No abstract

In the standard picture of the crust of a neutron star, matter there is simple: a body-centered-cubic lattice of nuclei immersed in an essentially uniform electron gas. We show that, at densities above that for neutron drip (∼4 × 10 11 g cm −3 or roughly one-thousandth of nuclear matter density), the interstitial neutrons give rise to an attractive interaction between nuclei that renders the lattice unstable. We argue that the likely equilibrium structure is similar to that in displacive ferroelectric materials such as BaTiO 3 . As a consequence, the properties of matter in the inner crust are expected to be much richer than previously appreciated, and we mention possible consequences for observable neutron star properties. DOI: 10.1103/PhysRevLett.112.112504 PACS numbers: 21.65.-f, 26.60.Gj, 67.10.Jn, 97.60.Jd Many technologically important properties of terrestrial metals are governed by the fact that these materials exhibit a variety of crystal structures. Pure metals have many different phases [1]. For alloys, even more possibilities exist, and these have far-reaching implications: e.g., the strength of steels is determined to a high degree by the existence of different crystal structures. Here we consider matter in the outer parts of a neutron star (its crust), which is important for interpreting observations of neutron stars even though it comprises only a small fraction of the total mass of the star. In the traditional view, this matter is simple, because correlations between electrons, which are crucial for terrestrial matter, play little role. However, at densities above one-thousandth of nuclear density, matter consists of a crystal lattice of atomic nuclei permeated by neutrons [2]. The neutrons behave like a second component in a binary alloy, and we argue that, as a consequence, the properties of matter are more similar to those of terrestrial solids than has been previously appreciated. Specifically, the neutrons give rise to an attractive interaction between nuclei which makes the lattice unstable to clumping of nuclei in a manner similar to the formation of inhomogeneous regions in metallic alloys (spinodal decomposition) [3]. While the attraction is insufficient to make matter unstable to long-wavelength distortions, it can destabilize matter at finite wavelengths where the effective interaction between nuclei due to their electrical charges is reduced. We describe a number of possible consequences for observable properties of neutron stars.To set the scene, we consider the condition for thermodynamic stability of the system of nuclei immersed in a sea of neutrons, together with a background of electrons whose average density is the same as that of the protons to ensure electrical neutrality. The system may thus be regarded as having two components: the neutrons (both those in nuclei and the interstitial ones) and the charged particles. For most of the life of a neutron star, the temperature is so low that thermal effects may be neglected. In that case, the condition for stability is that th...