Thomas–Fermi approximation for the equation of state of nuclear matter: A semi-classical approach from the Landau Fermi-Liquid theory

The equation of state (EOS) of nuclear matter is investigated in a semi-classical mean-field (MF) approach. Starting from the phase-space NN-interaction of Myers and Swiatecki [Nucl. Phys. A 601 (1996) 141], the EOS of nuclear matter by the Thomas–Fermi approximation is derived. A self-consistent semi-classical approach is presented by employing the Landau Fermi-Liquid theory (LFT). In our statistical approach, the phase-space occupation number can be expressed in terms of an extended effective mass which is affected by both temperature and nucleonic density. Accordingly, an explicit expression of the nucleonic chemical potential inside the nucleonic occupation number can be obtained. Special attention is also devoted to the density dependence of the nuclear symmetry free energy at different temperatures. The results of this model are compared with other theoretical predictions.