Extension of the QPM to T ≠ 0 Based on the Formalism of the Thermo Field Dynamics

The way of extending the quasiparticle-phonon nuclear model (QPM) to finite temperature is presented. It is based on a formalism of the thermo field dynamics (TFD). After formal doubling of the single-particle degrees of freedom by introducing the so called tilde-states, the usual and thermal Bogolyubov transformations are carried out. The coefficients of the transformations are determined by minimizing the free energy potential of a hot nucleus in the thermal vacuum state taking into account only single particle and pairing terms of the QPM Hamiltonian. Then the thermal phonon operator is introduced as a linear superposition of forward - backward bi thermal quasiparticle amplitudes, and with the variational principle the thermal RPA equations are derived. The expression for the thermal QPM Hamiltonian in terms of thermal quasiparticles and thermal phonons is given which contains the interaction of these two types of excitation modes. The equation for the states taking into account the mixing of one- and two-thermal phonon components and the expression of the corresponding coupling matrix element are derived. (author). 16 refs