The Equation of state (EOS) of dense baryonic matter plays an important role in study of
Nuclear physics. On the basis of Thomas-Fermi approximation as a
semi-classical mean-field method, the EOS at
finite temperature for different structures of baryonic matter
such as symmetric and asymmetric nuclear matter, pure neutron
matter and beta stable matter are determined by using extended
phenomenological nucleon-nucleon interaction of Seyler and
Blanchard, presented by Myers and Swiatecki.
By a functional variation an explicit form of distribution function has been
derived. In our statistical approach, the thermal properties of
these dense structures are studied. The quantities such as free
energy, energy, entropy, specific heat capacity, incompressibility
and the pressure which is known to be the EOS are calculated as
the functionals of the distribution function for given temperature
and density. Special attention is also payed to the investigation
of critical behavior of these systems. As a result, the critical
temperature and critical exponent of symmetric nuclear matter are
found while there is no phase transition in the pure neutron
matter and beta stable matter. Our results are in good agreement
with experimental predictions and other theoretical
investigations.