论文标题
中子恒星内面包：核量有限尺寸效应减少剪切模量
Neutron star inner crust: reduction of shear modulus by nuclei finite size effect
论文作者
论文摘要
中子星形外壳的弹性对于对观测值的充分解释很重要。要描述弹性特性，应该依靠理论模型。最广泛使用的是库仑晶体模型（在中和均匀背景上的点状电荷系统），在某些作品中，它可以用于电子筛选。这些模型忽略了核的有限尺寸。除了最内层的地壳层外，这种近似是合理的，其中核大小与核间间距相当。尽管如此，即使在那些密集的层中，如果假设核是球形对称的，那么应用库仑晶体结果似乎是合理的：它们之间的库仑相互作用应与点状电荷之间的相互作用相同。然而，正如我们在这里所指出的那样，该论点确实是正确的，地壳晶格的剪切剪切在晶格引用附近产生（微观）四极杆静电电位，从而诱导细胞核上的变形。我们使用离子球体模型（这是众所周知的离子球模型的概括），在可压缩液滴模型中分析该问题。特别是，对于基态外壳组成，有效的剪切模量降低了$ 1-u^{5/3}/（2+3 \，U-4 \，U^{1/3}）$，其中u是填充因子（核体积的比例与细胞体积与细胞的体积的比率）。该结果是通用的，不取决于应用的核子相互作用模型。对于内壳的最内层层，U〜0.2导致剪切模量减少约25％，这对于正确解释了磁弹尾尾的准周期振荡可能很重要。
The elasticity of neutron star crust is important for adequate interpretation of observations. To describe elastic properties one should rely on theoretical models. The most widely used is Coulomb crystal model (system of point-like charges on neutralizing uniform background), in some works it is corrected for electron screening. These models neglect finite size of nuclei. This approximation is well justified except for the innermost crustal layers, where nuclei size becomes comparable with the inter-nuclear spacing. Still, even in those dense layers it seems reasonable to apply the Coulomb crystal result, if one assumes that nuclei are spherically symmetric: Coulomb interaction between them should be the same as interaction between point-like charges. This argument is indeed correct, however, as we point here, shear of crustal lattice generates (microscopic) quadrupole electrostatic potential in a vicinity of lattice cites, which induces deformation on the nuclei. We analyze this problem analytically within compressible liquid drop model, using ionic spheroid model (which is generalization of well known ion sphere model). In particular, for ground state crust composition the effective shear modulus is reduced for a factor of $1-u^{5/3}/(2+3\,u-4\,u^{1/3})$, where u is the filling factor (ratio of the nuclei volume to the volume of the cell). This result is universal and does not depend on the applied nucleon interaction model. For the innermost layers of inner crust u~0.2 leading to reduction of the shear modulus by ~25%, which can be important for correct interpretation of quasi-periodic oscillations in the tails of magnetar flares.
