Energy density functional within the local-scale transformation method

A local density formulation of the local-scale transformation method is given. The obtained kinetic energy density consists of two terms: the so-called Weizsacker correction term and the Thomas-Fermi like kinetic energy density term. The latter is an exact expression for an infinite system. The problem of the gradient corrections to the kinetic energy density is considered which appears as a result of introducing of v2/c2-relativistic corrections. It is shown that the Hartree-Fock approximation becomes ineffective for describing the 1s-shell nuclei. Therefore the methods going beyond the Hartree-Fock one should be used in these cases