The detailed knowledge of the inner crust properties of neutron stars might be important to explain different phenomena such as pulsar glitches or the possibility of an {\it r-process} site in neutron star mergers. It has been shown in the literature that quantal effects like shell correction or pairing may play a relevant role to determine the composition of the inner crust of the neutron star. In this paper we construct the equation of state of the inner crust using the finite-range Gogny interactions, where the mean field and the pairing field are calculated with same interaction. We have used the semiclassical Variational Wigner-Kirkwood method along with shell and pairing corrections calculated with the Strutinsky integral method and the BCS approximation, respectively. Our results are compared with those of some popular models from the literature. We report a unified equation of state of the inner crust and core computed with the D1M* Gogny force, which was specifically fabricated for astrophysical calculations.

中文翻译：

---

戈尼相互作用中子星内壳的结构和组成

中子星内壳特性的详细知识对于解释不同的现象可能很重要，例如脉冲星故障或中子星合并中 {\it r-process} 站点的可能性。文献表明，像壳校正或配对这样的量子效应可能在确定中子星内壳的成分方面发挥相关作用。在本文中，我们利用有限范围的 Gogny 相互作用构造了内地壳的状态方程，其中平均场和配对场是用相同的相互作用计算的。我们使用了半经典变分 Wigner-Kirkwood 方法以及分别使用 Strutinsky 积分方法和 BCS 近似计算的壳和配对校正。我们的结果与文献中一些流行模型的结果进行了比较。我们报告了使用 D1M* Gogny 力计算的内壳和地核的统一状态方程，该方程是专门为天体物理计算而制造的。