Semiclassical description of finite fermion systems at finite temperature in a generalised Routhian approach

A semiclassical description at finite temperature is presented for an N fermion system experiencing velocity fields coupling to the linear momentum of each of the particles. Spin degrees of freedom are also considered. Analytical expressions are derived for various local and integrated physical quantities in the framework of the Extended Thomas–Fermi method. Low and high-temperature limits are carefully examined. This formalism is then applied to the particular case of hot rotating nuclei.