Novel analytic calculation of electron gas properties

A new technique for calculation of the electron gas radial distribution function g(r(12)) and the groundstate energy is developed based on the idea that the probability amplitude psi(r(12)) = root Jg(r(12)) has to satisfy a zero-energy Schrodinger equation where the effective interaction is the sum of the Coulomb force and the induced interaction upsilon(c) + W(r). In the case of electron gas with positive background we write the induced potential in the form W-B + W-e where W-B(r) is the known bosonic reference potential and W-e(r) is a fermionic correction determined from the fact that the Coulomb force for low r(s) is switched off. The coupling constant integration produces energies which agree very closely with Green's function Monte Carlo results.