Nuclear collective dynamics with subsidiary conditions: A quantized Hamiltonian which allows for dissipative motion

Abstract

We apply the method of Bohm and Pines to find a Hamiltonian for the coupled system of nucleonic plus collective variables. The deficiency of having too many degrees of freedom is handled by means of subsidiary conditions. The problem is formulated and solved within a locally harmonic approximation and for one collective degree of freedom. The Hamiltonian and the subsidiary conditions are set up such that for average motion one regains the same solutions as obtained in a suitable mean field approach. As applications we study an analytically solvable, schematic model, treat the example of realistic, undamped nuclear vibrations, to finally discuss large scale motion of dissipative systems. The undamped case is solved by means of canonical transformations to decouple nucleonic and collective degrees of freedom. We argue that this is no longer possible for damped motion and treat the latter case by linear response theory. This allows us to study average motion and, for vibrations, their fluctuations in thermal equilibrium.