  Variational and diffusion quantum Monte Carlo methods are employed to
investigate the zero-temperature phase diagram of the three-dimensional
homogeneous electron gas at very low density. Fermi fluid and body-centered
cubic Wigner crystal ground state energies are determined using
Slater-Jastrow-backflow and Slater-Jastrow many-body wave functions at
different densities and spin polarizations in finite simulation cells.
Finite-size errors are removed using twist-averaged boundary conditions and
extrapolation of the energy per particle to the thermodynamic limit of infinite
system size. Unlike previous studies, our results show that the electron gas
undergoes a first-order quantum phase transition directly from a paramagnetic
fluid to a body-centered cubic crystal at density parameter $r_\text{s} =
86.6(7)$, with no region of stability for an itinerant ferromagnetic fluid.
However there is a possible magnetic phase transition from an antiferromagnetic
crystal to a ferromagnetic crystal at $r_\text{s}=93(3)$.
