Extended thermal random phase approximation equation for nuclear collective excitation at finite temperature.

Abstract

To take systematic account of thermal correlation effect on the mean field, the thermal random phase approximation formalism is extended based on the thermofield dynamics scheme. The random phase approximation phonon operator is expressed in terms of the thermofield dynamics quasiparticle operators with a tilde as well as those without a tilde, and the increase of the dimensionality of variational parameter manifold enables us to derive the extended thermal random phase approximation equation from deeper minimum of grand potential. It is shown that the extended thermal random phase approximation equation is justified also from viewpoint of time-dependent formalism. The method of constrained variation applied to the first extended thermal random phase approximation can be straightforwardly generalized to the second, or higher extended thermal random phase approximation. Extended expressions are given also for the stability condition of thermal Hartree-Fock-Bogoliubov approximation and the energy-weighted sum rule.