论文标题
VOIGT近似中的中子恒星外壳：应力 - 应变张量的一般对称性和有效剪切模量的通用估计值
Neutron star crust in Voigt approximation: general symmetry of the stress-strain tensor and an universal estimate for the effective shear modulus
论文作者
论文摘要
我讨论当原子核被视为无振动点电荷时，在静态库仑固体模型框架中，中子星形壳的弹性特性。电子筛选被忽略了。结果也适用于固化的白色矮人核心和其他材料，可以将其建模为库仑固体（尘土高血浆，捕获的离子等）。我证明，应力 - 应变张量的库仑部分具有其他对称性：收缩$ b_ {ijil} = 0 $。它不取决于结构（结晶或无定形）和组成。我表明，由于这种对称性，多晶或无定形物质的有效（voigt平均）剪切模量等于在未构造状态下的库仑（madelung）能量密度的$ -2/15 $。此结果是一般且在应用模型中精确的。由于使用了线性混合规则和离子球模型，因此我可以建议对有效剪切模量的简单通用估计：$ \ sum_z 0.12 \，n_z z^{5/3} e^2 /a_ \ mathrm {e} $。在这里求和是对离子物种进行的，$ n_z $是带电$ ze $的离子的数字密度。最后，$ a_ \ mathrm {e} =（4πn_\ mathrm {e}/3）^{ - 1/3} $是电子球半径。假设Quasineutrality条件$ N_ \ MATHRM {E} = \ sum_z z n_z $。
I discuss elastic properties of neutron star crust in the framework of static Coulomb solid model when atomic nuclei are treated as non-vibrating point charges; electron screening is neglected. The results are also applicable for solidified white dwarf cores and other materials, which can be modeled as Coulomb solids (dusty plasma, trapped ions, etc.). I demonstrate that the Coulomb part of the stress-strain tensor has additional symmetry: contraction $B_{ijil}=0$. It does not depend on the structure (crystalline or amorphous) and composition. I show as a result of this symmetry the effective (Voigt averaged) shear modulus of the polycrystalline or amorphous matter to be equal to $-2/15$ of the Coulomb (Madelung) energy density at undeformed state. This result is general and exact within the model applied. Since the linear mixing rule and the ion sphere model are used, I can suggest a simple universal estimate for the effective shear modulus: $\sum_Z 0.12\, n_Z Z^{5/3}e^2 /a_\mathrm{e}$. Here summation is taken over ion species, $n_Z$ is number density of ions with charge $Ze$. Finally $a_\mathrm{e}=(4 πn_\mathrm{e}/3)^{-1/3}$ is electron sphere radius. Quasineutrality condition $n_\mathrm{e}=\sum_Z Z n_Z$ is assumed.
