AN APPROXIMATE EXPRESSION FOR ANALYTICAL PARTS OF EFFECTIVE RANDOM PHASE APPROXIMATION POTENTIAL IN AN INTERACTING ELECTRON GAS

An approximate expression for the analytical parts Re V+ and Re V- of the real part of the effective random phase approximation potential in an interacting electron gas is obtained by using sum rules and the asymptotic properties of the effective potential. Using this procedure it is possible to write down, for instance, simple analytical expressions for the plasmon dispersion relation and the Fourier transform of the pair distribution function. Moreover, a function giving the weight of collective excitations as a function of the excitation wave vector can be defined and thus the difference between the value of the cutoff zc, estimated from different experiments can be explained. © 1969.