The thermo field theory of nuclear collective motion

The dynamic equation of the Liquid Drop Model of collective motion is derived from the statistical quantum field theory of finite Fermi systems under the assumption that there is only one collective mode, whose characteristic frequencies are small compared to single-particle frequencies. The time evolution of the nucleus is characterized by the statistical matrix ρχ, describing thermal equilibrium at fixed values of the expectancies of the operators Q, P, M of coordinate, momentum and mass of slow collective mode. Explicit expressions for ρχ, P, M are obtained using the idea that collective motion in hot nuclei emerges because the randomly distributed phase of the nucleon field operator acquires a regular component χx. The time evolution equations for the expectancies of Heisenberg operators Qt, Pt, Mt are converted into the dynamic equation for the collective coordinate qt=tr(Qtρχ) of the same form, as the dynamic equation of the Liquid Drop Model. This allows us to identify the microscopic expressions for collective mass, deformation force, and friction coefficient. To make these expressions tractable, the thermally equilibrated particle motion is modelled in terms of the temperature-dependent Hartree–Fock equations with the Skyrme force.