Improved variational wave functions for simple quantum liquids

We review variational calculations with a Jastrow wave function and show they are inadequate to calculate the zero-temperature equation of state E(ρ) for liquid helium. The importance of the Feynman-Cohen backflow around a moving particle is then discussed, and a variational wave function incorporating backflow is proposed. Results with this wave function are discussed for ³He, ⁴He and the v₂ potential model of nuclear matter. In both ⁴He and ³He the new wave function gives an energy and equilibrium density much closer to the experimental values than the Jastrow form. In the v₂ model the addition of the backflow terms to the Jastrow correlation lowers the energy by 2-3 MeV. Spin-isospin correlations can simulate the state dependence of the backflow correlation at small momenta. However, at nuclear-matter densities they can produce only about half of the lowering due to backflow.