Effect of screening on exchange effects for an inhomogeneous electron gas at finite temperatures

Recently, Gupta and Rajagopal [Phys. Rev. A 21, 2064 (1980)] have calculated thermodynamic-exchange energy and potential in an "exchange-only" approximation and later calculated the correlation potential exactly within the random-phase approximation [Phys. Rev. A 22, 2792 (1980)]. In this paper we estimate the effect of screening in an approximate way. The formula obtained for the correlation potential is shown to be the product of two functions, one being that of density and the other being that of dimensionless temperature. The calculated values agree reasonably in the intermediate degeneracy region and are good at higher temperatures and densities. It is shown that the specific heat for the system can also be expressed in terms of the same parameters and the (T/lnT)-type divergence disappears.