A pion condensate as a more favorable ground state of high density neutron matter via the auxiliary field GFMC method

A Pion Condensate in dense nuclear matter may occur in the inner core of neutron stars. The FHNC/SOC of Akmal-Pandharipande show a "pion-excess" response that was attributed to a pion condensate. The present calculation aim to show the ground state of a spin density wave, representing the pion condensate, is lower than a liquid phase energy. The computation uses the auxiliary field GFMC method with fixed phase constraint for a realistic hamiltonian that has the argonne v₈′ potential for two-body interaction with the urbanna UIX potential for three-body interaction. Neutrons fill closed shells in a periodic box. The energy difference is about 6% at a density, ρ, about five times the nuclear equilibrium density, ρ_o. The phase transition seems to be of second-order kind with an estimated critical density ρ_c / ρ_o ~ 3.1 and spin-density wavelength λ_c ~ 2.8 fm.