Approximate Energy Expression for Spin-Polarized Fermi Liquids

An approximate energy expression is proposed for arbitrarily spin-polarized Fermi liquids with central two-body forces. It is explicitly expressed as a functional of spin-dependent radial distribution functions and can be used conveniently in the variational method. It includes the potential energies completely and the kinetic energies up to main parts of the three-body cluster terms. This approximation is similar to that used previously for spinunpolarized and fully polarized matter. A notable feature of this expression is that it guarantees the necessary conditions on arbitrarily spin-polarized structure functions automatically. The Euler-Lagrange equations are derived from this energy expression and are numerically solved for arbitrarily spin-polarized liquid 3 He. The results for liquid 3 He with the HFDHE2 potential are consistent with the nearly ferromagnetic property.