Statistical functional of nuclear energy in noninteracting quasi-particle model

Rules are calculated for constructing a statistical mean energy functional with account of quantum corrections to the Thomas-Fermi approximation for the non-interacting quasi particle model. In addition to the standard dependence on the neutron and proton densities and their entropies the functional contains also terms with gradients of these quantities. Conditions of the thermodynamical equilibrium are not changed. The results obtained are valid also in the case where the occupation of the nucleon states is not of the Fermi type