Effective pair potentials for the noninteracting spin-1/2 Fermi gas

Abstract

The N-particle configurational probability density P(N) of a noninteracting Fermi gas may be approximated as P(N) ≃ Πi<je−u(rij) / ∫d 3NrΠi<je −u(rij), where u(r) is an effective pair potential. Our reason for considering these potentials is that they have been successfully used in computing properties of interacting Fermi systems. We define the best effective potential to be the one whose corresponding two-body distribution function is closest to the exact two-body distribution function. A method for calculating the best u(r) is not known. Lado has calculated u(r) by using the Born-Green-Yvon integrodifferential equation relating u(r) to the two- and three-body distribution functions. Effective potentials may also be calculated using the hypernetted chain and Percus-Yevick integral equations. It is found that potentials computed by the above three methods are in fairly close agreement. The principal purpose of this paper is to present tables of effective potentials approximating both the spin-summed system and parallel spin subsystem probability densities for a system of noninteracting spin-1/2 fermions.