Large amplitude collective motion

In this paper, starting from the concept of exactly decoupled classical motion, the conditions for such motion to occur are derived and studied, leading to a generalized concept of valley, previously known only in the one dimensional case. A summary of additional theoretical results is given and the relationship to the local harmonic formulation established. Examples of exact and approximate decoupling are described, and the latter concept is given a precise meaning. The formalism is then transcribed to time dependent Hartree-Fock theory and is seen to yield a generalization of the usual cranking method for constructing a collective Hamiltonian, in that the cranking operators must be determined self consistently. An approximate method of solving the new problem gives the exact solution for a class of simplified models