Similarity and contrasts between thermodynamic properties at the critical point of liquid alkali metals and of electron-hole droplets

The recent experimental study by means of time-resolved luminescence measurements of an electron-hole liquid (EHL) in diamond by Shimano et al. [Phys. Rev. Lett. 88 (2002) 057404] prompts us to compare and contrast critical temperature T_c and critical density n_c relations in liquid alkali metals with those in electron-hole liquids. The conclusion drawn is that these systems have similarities with regard to critical properties. In both cases the critical temperature is related to the cube root of the critical density. The existence of this relation is traced to Coulomb interactions and to systematic trends in the dielectric constant of the electron-hole systems. Finally a brief comparison between the alkalis and EHLs of the critical values for the compressibility ratio Z_c is also given

On the Static Dielectric Permittivity for Coulomb System in the Long Wavelength Limit

On the basis of the exact relations the general formula for the static dielectric permittivity for Coulomb system is found in the region of small wave vectors. The obtained formula describes the dielectric function of the Coulomb system in both limits: in the "metallic" state and in the "dielectric" one. On this basis the determinations of the "apparent" dielectric and the "apparent" radius of screening are introduced. In the random phase approximation (RPA) the exact relations for the function dielectric function of the electron gas in the long-wavelength region of the wave vectors are found for an arbitrary degeneration of the particles.Comment: 5 pages, no figure