Properties of nuclei in the inner crusts of neutron stars in the relativistic mean-field theory

Abstract

We study the properties of nuclei in the inner crusts of neutron stars based on the Boguta-Bodmer nonlinear model in the relativistic mean-field theory. We carefully determine the surface diffuseness of the nuclei as the density of matter increases. The imaginary time step method is used to solve the Euler-Lagrange equation derived from the variational principle applied to the semiclassical energy density. It is shown that with increasing density, the spherical nuclei become more neutron rich and eventually merge to form a uniform liquid of neutrons, protons, and electrons. We find that the smaller the value of the incompressibility K, the lower the density at which the phase transition to uniform matter occurs. The relativistic extended Thomas-Fermi method is generalized to investigate nonspherical nuclei. Our results show that the spherical nucleus phase is the only equilibrium state in the inner crusts of neutron stars.

Symmetry energy at subnuclear densities and nuclei in neutron star crusts

“…We thus conclude that the absence of the pasta phases seen in Refs. [6,11,12] from the EOS model with relatively high pressure of neutron matter at subnuclear densities is consistent with our result. The onset density of proton clustering in uniform nuclear matter as a function of L. For comparison, we plot the density corresponding to u = 1/8 in the phase with spherical nuclei, which is taken from Fig.…”

“…It was found that the density at which the system dissolves into uniform matter increases with increasing µ (0) p . However, it remains to be clarified why some nuclear models [6,11,12] predict the absence of bubbles and nonspherical nuclei. It is important to note that these models predict relatively high pressure for pure neutron matter (or, equivalently, relatively small symmetry energy) at densities around half the normal nuclear density, whereas the work by Watanabe et al [10] used a parametrization [13] based on the microscopic calculations by Siemens and Pandharipande [14] as the EOS of pure neutron matter and fix the density dependence of the symmetry energy.…”

Inner edge of neutron-star crust with SLy effective nucleon-nucleon interactions

“…Recent calculations of this quantity 1 [17,11,18,8] give ρ edge 0.08 − 0.10 fm −3 , substantially lower than the estimate close to the normal nuclear density ρ 0 = 0.16 fm −3 , derived in the classical paper of Baym et al [1]. Some theoretical calculations predict exotic distributions of nuclear matter (rods, plates, etc.)…”

“…within the bottom layers of the crust [17,11,9]. However, the presence of exotic nuclei depends on the effective nucleon-nucleon (N-N) force used; for some forces, spherical nuclei are present down to the inner edge of the crust [17,8]. Presence of exotic nuclei would lead to different transport and elastic properties of the crust, compared to the standard case of a Coulomb crystal formed by spherical nuclei [17,13].…”

A Survey of the Parameter Space of the Compressible Liquid Drop Model as Applied to the Neutron Star Inner Crust

“…Third, effects that act over ranges greater than the unit cell are not consistently accommodated in the CLDM; larger scale self-organization of pasta phases and long-wavelength transport effects are all unaccounted for. Many of these problems are eliminated by more sophisticated models such as Thomas-Fermi (TF), Extended TF (ETF) and ETF + Strutinsky Integral (ETFSI) (e.g., Buchler & Barkat 1971;Oyamatsu 1993;Cheng et al 1997;Onsi et al 2008, where the latter includes a self-consistent treatment of shell effects), the 1D or 3D-Hartree-Fock (HF) methods (e.g., Monrozeau et al 2007;Negele & Vautherin 1973;Montani et al 2004;Baldo et al 2005;Magierski & Heenen 2002;Gögelein et al 2008;Newton & Stone 2009, the latter of which relieves the spherical-WS approximation), and quantum molecular dynamics (QMD) methods (Maruyama et al 1998;Horowitz et al 2004;Watanabe et al 2001;Sonoda et al 2007). Certain of these methods are too computationally demanding for the kind of parameter survey we will present, so as a first step will limit ourselves to the CLDM, with a view to expanding the methodology in future.…”