Pion condensation and the σ-model in liquid neutron matter

The nature of the ground state of neutron matter at neutron star densities is discussed, starting from the linear σ-model Lagrangian. It is found that there is a possibility of a new, previously unknown, type of condensation, which involves coherent, non-vanishing expectation values of the neutral meson fields of the theory, the σ and π⁰ fields. The σπ⁰ condensate would, like normal neutron matter, develop its own π^? condensate. It is shown that the most general, translationally invariant, condensate is a combined σπ⁰ and π^? condensate with arbitrary, independent, wave numbers. The wave vectors of the condensates are determined by a minimization process, and are found to be non-vanishing and perpendicular.The σπ⁰ condensate corresponds to a state which is very different than previously considered states of neutron matter: all neutron spins are aligned, presumably with some macroscopic domain structure. Thus, criteria for the occurence of this condensate depend on the energy difference between very different states. This means that any prediction as to whether or not the state actually occurs in nature must at the moment be regarded as uncertain. However, using available hyperneted-chain calculations of the contribution to the energies from the direct neutron-neutron forces, it is demonstrated that a σπ⁰ condensate (with its accompanying π^? condensate) might well occur at neutron densities above perhaps 0.5 particles/fm³.This paper leans heavily on the linear σ-model. However, the neutral condensate is a general consequence of chiral symmetry, and can thus also be obtained e.g. from Weinberg's Lagrangian.