependent projection operator method of Willis and Picard to the Liouville equation in the DCC system. This application makes it possible to treat both time evolution of a reduced distribution function for the relevant variables and that of a reduced distribution function for the irrelevant variables in a self-consistent way, without introducing any statistical hypothesis for the reduced irrelevant distribution function. The general coupled master equations in the DCC system thus obtained are rich enough to explore the microscopic mechanism responsible for dissipative behaviour of the large-amplitude collective motion, in connection with the stability problem of the collective subspace obtained by the SCC method.