Progress in Monte Carlo calculations of Fermi systems: normal liquid 3He

The application of the diffusion Monte Carlo method to a strongly interacting Fermi system as normal liquid $^3$He is explored. We show that the fixed-node method together with the released-node technique and a systematic method to analytically improve the nodal surface constitute an efficient strategy to improve the calculation up to a desired accuracy. This methodology shows unambiguously that backflow correlations, when properly optimized, are enough to generate an equation of state of liquid $^3$He in excellent agreement with experimental data from equilibrium up to freezing.