标题： 中子星内壳层：结构和超导性的统一描述 显示英文标题

标题： Inner crust of neutron stars: Unified description of structure and superconductivity

摘要： 使用由手征有效场论和双幻数核的基态能量约束的Skyrme模型Sk$\chi$450，我们探讨了致密物质的宏观静态能谱。 物质结构被理想化为1、2或3维周期性库仑晶格（面食相），在平均重子密度范围为$0.005n_0-0.5n_0$的情况下，具有$n_0\sim0.16$fm$^{-3}$，对应于中子星的内壳层。 在早期的研究中，这种情形下的核体和表面性质是基于不同的核相互作用进行描述的。 因此，基于这些数值结果对内壳层结构的预测并不一定是自洽的。 在本工作中，我们通过以统一的方式描述核性质和质子-质子库珀配对来解决这个问题，\emph{即}基于相同的核相互作用。 我们在扩展的Thomas-Fermi水平上计算了表面张力到领先阶（平面表面）和次领阶（从非零主曲率）的值。 接下来，我们在可压缩液滴模型（LDM）内开发并求解一组方程，这为我们提供了关于核结构宏观静态能谱的所有必要信息。 我们发现曲率修正以相关方式改变了基态。 我们还发现，通常情况下，不同面食相之间的能量差小于温度为$\sim10^8-10^9$K时的热能，这意味着真实的核面食相可能是多形的。 最后，对于1维面食相，我们评估了质子的超导相干长度、伦敦穿透深度和超导能隙。 我们的结果为面食相丰富的磁性特性提供了初步见解。 显示英文摘要

摘要： Using the Skyrme model Sk$\chi$450 constrained by the chiral effective field theory and the ground-state energies of doubly-magic nuclei, we explore the macroscopic static energy spectrum of dense matter. Structure of the matter is idealized as 1-, 2- or 3-dimensional periodic Coulomb lattices (pasta phases) at average baryon density in the range of $0.005n_0-0.5n_0$ with $n_0\sim0.16$ fm$^{-3}$, corresponding to the inner crust of neutron stars. In the earlier work, the bulk and the surface nuclear properties in this scenario were described on the basis of different nuclear interactions. As a result, predictions for the inner crust structure based on those numerical results are not necessarily self-consistent. In this work, we solve this problem by describing the nuclear properties and proton-proton Cooper pairing in a unified manner, \emph{i.e.} based on the same nuclear interaction. We calculate the surface tension to the leading order (planar surface) and to the next-to-leading order (from nonzero principal curvature) at the Extended Thomas-Fermi level. Next, we develop and solve a system of equations within the compressible liquid drop model (LDM), which provides us with all necessary information about the macroscopic static energy spectrum of the nuclear structure. We find that the curvature corrections change the ground state in a relevant way. We also find that, typically, the energy differences between the different pasta phases are less than the thermal energy for temperatures $\sim10^8-10^9$ K, which implies that the real nuclear pasta phases are likely polymorphic. Finally, for 1-dimensional pasta phase we evaluate the superconducting coherence length of protons, the London penetration depth and the superconducting energy gap. Our results offer a preliminary insight into rich magnetic properties of the pasta phases.