Towards exact analytic calculation of electron gas

: Kallio A, Piilo J

Publisher: CZECHOSLOVAK JNL OF PHYSICS

: 1996

: Czechoslovak Journal of Physics

: CZECHOSLOVAK JOURNAL OF PHYSICS

: CZECH J PHYS

: 46

: 2641

: 2642

: 2

: 0011-4626

DOI: https://doi.org/10.1007/BF02570307

A new technique for calculation of electron gas radial distribution function g(r(12)) and ground-state energy is developed based on the idea that the probability amplitude psi(r(12)) = root(r(12)) has to satisfy a zero energy Schrodinger equation where the effective interaction is sum of Coulomb force and the induced interaction v(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 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 exact energy expression with coupling constant integration produces energies which agree very closely with Green's function Monte Carlo results.