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Using mean-field and semi-classical approximation of Thomas-Fermi, within a statistical model, equation of state and critical properties of symmetric nuclear matter is studied. In this model, two body and phenomenological interaction of Myers and Swiatecki is used in phase space. By performing a functional variation of the total Helmholtz free energy of system with respect to the nucleonic distribution function in phase space to reach an equilibrium state according to the second low of thermodynamics, we obtain expressions for the effective mass which is only density dependent and the effective one-body potential whereby the key quantity of the extended effective mass with both density and temperature dependency is determined. Accordingly, we reach to the explicit form of distribution function. In this mode, extensive thermodynamic quantities such as, inner energy, entropy and Helmholtz free energy are determined as the functionals of the distribution function for given temperature and density. In this research special attentions has been paid to the critical behavior and stability of symmetric nuclear matter. Our findings about the quantities which describe critical behavior of symmetric nuclear matter are in good agreement with other proposed models.

Thomas-Fermi calculations for determination of critical properties of symmetric nuclear matter on the basis of extended effective mass approach