There has been much theoretical speculation on exotic states of nuclear matter, and in particular, at high densities relative to the equilibrium infinite nuclear matter density, rho_o, pion condensation is believed to be a stable phase for highly dense nuclei and hadronic matter in general. This phase is a possible candidate for the state of matter at the inner core of neutron stars. Exploring such theoretically conjectured phenomena has only been recently possible for pure neutron matter with the auxiliary field green function monte carlo. In this work, a new and better equation of state is produced which shows a more energetically favored state of neutron matter at high densities, rho >> rho_o. Calculations were made with a realistic two and three-body interactions: the Argonne v_8' and the Urbana UIX potentials. The results show that a pion condensate phase, of second order type, leads to an optimal energy gain of about 6% past a critical density rho_c / rho_o ~ 3.1.
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