TFD extension of a self-consistent RPA to finite temperature

In the present report a fully consistent version of a thermal self-consistent random phase approximation is presented. The formalism of the thermo-field dynamics (TFD) was used. For the first time it was applied to nuclear structure problem. The TFD is a real time formalism, in contrast with the thermal Green function method, temperature and time are independent variables within TFD. The formalism is convenient for present purposes because temperature effects arise explicitly as T-dependent vertices, thus providing a good starting point for various approximations. Moreover, the TFD approach is most powerful being combined with variational methods which are the main tools in the present consideration