Quantum statistical theory of damped collective transition in highly excited nuclei

We formulate a quantum statistical theory for damping of the collective transition embedded in the highly excited states of nuclei. The theory is formulated on a general basis which assumes no detailed specification of model Hamiltonian. It provides us with a framework which can be used further for microscopic or model calculations. A definite expression is derived for the strength functions of the collective transition in terms of the response function for the intrinsic (irrelevant) degrees of freedom. Two kinds of the damping mechanism, the intrinsic damping and the fluctuational damping, are treated on a unified basis. It is shown that the motional narrowing is a phenomenon which is inherent to the dynamics of the finite quantum system irrespective of statistical ansatz used phenomenologically. The condition of the motional narrowing phenomenon is discussed in terms of characteristic quantities, e.g., relaxation time of the intrinsic response functions. (author)