Structural Expansion for the Ground-State Energy of Simple Metals. IV: Static Dielectric Function

In order to obtain the static dielectric function of electron gas in the region rs=1.0∼3.0, the second-order polarization terms are figured out comprehensively with the Thomas-Fermi screened interaction. Particularly detailed study is given for ε(q, 0) in the limit q=0 with inclusion of the dynamical effect. The resulting function ε(q, 0) is presented by incorporating the present results into our previous ones for the first-order polarization terms with full account of the dynamical effect.